Measurement of bond dissociation energies of transition metal molecules

Measuring thermochemical and kinetic properties of chemical systems has always; been a central theme of chemistry. Knowing these properties assists us in assessing; whether or not a chemical reaction is energetically feasible, efficient, and worthwhile.; Theoretical chemistry has now developed sufficiently to be useful for predicting; molecular properties and the outcomes of reactions that have yet to be observed. This is; relatively straightforward when there are few electrons involved, but calculations become; more inaccurate when treating heavy atoms and molecules with many electrons. In; particularly, transition metals, lanthanides, and actinides, with their partially filled d and f; orbitals, are not easily treated. Moreover, as the atomic number increases, the increasing; charge of the nucleus pulls the electrons closer, causing them to move more quickly.; Relativistic effects begin to emerge, and the Schrödinger equation becomes invalid. The; neglect of relativistic effects, combined with difficulties in correlating the motion of large; numbers of electrons, can lead to significant errors in computational results.; Computational chemists are working to develop more accurate approximations for; modeling chemical behavior, and a particular focus of recent computational work has; been on these more difficult open d and f subshell species.

MEASUREMENT OF BOND DISSOCIATION ENERGIES OF TRANSITION METAL MOLECULES by Jordan Avery Franchina A Senior Honors Thesis Submitted to the Faculty of The University of Utah In Partial Fulfillment of the Requirements for the Honors Degree in Bachelor of Science In The Department of Chemistry Approved: ______________________________ Michael D. Morse Thesis Faculty Supervisor _____________________________ Cynthia Burrows Chair, Department of Chemistry _______________________________ Tom Richmond Honors Faculty Advisor _____________________________ Sylvia D. Torti Dean, Honors College April 2018 Copyright © 2018 All Rights Reserved TABLE OF CONTENTS INTRODUCTION 1 ACKNOWLEDGEMENTS 4 FIRST PUBLICATION BOND DISSOCIATION ENERGIES OF DIATOMIC TRANSITION METAL SELENIDES: TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe (2016) SECOND PUBLICATION BOND DISSOCIATION ENERGIES OF TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi (2017) ii INTRODUCTION 1 Measuring thermochemical and kinetic properties of chemical systems has always been a central theme of chemistry. Knowing these properties assists us in assessing whether or not a chemical reaction is energetically feasible, efficient, and worthwhile. Theoretical chemistry has now developed sufficiently to be useful for predicting molecular properties and the outcomes of reactions that have yet to be observed. This is relatively straightforward when there are few electrons involved, but calculations become more inaccurate when treating heavy atoms and molecules with many electrons. In particularly, transition metals, lanthanides, and actinides, with their partially filled d and f orbitals, are not easily treated. Moreover, as the atomic number increases, the increasing charge of the nucleus pulls the electrons closer, causing them to move more quickly. Relativistic effects begin to emerge, and the Schrödinger equation becomes invalid. The neglect of relativistic effects, combined with difficulties in correlating the motion of large numbers of electrons, can lead to significant errors in computational results. Computational chemists are working to develop more accurate approximations for modeling chemical behavior, and a particular focus of recent computational work has been on these more difficult open d and f subshell species. Bond dissociation energies (BDEs) are among the most difficult of properties to calculate to good accuracy, even though they are of fundamental importance in predicting thermochemical behavior. The main reason for this problem is that it is hard to correlate the electrons to the same level of accuracy in a calculation on the assembled molecule as in the separated atoms, simply because there are more electrons to correlate in the molecule than in the separated atoms. Computational chemists would like to be able to 2 test their methodology on molecules whose BDEs are well-known, but a major difficulty has been the limited number of transition metal – main group bond energies that have been measured, combined with the low precision of the values that have been obtained. The precise values of BDEs measured in this work and in other work from the Morse group set a new standard that can be used to test computational methods. Bond dissociation energies are critical to know how combinations of various atomic species will bond to one another. Understanding how strong or weak the bonds are will help to develop new materials and better predict their properties. It will also enable chemists to assess whether a chemical reaction under consideration is energetically feasible. These measurements are applicable in a wide variety of fields, including catalysis, surface chemistry, and organometallic chemistry. A particular application of interest is in computer microchip manufacturing. As electronic circuits are miniaturized further, the space between circuit elements on a chip decreases. This is predicted to lead to significant deviations in electrical behavior due to silicon-metal interactions. Although the BDEs reported in this work do not directly bear on the electronic properties of bulk materials, computational methods that treat these systems will be more reliable if they can be shown to accurately reproduce BDEs that have been precisely measured. The following articles on which I am a contributing author were collaboratively written by the Morse group and published in the Journal of Chemical Physics. The first article, “Bond dissociation energies of diatomic transition metal selenides: TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe” (2016), addresses the methods, experiments, and analysis of data measuring the bond dissociation energies of transition metal selenides. Similarly, the second article, “Bond dissociation energies of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi” (2017), addresses the same transition metals bonded to silicon. For both experiments, 3 little to no literature on the bond dissociation energies existed prior to this work. Since beginning their measurements of the BDEs of transition metal-main group bonds, the Morse group has published 26 measured BDEs and is preparing to publish 22 additional values. These results typically provide either the first measurement for a transition metalmain group BDE or reduce the uncertainty of previous measurements by a factor of 10 to 100. The following articles are reproduced from J. J. Sorensen, T. D. Persinger, A. Sevy, J. A. Franchina, E. L. Johnson, and M. D. Morse, J. Chem. Phys. 145, 214308 (2016) and A. Sevy, J. J. Sorensen, T. D. Persinger, J. A. Franchina, E. L. Johnson, and M. D. Morse, J. Chem. Phys. 147, 084301 (2017) with the permission of AIP Publishing. ACKNOWLEDGEMENTS 4 I am very thankful for Dr. Michael Morse for introducing me to the fascinating world of quantum chemistry and the opportunity to be a member of his research team. He has an innate ability to make the most difficult concepts in chemistry understandable and enjoyable. I will always be grateful for the kindness and friendship he showed to me and the rest of his group. He has shown me what the qualities of a leader, mentor, teacher, and friend are. I appreciate the assistance of the graduate and undergraduate students in the Morse Group for their patience and understanding in teaching me the workings of the laboratory. Natascha Knowlton, my undergraduate advisor, has given constant encouragement, insight, and positive outlook when I needed to make difficult decisions regarding my undergraduate degree. She is an incredibly dedicated advisor, showing a deep connection and investment in students’ success. The department of chemistry is lucky to have such a wonderful advisor. It would be remiss to not acknowledge Greg Owens, my first chemistry professor at the University of Utah, for igniting my passion for chemistry and the general pursuit of knowledge. He gave me the tools I needed to succeed and enjoy pursuing a bachelor’s degree in chemistry. None of this would have been possible without the support of my family. My parents have been a constant source of love and encouragement. Many of my successes began with leaps of faith fueled by the knowledge that they believed in me. During my undergraduate career, I fell in love with and married my best friend Michelle Davis. She, like my parents, has been a source of motivation that has kept me going through the most challenging times of my undergraduate degree. THE JOURNAL OF CHEMICAL PHYSICS 145, 214308 (2016) Bond dissociation energies of diatomic transition metal selenides: TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe Jason J. Sorensen, Thomas D. Persinger, Andrew Sevy, Jordan A. Franchina, Eric L. Johnson, and Michael D. Morsea) Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, USA (Received 7 September 2016; accepted 12 November 2016; published online 2 December 2016) Predissociation thresholds have been observed in the resonant two-photon ionization spectra of TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe. It is argued that the sharp onset of predissociation corresponds to the bond dissociation energy in each of these molecules due to their high density of states as the ground separated atom limit is approached. The bond dissociation energies obtained are D0 (TiSe) = 3.998(6) eV, D0 (ZrSe) = 4.902(3) eV, D0 (HfSe) = 5.154(4) eV, D0 (VSe) = 3.884(3) eV, D0 (NbSe) = 4.834(3) eV, and D0 (TaSe) = 4.705(3) eV. Using these dissociation energies, the enthalpies of formation were found to be ∆f,0K Ho (TiSe(g)) = 320.6 ± 16.8 kJ mol−1 , ∆f,0K Ho (ZrSe(g)) = 371.1 ± 8.5 kJ mol−1 , ∆f,0K Ho (HfSe(g)) = 356.1 ± 6.5 kJ mol−1 , ∆f,0K Ho (VSe(g)) = 372.9 ± 8.1 kJ mol−1 , ∆f,0K Ho (NbSe(g)) = 498.9 ± 8.1 kJ mol−1 , and ∆f,0K Ho (TaSe(g)) = 562.9 ± 1.5 kJ mol−1 . Comparisons are made to previous work, when available. Also reported are calculated ground state electronic configurations and terms, dipole moments, vibrational frequencies, bond lengths, and bond dissociation energies for each molecule. A strong correlation of the measured bond dissociation energy with the radial expectation value, hrind , for the metal atom is found. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4968601] I. INTRODUCTION The making and breaking of chemical bonds are arguably the most fundamental processes in all of chemistry. The transition metals are of particular interest in this regard, as they are often employed to facilitate the controlled formation of new chemical bonds, especially in the fields of organometallic chemistry, surface chemistry, and catalysis. Thus, the nature of transition metal bonding to main group atoms is an area of great interest. The chemical bonding between transition metals and selenium is of technological interest in several fields, including pseudocapacitor electrodes,1 semiconductors,2 and electrocatalysts.3,4 Despite this interest in bulk transition metal selenides, little is known about the more fundamental chemical bonding in diatomic transition metal selenides. To our knowledge, only two diatomic transition metal selenides have received any spectroscopic scrutiny at all, with spectroscopic studies published only on MnSe5 and CuSe.6 One of the grand goals of computational chemistry is to predict accurately the thermochemistry and activation energies of chemical reactions, so that improvements in our understanding of reaction mechanisms and kinetics, and ultimately in catalyst design, may be made. To model such reactions satisfactorily, the computational method must be able to represent each step along the reaction path accurately, including reactants, products, and all applicable transition states. Accurate calculations of the energetics of the reactants and products permit the thermochemistry to be derived, while accurate calculations of the transition state are necessary to model reaction a) Author to whom correspondence should be addressed. Electronic mail: [e-mail] 0021-9606/2016/145(21)/214308/10/$30.00 kinetics. As the transition state often corresponds to a partially dissociated system, computational methods that fail to calculate bond dissociation energies (BDEs) accurately may also fail to provide accurate values for transition state energies. Thus, the computation of accurate thermochemistry is a key goal of computational chemistry. Even though BDEs are among the most useful quantities that computational chemistry can provide, highly accurate computational methods, particularly methods that can be scaled to treat larger systems, remain elusive. This is because of the difficulty in treating electron correlation in the initial molecule to the same level of accuracy as in the dissociated products. This is often possible for systems composed of main group elements; the increased electronic complexity in the dand f -block metals presents significant difficulties for current computational methods, however.7–9 One of the significant obstacles in improving current theoretical methods is the lack of precisely determined experimental BDEs to serve as points of comparison. Such precise values set a standard upon which various computational methods may be tested for accuracy.7–9 Computational methods are considered to have achieved “chemical accuracy” if the thermochemical property can be computed to within 1.0 kcal mol 1 (0.04 eV) of experiment.10 This result may be achieved for many main group molecules. On the other hand, for the more difficult transition-metal containing molecules, the accepted tolerance for “chemical accuracy” is within 3.0 kcal mol 1 (0.13 eV) of experiment due to the greater difficulties associated with these species.10 A significant challenge is that many experimental values themselves are not known to this level of certainty, and in some cases error limits may be significantly underestimated. To alleviate this deficit, in a recent publication, we have reported the BDEs of VC, VN, and VS to a 145, 214308-1 Published by AIP Publishing. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-2 Sorensen et al. precision of 0.003 eV, or better.11 In this article, we extend this work to provide BDEs of TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe, measured by the observation of a sharp predissociation threshold in the resonant two-photon ionization (R2PI) spectra of these molecules. As in our previous measurements,11 all reported values have an accuracy that is well within the required “chemical accuracy” of main group compounds. Very little previous work has been reported on these diatomic transition metal selenides. Of the molecules investigated here, the BDE has been previously measured only for VSe.12 An estimated BDE for TiSe has also been reported,13 based on extrapolation from experimental values of other titanium-containing compounds. In addition, Wu, Wang, and Su have computed BDE values for TiSe and VSe using density functional theory (DFT) calculations.14 The ground states of TiSe and VSe were also calculated by Wu, Wang, and Su to be 3 ∆, corresponding to the 1σ2 2σ2 1π4 1δ1 3σ1 configuration, and 4 Σ− , corresponding to the 1σ2 2σ2 1π4 1δ2 3σ1 configuration, respectively.14 Here, the orbital numbering scheme only includes valence molecular orbitals that derive primarily from the atomic valence orbitals (3d and 4s on Ti or V, 4s and 4p on Se). To date, there have been no spectroscopic studies on any of these molecules, so there are no experimental data available that could be used to deduce the ground terms. When rotationally resolved spectra are available, it is possible to deduce that ground state Ω00 value experimentally, which places severe constraints on the possible term symbol, and as a result, on the ground molecular configuration of the molecule. In many cases, the observed Ω00 value constrains the choices sufficiently that only a single configuration and term are plausible. Unfortunately, the lack of rotationally resolved spectra prevents such a determination for the molecules considered here. As no previous work of any kind has been reported on ZrSe, HfSe, NbSe, or TaSe, density functional calculations have been performed on all six molecules, and the results are presented. II. EXPERIMENTAL Hydrogen selenide gas was synthesized by acid hydrolysis of ZnSe powder in an apparatus that was slowly flushed with helium. Concentrated HCl was added to a flask containing ZnSe powder and was gently heated. The resulting H2 Se vapor was carried by the He flow through a CaCl2 drying tube to remove water vapor and then was passed through two liquid nitrogen traps ( 196 ◦ C), which condensed the H2 Se product. When the reaction had stopped, the traps were evacuated while the product remained frozen. At that point, the traps were connected to an evacuated gas cylinder and were allowed to warm to room temperature, filling the gas tank with hydrogen selenide gas. The H2 Se was then diluted with helium to approximately 0.25% H2 Se by pressure. The experimental process is identical to our previous work on VC, VN, and VS.11 A metal disk of Ti, Zr, Hf, V:Mo (1:1), Nb, or Ta was laser ablated by the third harmonic output of a Nd:YAG laser (355 nm). The metal samples were rotated and translated to ensure that holes were not drilled into the sample and that the molecule production remained reasonably stable. The resulting metal plasma was then carried by a pulse J. Chem. Phys. 145, 214308 (2016) of the H2 Se gas mixture through a 1.3 cm long reaction zone before undergoing supersonic expansion into vacuum from a 3 mm orifice, cooling the gaseous reaction products to about 10 K. The expanding gas was skimmed to 1 cm in diameter as it passed into the second chamber. The beam was then exposed to tunable laser radiation in the range of 300-234 nm produced by an optical parametric oscillator (OPO) laser, which was counterpropagated along the molecular beam. After approximately 20 ns, radiation from a KrF excimer laser (248 nm, 5.00 eV), directed perpendicular to the molecular beam, was used to ionize the species in the beam. The resulting ions were then accelerated in a Wiley-McLaren ion source into a reflectron time-of-flight mass spectrometer.15,16 Ion signals were measured with a microchannel plate detector, preamplified, and digitized for further processing. The process was repeated at a rate of 10 Hz, and 30 shots were averaged for each wavelength point. To improve the signal to noise ratio, three to four scans were averaged for each spectrum. III. COMPUTATIONS All calculations were performed in Gaussian 0917 using the B3LYP density functional theory method18,19 and the LANL2DZ basis set.20 This basis set utilizes an effective core potential (ECP), which was parameterized to reproduce calculations that treated the core terms with the inclusion of scalar relativistic effects, in particular the mass-velocity and Darwin relativistic terms. The ECP treats each of these atoms somewhat differently. For Ti and V, it treats electrons through [Ne] as core electrons. For Se, Zr, and Nb, the core electrons are [Ar] plus the 3d electrons. Lastly, Hf and Ta have [Kr] plus 4d and 4f electrons treated in the core potential. Unrestricted optimization and frequency calculations were performed to deduce the ground state configurations for each metal selenide along with bond lengths, dipole moments, vibrational frequencies, and BDEs. All calculations were performed in the C2v point group and neglected spin orbit coupling. In each case, two proposed ground state configurations were tested to see which lay lower in energy. For TiSe, ZrSe, and HfSe, the proposed ground states were 1σ2 2σ2 1π4 1δ1 3σ1 , 3 ∆ and 1σ2 2σ2 1π4 3σ2 , 1 Σ+ based on trends observed in their corresponding oxide21–23 and sulfide24–26 ground states. For VSe, NbSe, and TaSe, similar trends in their respective oxides27–29 and sulfides30–32 were used to deduce that the probable ground states were 1σ2 2σ2 1π4 1δ2 3σ1 , 4 Σ− and 1σ2 2σ2 1π4 3σ2 1δ1 , 2 ∆. IV. RESULTS A. Computations Table I displays the dipole moments (µ, Debye), vibrational frequencies (ωe , cm 1 ), bond lengths (re , Å), term energies (Te , eV), and DFT predicted BDEs (D0 , eV) obtained for TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe. These values were calculated for each molecule considering only the two proposed spin multiplicities indicated above. Term energies are reported relative to the calculated ground term. Table I also provides a spin-orbit corrected value of the BDE in the last Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-3 Sorensen et al. J. Chem. Phys. 145, 214308 (2016) TABLE I. Calculated molecular configurations and terms and molecular properties for TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe. These results are reported for the two most likely candidates for the ground state. Molecule TiSe ZrSe HfSe VSe NbSe TaSe a Electronic term Term energy, Te (eV)a Dipole moment, µ (Debye) Vibrational frequency, ωe (cm 1 ) Bond length, re (Å) Dissociation energy, D0 (eV) Spin-orbit corrected D0 (eV)b 1δ1 3σ1 , 3 ∆ (Ω = 1) 3σ2 , 1 Σ+ (Ω = 0+ ) 1δ1 3σ1 , 3 ∆ (Ω = 1) 3σ2 , 1 Σ+ (Ω = 0+ ) 3σ2 , 1 Σ+ (Ω = 0+ ) 1δ1 3σ1 , 3 ∆ (Ω = 1) 1δ2 3σ1 , 4 Σ− (Ω = 1/2, 3/2) 1δ1 3σ2 , 2 ∆ (Ω = 3/2) 2 1δ 3σ1 , 4 Σ− (Ω = 1/2, 3/2) 1δ1 3σ2 , 2 ∆ (Ω = 3/2) 1δ1 3σ2 , 2 ∆ (Ω = 3/2) 2 1δ 3σ1 , 4 Σ− (Ω = 1/2, 3/2) 0 1.27 0 0.43 0 0.53 0 1.27 0 0.70 0 0.11 6.11 4.40 5.69 4.07 4.20 5.71 5.84 4.07 4.83 4.67 3.15 4.69 399 445 359 383 340 316 368 386 360 374 350 330 2.255 2.186 2.372 2.330 2.319 2.356 2.246 2.184 2.316 2.304 2.274 2.306 4.082 2.810 4.699 4.264 4.763 4.237 3.710 2.443 4.167 3.469 4.101 3.997 3.952 2.665 4.540 4.057 4.306 3.976 3.553 2.308 3.971 3.338 3.788 3.437 Term energies ignore spin-orbit interaction, which stabilizes the lowest Ω-level, particularly for ∆ terms involving the 5d metals HfSe and TaSe. Section V D 2 for a description of how the spin-orbit correction to D0 was estimated. b See column. See Section V D 2 for an explanation of how this correction was estimated. In these molecules, we number the molecular orbitals based on the valence nd and (n + 1)s orbitals of the metal atom and the valence 4s and 4p orbitals of selenium. A qualitative molecular orbital diagram is presented in Figure 1. The 1σ orbital is primarily core-like and is dominated by a selenium 4s character. The 2σ and 1π orbitals are the bonding orbitals that are primarily linear combinations of the metal ndσ and ndπ orbitals with the corresponding 4pσ and 4pπ orbitals of selenium. All of these are filled in the low-lying states of the investigated molecules. Lying above these are the 1δ and 3σ orbitals, which are composed primarily of metal ndδ and (n + 1)s character, respectively, and are best characterized as nonbonding. Finally, at higher energies are the 2π and 4σ orbitals, which are the antibonding combinations of the ndπ and ndσ orbitals, respectively, with the selenium 4pπ and 4pσ orbitals. The candidates for the ground states in the investigated molecules fill the 1σ, 2σ, and 1π orbitals and place the FIG. 1. Qualitative molecular orbital diagram for the transition metal selenides. The molecular orbitals displayed were calculated for HfSe. Orbital energies are not to scale. remaining two or three electrons in the nonbonding 1δ or 3σ orbitals. In our discussions of the isovalent oxides and sulfides, we use the same numbering scheme for the molecular orbitals that derive from the valence orbitals of oxygen (2s, 2p) or sulfur (3s, 3p). As one might expect, the relative energies of these orbitals, particularly the 3σ and 1δ orbitals, vary as one moves from one metal to another. The experimentally determined ground states of TiO and TiS are 1σ2 2σ2 1π4 1δ1 3σ1 , 3 ∆1 ,21,24 which also emerges as the computationally predicted ground state of TiSe. Similarly, the experimentally determined ground states of VO and VS are both 1σ2 2σ2 1π4 1δ2 3σ1 , 4 Σ− ,27,30 as is computationally found for VSe. In fact, throughout the entire set of six metals, experiment finds that the corresponding MO and MS molecules always have the same ground electronic configuration and term, and in every case except for Zr, our computed ground configuration and term for the MSe species agrees with the known ground term of the MO and MS molecules. In the lighter members of a given group, the metal s-like 3σ orbital is singly occupied, leading to ground terms of 1σ2 2σ2 1π4 1δ1 3σ1 , 3 ∆1 , in TiO,21 TiS,22 and in our calculations of TiSe and ZrSe. Similarly, in the lighter group 5 chalcogenides VO,27 VS,30 NbO,28 NbS,31 and calculated in VSe and NbSe, the ground term is 1σ2 2σ2 1π4 1δ2 3σ1 , 4 Σ− , again leaving the 3σ orbital singly occupied. In the 5d metal chalcogenides, relativistic stabilization of the 6s orbital leads to double occupation of the 3σ orbital, giving ground terms of 1σ2 2σ2 1π4 3σ2 , 1 Σ+ in HfO,23 HfS,26 and calculated in HfSe, and ground terms of 1σ2 2σ2 1π4 3σ2 1δ1 , 2 ∆3/2 in TaO,29 TaS,32 and calculated in TaSe. The unusual situation occurs in ZrSe, where our calculation identifies the ground state to be 1σ2 2σ2 1π4 1δ1 3σ1 , 3 ∆ , as opposed to the experimentally known 1σ2 2σ2 1π4 3σ2 , 1 1 Σ + ground states of ZrO and ZrS.22,25 We do not consider our results to be definitive for ZrSe, in part because we were only concerned with identifying the singlet and triplet candidates for the ground state, not establishing their definitive energy ordering. To computationally determine the energy ordering would require a more sophisticated calculation, which was Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-4 Sorensen et al. J. Chem. Phys. 145, 214308 (2016) FIG. 2. Resonant two-photon ionization spectrum of 48 Ti80 Se (blue) along with the spectrum of the minor isotope 46 Ti (red), which was used for calibration. FIG. 4. Resonant two-photon ionization spectrum of 178 Hf80 Se (blue) along with the spectrum of the impurity 90 Zr (black) and the minor isotope 174 Hf, which were used for calibration. beyond the scope of this investigation. In addition, the known 3 ∆ -1 Σ + separation in ZrO (1080 cm−1 )33 is much smaller 1 than in TiO (2973 cm−1 ),34 HfO (9231 cm−1 ),23 or HfS (6631 cm−1 ).26 This suggests that the corresponding splitting in ZrS and ZrSe will also be small, making a definitive computational assignment of the ZrSe ground state more problematic than for the other molecules. predissociation threshold is clearly identified by an abrupt drop to baseline, with negligible ion signal above the threshold. In the case of TiSe, a weak shoulder persists a bit above the sharp drop; we have increased our proposed error limit to include this shoulder. In all cases, the proposed error limit is indicated by the horizontal bar that lies at the top of the arrow indicating the location of the threshold. The bond dissociation energies, D0 , are tabulated in Table II for each metal selenide. The standard enthalpies of formation for each gaseous metal selenide, ∆f,0K Ho (MSe(g)) are also listed. These were determined using the BDEs determined in this work along with the standard enthalpies of formation for each gaseous metal, ∆f,0K Ho (M(g)), as found in the fourth edition JANAF tables,35 and the enthalpy of formation of gaseous atomic Se, ∆f,0K Ho (Se(g)) = 235.4 ± 1.5 kJ mol−1 .13 B. Bond dissociation energies and enthalpies of formation Displayed in Figures 2–7 are the R2PI spectra of TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe near the predissociation threshold along with the atomic transitions that were used for calibration. With the possible exception of TiSe, in all cases the FIG. 3. Resonant two-photon ionization spectrum of 90 Zr80 Se (blue) along with the spectrum of the minor isotope 96 Zr (red), which was used for calibration. FIG. 5. Resonant two-photon ionization spectrum of 51 V80 Se (blue) along with the spectrum of the minor isotope 50 V (red), which was used for calibration. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-5 Sorensen et al. J. Chem. Phys. 145, 214308 (2016) FIG. 6. Resonant two-photon ionization spectrum of 93 Nb80 Se (blue) along with the spectrum of the impurity 96 Zr (red), present in an earlier experiment, which was used for calibration. We note that by far the largest contribution to the uncertainty in these values comes from the uncertainty in the enthalpy of formation of the gaseous metal atom. Table II also lists the spin-orbit corrected computed BDE using the B3LYP/ LANL2DZ method, along with the deviation between this computed value and our measurement. It is obvious that this computational method fails badly in predicting the BDE for these molecules. V. DISCUSSION A. TiSe, ZrSe, and HfSe Our calculations indicate that the ground terms for TiSe and ZrSe are 3 ∆1 and the ground term for HfSe is 1 Σ0++ . In the cases of TiSe and HfSe, these ground state assignments conform to trends seen in the experimental ground states of TiO,21 TiS,24 HfO,23 and HfS.26 However, the expected ground state for ZrSe was 1 Σ0++ , based on the known ground states of ZrO and ZrS.22,25 As it turns out, a definitive assignment of the ground state symmetry is not necessary for the analysis of the predissociation threshold data in these particular molecules. FIG. 7. Resonant two-photon ionization spectrum of 181 Ta80 Se (blue) along with the spectrum of 181 Ta (red), which was used for calibration. Because Ta has no minor isotopes of sufficient abundance to provide an atomic spectrum and the 181 Ta mass peak was quite intense, the calibration spectrum was obtained by recording the signal in the high-mass tail of this peak in the TOFMS. The purpose of our calculations was to determine if any symmetry-based restrictions might exist that could make it difficult for the initially excited states to predissociate to atoms in their ground spin-orbit levels. For this analysis, we note that the ground separated atom limit for TiSe, ZrSe, and HfSe is d2 s2 , 3 F + s2 p4 , 3 P .36 This separated atom limit produces molec2g 2g ular levels with Ω = 0+ , 0− , 1, 2, 3, and 4. If the ground molecular state is 1 Σ0++ , as is calculated for HfSe, then states with Ω = 0+ and 1 may be accessed in dipole-allowed transitions from the ground state. Both of these can dissociate to ground level atoms while preserving the Ω quantum number. Likewise, if the ground molecular state is 3 ∆1 , as is calculated for TiSe and ZrSe, molecular states with Ω = 0+ , 0− , 1, and 2 may be accessed in dipole-allowed transitions. Again, all of these can dissociate to ground level separated atoms while preserving the Ω quantum number. Even though there is some doubt concerning the ZrSe ground state, we can safely conclude that the excited states of ZrSe that are produced in our experiment can dissociate at the ground separated atom limit without requiring a change in Ω. Thus, we are confident that the TABLE II. Measured BDEs, D0 , and enthalpies of formation, ∆f,0K Ho for MSe molecules. Molecule D0 (cm−1 ) D0 (kJ mol−1 ) D0 (eV) ∆f,0K Ho (M(g)) (kJ mol−1 )a ∆f,0K Ho (MSe(g)) (kJ mol−1 )b Calculated D0 , with spin-orbit correction (eV)c Computational error (eV)d TiSe ZrSe HfSe VSe NbSe TaSe 32 242(50) 39 540(25) 41 567(30) 31 326(25) 38 989(20) 37 945(25) 385.8(6) 473.0(3) 497.3(4) 374.8(3) 466.4(3) 454.0(3) 3.998(6) 4.902(3) 5.154(4) 3.884(3) 4.834(3) 4.705(3) 470.9 ± 17 608.7 ± 8 618.0 ± 6 512.2 ± 8 729.9 ± 8 781.5 320.6 ± 16.8 371.1 ± 8.5 356.1 ± 6.5 372.9 ± 8.1 498.9 ± 8.1 562.9 ± 1.5 3.952 4.540 4.306 3.553 3.971 3.788 −0.046 −0.362 −0.848 −0.331 −0.863 −0.917 a From Ref. 35. using ∆f,0K Ho (Se(g)) = 235.4 ± 1.5 kJ mol−1 , from Ref. 13. c See Section V D 2 for a description of how the spin-orbit correction to D was estimated. 0 d Defined as the computed D , with spin-orbit correction, minus the measured D value. 0 0 b Computed Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-6 Sorensen et al. abrupt predissociation thresholds found in these molecules correspond to the true bond dissociation energies of the molecules. The BDE for TiSe has previously been extrapolated from the BDEs of other titanium-containing molecules as D0 (TiSe) = 3.95(43) eV.13 Wu, Wang, and Su also report a DFT calculated BDE for TiSe of D0 (TiSe) = 4.11 eV and we calculate a value of D0 (TiSe) = 4.082 eV (3.952 eV when estimated spin-orbit corrections are included).14 Our experimental value, D0 (TiSe) = 3.998(6) eV, agrees well with the previous experimental estimate, but with a 70-fold reduction in the error limit. It also demonstrates that the BDEs calculated by Wu, Wang, and Su14 and ourselves both lie within the range of expected chemical accuracy, if one adopts the looser standard suggested for transition metal molecules.10 As far as we are aware, no previous work has been reported on the BDEs of either ZrSe or HfSe, for which we find D0 (ZrSe) = 4.902(3) eV and D0 (HfSe) = 5.154(4) eV. The calculated BDEs that we obtain using the B3LYP method and the LANL2DZ basis set, D0 (ZrSe) = 4.699 eV and D0 (HfSe) = 4.763 eV, are significantly lower than our experimental values. These computed values are in even greater disagreement with experiment when the effects of spin-orbit interaction are considered. J. Chem. Phys. 145, 214308 (2016) C. NbSe As was found for VSe, the ground term of NbSe was calculated to be 1σ2 2σ2 1π4 1δ2 3σ1 , 4 Σ− , leading to possible Ω00 values of 1/2 and 3/2. Again, this gives dipole allowed transitions to excited states with Ω0 = 1/2, 3/2, or 5/2. The separated atom limit for NbSe differs from that of VSe and TaSe, however, and is Nb, d4 s1 , 6 D1/2g + Se, s2 p4 , 3 P2g .36 This limit leads to molecular states with Ω-values of Ω = 1/2, 3/2, and 5/2. Just as was found for the previous molecules, all of the excited states that can be reached in excitations from the ground state can dissociate to the separated atoms in their ground levels while preserving the value of Ω. Again, we can be confident that the observed sharp predissociation threshold corresponds to the production of the separated atoms in their ground levels and is therefore a measurement of the actual bond dissociation energy of the molecule. On this basis, we assign D0 (NbSe) = 4.834(3) eV. To our knowledge, no previous experimental work on the bond dissociation energy of NbSe has been reported. Our calculated BDE of D0 (NbSe) = 4.167 eV is much lower than the measured value, far outside the range required for chemical accuracy. When spin-orbit corrections are included, the error in the computed value again becomes significantly worse. D. Error considerations B. VSe and TaSe 1. Experimental sources of error The ground term of VSe was calculated to be 1σ2 2σ2 1π4 3σ1 , 4 Σ− , giving Ω00 = 1/2 and 3/2; the calculated ground term of TaSe was 1σ2 2σ2 1π4 3σ2 1δ1 , 2 ∆, giving Ω00 = 3/2 for the lowest spin-orbit component. These ground levels lead to dipole-allowed transitions to states with Ω0 = 1/2, 3/2, or 5/2. Both VSe and TaSe have a ground separated atom limit of V/Ta, d3 s2 , 4 F3/2g + Se, s2 p4 , 3 P2g ,36 which produces potential curves with Ω = 1/2, 3/2, 5/2, and 7/2. Thus, any states that may be excited can predissociate to atoms in their ground spinorbit levels while still preserving their Ω quantum number. Therefore, the sharp predissociation thresholds observed in VSe and TaSe may safely be assigned as the BDEs for these molecules. The only previously reported BDE for VSe is D0 (VSe) = 3.55(22) eV, measured using Knudsen effusion mass spectroscopy.12 Wu, Wang, and Su again report a value obtained from density functional calculations of D0 (VSe) = 3.76 eV, which agrees well with our calculated BDE of D0 (VSe) = 3.710 eV.14 Our measured value, obtained from the observed predissociation threshold, is D0 (VSe) = 3.884(3) eV. This lies significantly outside the range of the previous measurement and shows that both the DFT result of Wu, Wang, and Su and our DFT result lie barely within the range required for chemical accuracy in calculations on transition metal molecules. When corrections for spin-orbit effects are included, the agreement between computation and experiment worsens. No previous experimental work has been done on the bond dissociation energy of TaSe, for which we find D0 (TaSe) = 4.705(3) eV. Again, our calculated BDE value of D0 (TaSe) = 4.101 eV is significantly smaller than the measured value, and the error becomes nearly 1 eV when spin-orbit corrections are included. The error limits quoted in this investigation are much smaller than those reported in other methods, so it is worthwhile describing the assumptions behind them. In general, errors can arise from either statistical uncertainties or errors of interpretation. The error limits presented for our values primarily reflect statistical uncertainties. The atomic line positions that we use to calibrate our spectra are known to be 0.1 cm−1 or better;36 this uncertainty is so small that it may be neglected. Our practice is to measure the line positions of a number of atomic lines that are close to the predissociation threshold, calculate the average error by comparing to the known wavenumbers, and then to shift the entire spectrum by the average error, to bring the atomic lines into alignment with their known positions. Of course, random deviations remain for the set of calibration lines. For the studies here, the rms errors in the shifted atomic line positions were less than 4 cm−1 . This is also negligible compared to other sources of error. A second source of error arises because the ion signals shown in Figures 2–7 drop to baseline over a finite interval. We choose the predissociation threshold to lie near the midpoint of the final drop to baseline and assign an error limit that encompasses the range over which the final drop to baseline occurs. This procedure implicitly includes the uncertainty that arises from the laser linewidth, which is in the range of 15 cm−1 for atomic lines recorded under the conditions in which power broadening is minimized. It might be thought that the existence of vibrationally excited molecules or rotationally warm molecules in the molecular beam could contribute to the uncertainty of the measurement, but we do not believe this to be the case. Vibrationally hot molecules would require a lower energy photon 1δ2 Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-7 Sorensen et al. J. Chem. Phys. 145, 214308 (2016) to reach the dissociation threshold than cold molecules, so they would exhibit a predissociation threshold that is shifted to lower wavenumbers by the ground state vibrational quantum. Although a fraction of the molecules will undoubtedly be in v00 = 1, our past experience shows that this will be a small fraction, probably below 10%. As a result, vibrationally hot molecules would produce a weak preliminary threshold at lower wavenumbers, where it would be embedded in the ion signal due to cold molecules. This would be difficult to detect; if detected, it would be readily distinguished from the sharp final drop to baseline. Thus, we do not believe that a small fraction of vibrationally excited molecules can compromise our measurement. It is a bit more complicated to consider rotationally excited molecules, but again we do not believe that rotational excitations will compromise our measurement significantly. Consider a ground state molecule with J00 = 10, for example. Such a molecule will possess a rotational energy of 110 B00, which could be roughly 10 cm−1 of energy. If the rotational energy could be fully utilized to reach the dissociation limit, this molecule would dissociate at a threshold roughly 10 cm−1 below that of a J00 = 0 molecule. However, when a J00 = 10 molecule is photoexcited, selection rules dictate that it will find itself in an excited state with J0 = 11, 10, or 9. While nonadiabatic and spin-orbit coupling can allow this molecule to hop from one potential curve to another, the value of J0 must be conserved. Furthermore, at long range, all potential curves associated with a given value of J0 are dominated by the repulsive centrifugal potential given by V (R) = J(J + 1) ~2 = B(R) J 0 J 0 + 1 . 2 2µR The discussion of centrifugal barriers to dissociation brings up another point: how do we know that there are no other barriers to dissociation at the ground separated atom limit? This is a thorny issue, as we have no way of estimating the magnitude of any such barriers, and we assume they are nonexistent. It is certain that the predissociation thresholds observed in these studies represent an upper limit to the thermochemical BDE. If a barrier were present, however, the true thermochemical BDE could be lower than what we observe. As discussed in our study of the BDEs of VC, VN, and VS,11 previous work on V2 demonstrated through the use of a thermochemical cycle that any barrier in the predissociation of V2 could be no larger than 0.002 eV. This is true despite the fact that V2 is an example that might be expected to display a barrier. The ground separated atom limit of 3d 3 4s2 , 3 F2 + 3d 3 4s2 , 3 F2 is expected to be repulsive at long distances due to the Pauli repulsion of the filled 4s subshells. The fact that no substantial barrier exists in the case of V2 gives us a reason to think that no substantial barrier to dissociation exists for the transition metal selenides as well. It would be useful to test this assumption by measuring precise BDEs for the transition metal selenide cations, MSe+ , along with the ionization energies of the MSe molecules, so that the thermochemical cycle D0 (MSe) + IE(M) = IE(MSe) + D0 (M + −Se) (5.3) could be used to verify the lack of a barrier to dissociation, as has been done in the case of V2 . 2. Computational sources of error (5.1) The long-range nature of the centrifugal potential leads to a centrifugal barrier to dissociation. Thus, a molecule that is initially in a rotational level specified by J00 will experience a shift in the dissociation threshold compared to a cold molecule of roughly ∆E = B R∗ J 0 J 0 + 1 − B 00J 00 J 00 + 1 . (5.2) Here R* represents the internuclear separation that gives the highest point on the centrifugal barrier. Because the two terms are subtracted, we believe that any error associated with rotationally excited molecules in the beam will be small. Furthermore, because the top of the centrifugal barrier is expected to lie at a larger value of R* than the ground state bond length, we expect B(R* ) < B00. As a result, the shift in the predissociation threshold for a rotationally hot molecule, given by (5.2), will be negative. The final drop to baseline therefore probably corresponds to the dissociation threshold for cold molecules because rotationally warm molecules will dissociate at slightly lower wavenumbers. The width of the drop to baseline probably results from the two primary effects: (1) the finite laser linewidth and (2) the population distribution of rotationally excited molecules in the beam, which experience a dissociation threshold shift given roughly by Equation (5.2). By choosing an error range that encompasses the width of the final drop of signal to baseline, we believe that our error limits are adequate to account for both effects. It is also worthwhile to consider the possibility of errors in the computed BDEs of these molecules. A source of error that becomes more important for the heavier molecules is the neglect of spin-orbit interaction. Spin-orbit interaction stabilizes the 3 F2 levels of Ti, Zr, and Hf, the 4 F3/2 levels of V and Ta, the 6 D1/2 level of Nb, and the 3 P2 level of Se. Similarly, the 3 ∆ levels of TiSe, ZrSe, and HfSe and the 2 ∆ 1 3/2 level of TaSe are also stabilized by spin-orbit interaction. The 4 Σ− (Ω = 1/2) levels of VSe and NbSe are likewise stabilized by spin-orbit interaction but only through their second-order interactions with other states. As a result, this will be less significant than in the other molecules, where first-order spin-orbit corrections to the energy are dominant. Similarly, spin-orbit stabilization of the 1 Σ+ states of TiSe, ZrSe, and HfSe cannot occur in first-order perturbation theory. Spin-orbit stabilization of the separated atoms has the effect of reducing the BDE from the computed value, while stabilization of the molecular ground state increases the BDE from the computed value. The energy of the ground atomic term, E(L,S), in the absence of spin-orbit interaction, may be estimated as the degeneracy weighted average of the known energies of the spin-orbit levels,36 P (2J + 1) E(L, S, J) . (5.4) E(L, S) = J P J (2J + 1) As the ground atomic level is at an energy defined to be zero, the spin-orbit stabilization of the ground level (taken to be a negative number, indicating stabilization) is −E(L,S) as Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-8 Sorensen et al. J. Chem. Phys. 145, 214308 (2016) TABLE III. Corrections for spin-orbit stabilization of the ground atomic and molecular levels.a Molecule TiSe ZrSe HfSe VSe NbSe TaSe Electronic term Term energy, Te (eV) ∆ESO (atoms) (eV) ∆ESO (molecule) (eV) ∆ESO (atoms) − ∆ESO (molecule)b 1δ1 3σ1 , 3 ∆ (Ω = 1) 3σ2 , 1 Σ+ (Ω = 0+ ) 1δ1 3σ1 , 3 ∆ (Ω = 1) 3σ2 , 1 Σ+ (Ω = 0+ ) 3σ2 , 1 Σ+ (Ω = 0+ ) 1δ1 3σ1 , 3 ∆ (Ω = 1) 1δ2 3σ1 , 4 Σ− (Ω = 1/2, 3/2) 1δ1 3σ2 , 2 ∆ (Ω = 3/2) 2 1δ 3σ1 , 4 Σ− (Ω = 1/2, 3/2) 1δ1 3σ2 , 2 ∆ (Ω = 3/2) 1δ1 3σ2 , 2 ∆ (Ω = 3/2) 1δ2 3σ1 , 4 Σ− (Ω = 1/2, 3/2) 0 1.27 0 0.43 0 0.53 0 1.27 0 0.70 0 0.11 −0.145 −0.145 −0.207 −0.207 −0.457 −0.457 −0.157 −0.157 −0.196 −0.196 −0.560 −0.560 −0.015 0.000 −0.048 0.000 0.000 −0.196 0.000 −0.022 0.000 −0.065 −0.247 0.000 −0.130 −0.145 −0.159 −0.207 −0.457 −0.261 −0.157 −0.135 −0.196 −0.131 −0.313 −0.560 a The spin-orbit stabilization of the ground atomic levels, given by ∆ESO (atoms), is described in the text. The spin-orbit stabilization of the ground molecular level, based on the electronic term, ignores second-order spin-orbit interactions and uses atomic spin-orbit parameters given by ζ3d (Ti) = 123 cm−1 , ζ4d (Zr) = 387 cm−1 , ζ5d (Hf) = 1578 cm−1 , ζ3d (V) = 177 cm−1 , ζ4d (Nb) = 524 cm−1 , and ζ5d (Ta) = 1995 cm−1 , taken from Ref. 37. b The energy difference, ∆ESO (atoms) − ∆ESO (molecule), provides the correction that should be added to the calculated BDE that is obtained in a method that ignores spin-orbit interactions. defined above. For convenience, the sum of the spin-orbit stabilization for the metal and selenium atoms is calculated from the known atomic energy levels and is listed in Table III as ∆ESO (atoms). To first order in perturbation theory, the spin-orbit stabilization of the ground molecular level is zero for the 1 Σ+ states of TiSe, ZrSe, and HfSe and for the 4 Σ− states of VSe, NbSe, and TaSe. There is a first-order stabilization of the ground spin-orbit level in the 3 ∆1 levels of TiSe, ZrSe, and HfSe and in the 2 ∆3/2 levels of VSe, NbSe, and TaSe, however. Using the methods described by Lefebvre-Brion and Field,37 it is readily shown that the spin orbit stabilization of the ground level in these 3 ∆ and 2 ∆ states may be estimated as −ζnd , where ζnd is the spin-orbit constant for the nd atomic orbital of the metal atom. These values are tabulated in Ref. 37. The spin-orbit stabilization of the molecular state is also given in Table III as ∆ESO (molecule). The net spin-orbit correction to the BDE calculated using a computational method that ignores spin-orbit interaction is given by ∆ESO (atoms) − ∆ESO (molecule) and is listed in Table III for the various possible molecular ground states. In all cases the correction is negative, indicating that the inclusion of spin-orbit interaction will reduce the calculated BDE of the molecule. With the sole exception of TiSe, all of the BDEs calculated using the B3LYP/LANL2DZ method are already smaller than the measured values. The inclusion of spin-orbit corrections only worsens the agreement. The fact that the spin-orbit correction depends critically on the electronic configurations of the separated atoms and of the bound molecule suggests that it will be difficult to develop a parameterization of density functional methods that can adequately treat a wide range of molecules, particularly those containing heavy atoms, unless spin-orbit interaction is explicitly included in the method. E. General observations In a previous study, we noted that in the multiply-bonded diatomic transition metals (Cr2 , V2 , CrW, NbCr, VNb, Mo2 , and Nb2 ), a strong correlation exists between the d-orbital radial expectation value, hrind , and the bond dissociation energy, D0 .38 It was rationalized that the main difficulty in achieving effective d orbital bonding arises from the small size of the d orbitals, particularly in relation to the valence s orbital. Larger d orbitals are able to overlap more effectively to make stronger bonds. For similar reasons, it is possible that the BDEs of the transition metal selenides might follow the same trend. The small BDEs of TiSe and VSe are in keeping with this trend because the 3d metals have considerably smaller d orbital radii than their heavier 4d and 5d congeners. To consider this correlation more quantitatively, we note that the values of hrind vary significantly with orbital occupation; the expectation value hrind is larger in d n+1 s1 configurations compared to d n s2 configurations, owing to the greater d-d electron repulsion in the former case. To account for this effect, we consider the 3σ molecular orbital to be purely of metal ns character and employ the hrind value taken from the d n+1 s1 configuration for molecules in which the 3σ orbital is singly occupied in the ground state. When the 3σ orbital is doubly occupied in the ground state, we employ the hrind value taken from the computations of the d n s2 configuration instead. When possible, we have used the hrind values obtained from numerical Dirac-Fock calculations, as tabulated by Desclaux.39 These values differ slightly between the d 3/2 and d 5/2 orbitals; we have taken the average of the two values. When the appropriate electronic configuration was not included in this tabulation, we have scaled the numerical Hartree-Fock results of Charlotte Froese-Fischer by an interpolated value of the ratio of the relativistic hrind value to the nonrelativistic one, as compiled by Desclaux.39,40 It seems likely that the ground terms of TiSe, VSe, and NbSe leave the 3σ orbital singly occupied, as is experimentally found in the analogues TiO, TiS, VO, VS, NbO, and NbS and as found in our calculations. Likewise, it is quite reasonable that the ground terms of HfSe and TaSe place two electrons in the 3σ orbital, as in the HfO, HfS, TaO, and TaS molecules and as found in our calculations. This is expected due to the relativistic stabilization of the 6s orbital in the metal atoms. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 214308-9 Sorensen et al. J. Chem. Phys. 145, 214308 (2016) TABLE IV. Radial expectation values, hrind , for the d n s2 and d n+1 s1 configurations.a Transition metal d n s2 (Å) d n+1 s1 (Å) Transition metal d n s2 (Å) d n+1 s1 (Å) Ti Zr Hf 0.7931b 1.1563b 1.2588b 0.9376c 1.2733c 1.4112c V Nb Ta 0.7200b 1.0410c 1.1414b 0.8259c 1.1267b 1.2365c a Values in bold correspond to the likely ground configuration of the metal in the MSe molecule and are used in Figure 8. b From Ref. 39. c Estimated from Refs. 40 and 39. In ZrSe, however, it is less certain whether the 3σ orbital is singly or doubly occupied. Our calculation suggests that it is singly occupied, while experimental data for the ZrO and ZrS analogues show it to be doubly occupied. Table IV provides the numerical Dirac-Fock calculated or estimated values of hrind for the d n s2 and d n+1 s1 configurations of the atoms. The bolded entries are used in Figure 8, where the measured bond dissociation energies are plotted vs. radial expectation value, hrind . Figure 8 displays a striking correlation between bond dissociation energy and the d-orbital radial expectation value, similar to what was found for the multiply-bonded diatomic transition metals. The red line in the figure represents a fitted line through the data points for TiSe, HfSe, VSe, NbSe, and TaSe, where the molecular configuration seems definite. For ZrSe, we have plotted the data points obtained for hrind calculated for both the 4d 2 5s2 (blue open square) and 4d 3 5s1 (red open circle) configurations of atomic Zr. If the trend holds for ZrSe, this plot suggests that the ground state of this molecule places two electrons in the 5s-like 3σ orbital, giving a 1σ2 2σ2 1π4 3σ2 , 1 Σ+ ground term, as is experimentally found in ZrO and ZrS. The correlation of bond dissociation energy and d-orbital radial expectation value seems too simplistic to completely account for the chemical bonding in these molecules. For example, it ignores differences in the ionization energy of the metal atom, which is clearly relevant to the ionic contributions to the chemical bonding. While five of the metals examined here have ionization energies in the range 6.73 ± 0.10 eV, tantalum has a significantly higher ionization energy, 7.55 eV. The higher ionization energy of tantalum apparently does not significantly influence its ability to bond to selenium, however. Likewise, this correlation neglects any differences in the promotion energy required to prepare the atoms for bonding and ignores any differential stabilization of the separated atom limit vs. the MSe molecule due to spin-orbit effects. All of these effects are undoubtedly important, but fail to show up in the simple correlation found in Figure 8. We hope to test this correlation further by studies on the group 3 transition metal selenides, ScSe, YSe, and LaSe. VI. CONCLUSION Predissociation thresholds for TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe were observed using resonant two-photon ionization spectroscopy, and from these observations, bond dissociation energies and enthalpies of formation were derived. Along with the previous work on the BDEs of VC, VN, and VS and forthcoming work on the BDEs of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi, these studies have shown that the onset of predissociation in a congested vibronic spectrum provides a reliable means of estimating the bond dissociation energy for many MC, MN, MSi, MS, and MSe molecules. We believe that this method is likely to succeed for any transition metal atom (including lanthanides and actinides) where the ground term of the transition metal atom is a highly degenerate D, F, or higher term. While transition metals with ground S terms will likely be problematic (Cr, Mo, Mn, Tc, Re, Pd, Cu, Ag, Au, Zn, Cd, and Hg), the method is highly promising for molecules containing the remaining transition metals (Sc, Y, La, Ti, Zr, Hf, V, Nb, Ta, W, Fe, Ru, Os, Co, Rh, Ir, Ni, Pt, and most of the lanthanides and actinides). ACKNOWLEDGMENTS The authors thank the National Science Foundation for support of this research under Grant No. CHE-1362152. We also thank Professors Richard Ernst and Thomas Richmond for their assistance in the synthesis of gaseous H2 Se. 1 X. FIG. 8. Correlation of bond dissociation energy with radial expectation value, hrind . Values obtained from d n s2 configurations are shown as blue squares and those obtained from d n+1 s1 configurations are shown as red circles. 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Fox, gaussian 09, Revision D.01, Gaussian, Inc., Wallingford, CT, 2009. 18 C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B: Condens. Matter Mater. Phys. 37, 785–789 (1988). 19 A. D. Becke, J. Chem. Phys. 98, 5648–5652 (1993). 20 P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 299–310 (1985). 21 W. H. Hocking, M. C. L. Gerry, and A. J. Merer, Can. J. Phys. 57, 54–68 (1979). J. Chem. Phys. 145, 214308 (2016) 22 P. D. Hammer and S. P. Davis, Astrophys. J. 237, L51–L53 (1980). A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 173, 37–43 (1995). 24 J. Jonsson and O. Launila, Mol. Phys. 79, 95–103 (1993). 25 B. Simard, S. A. Mitchell, and P. A. Hackett, J. Chem. Phys. 89, 1899–1904 (1988). 26 O. Launila, J. Jonsson, G. Edvinsson, and A. G. Taklif, J. Mol. Spectrosc. 177, 221–231 (1996). 27 A. S. C. Cheung, A. W. Taylor, and A. J. Merer, J. Mol. Spectrosc. 92, 391–409 (1982). 28 J. L. Femenias, G. Cheval, A. J. Merer, and U. Sassenberg, J. Mol. Spectrosc. 124, 348–368 (1987). 29 C. J. Cheetham and R. F. Barrow, Trans. Faraday Soc. 63, 1835–1845 (1967). 30 Q. Ran, W. S. Tam, A. S. C. Cheung, and A. J. Merer, J. Mol. Spectrosc. 220, 87–106 (2003). 31 O. Launila, J. Mol. Spectrosc. 229, 31–38 (2005). 32 S. Wallin, G. Edvinsson, and A. G. Taklif, J. Mol. Spectrosc. 192, 368–377 (1998). 33 L. A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 174, 93–99 (1995). 34 L. A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 173, 499–509 (1995). 35 M. W. Chase, Jr., NIST-JANAF Thermochemical Tables, 4th ed. (American Institute of Physics for the National Institute of Standards and Technology, Washington, DC, 1998). 36 A. E. Kramida, Y. Ralchenko, J. Reader, and NIST ASD Team, NIST Atomic Spectra Database, version 5.3, National Institute of Standards and Technology, Gaithersburg, MD, 2015. 37 H. Lefebvre-Brion and R. W. Field, The Spectra and Dynamics of Diatomic Molecules (Elsevier, Amsterdam, 2004). 38 D. J. Matthew, S. H. Oh, A. Sevy, and M. D. Morse, J. Chem. Phys. 144, 214306-1–214306-10 (2016). 39 J. P. Desclaux, At. Data Nucl. Data Tables 12, 311 (1973). 40 C. F. Fischer, The Hartree-Fock Method for Atoms (John Wiley & Sons, New York, 1977). 23 L. Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.101.69.28 On: Fri, 02 Dec 2016 19:01:33 THE JOURNAL OF CHEMICAL PHYSICS 147, 084301 (2017) Bond dissociation energies of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi Andrew Sevy,1 Jason J. Sorensen,1 Thomas D. Persinger,2 Jordan A. Franchina,1 Eric L. Johnson,3 and Michael D. Morse1 1 Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, USA of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA 3 Department of Chemistry and Biochemistry, Georgia Southern University, Statesboro, Georgia 30460, USA 2 Department (Received 2 June 2017; accepted 25 July 2017; published online 22 August 2017) Predissociation thresholds have been observed in the resonant two-photon ionization spectra of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi. It is argued that because of the high density of electronic states at the ground separated atom limit in these molecules, the predissociation threshold in each case corresponds to the thermochemical bond dissociation energy. The resulting bond dissociation energies are D0 (TiSi) = 2.201(3) eV, D0 (ZrSi) = 2.950(3) eV, D0 (HfSi) = 2.871(3) eV, D0 (VSi) = 2.234(3) eV, D0 (NbSi) = 3.080(3) eV, and D0 (TaSi) = 2.999(3) eV. The enthalpies of formation were also calculated as ∆f,0K H°(TiSi(g)) = 705(19) kJ mol 1 , ∆f,0K H°(ZrSi(g)) = 770(12) kJ mol 1 , ∆f,0K H°(HfSi(g)) = 787(10) kJ mol 1 , ∆f,0K H°(VSi(g)) = 743(11) kJ mol 1 , ∆f,0K H°(NbSi(g)) = 879(11) kJ mol 1 , and ∆f,0K H°(TaSi(g)) = 938(8) kJ mol 1 . Using thermochemical cycles, ionization energies of IE(TiSi) = 6.49(17) eV and IE(VSi) = 6.61(15) eV and bond dissociation energies of the ZrSi and NbSi anions, D0 (Zr–Si ) ≤ 3.149(15) eV, D0 (Zr –Si) ≤ 4.108(20) eV, D0 (Nb–Si ) ≤ 3.525(31) eV, and D0 (Nb –Si) ≤ 4.017(39) eV, have also been obtained. Calculations on the possible low-lying electronic states of each species are also reported. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4986213] 3P I. INTRODUCTION The ability to perform any sort of chemical transformation successfully is governed by the thermodynamics and kinetics of the transformation. Although kinetic difficulties may be overcome through the use of an appropriate catalyst, thermodynamic restrictions cannot be circumvented without changing the reactants. Because of this fundamental fact, accurate thermochemical knowledge is crucial if we wish to be able to predict whether a reaction is feasible or not. Accurate thermochemical data (±1 kcal/mol) are available for many organic systems,1 and computational chemistry has advanced to the point that thermochemical quantities such as bond dissociation energies (BDEs) are readily calculated for organic and many main group systems.2–6 In contrast, thermochemical data for the d- and f -block elements are far more difficult to obtain computationally,6–9 and experimental data are more limited and often have large uncertainties.10 A goal of recent work from our laboratory is to provide accurate BDEs for a large number of small transition metal molecules, which may then be used to guide our thinking about chemical bonding in these species. These improved measurements will also serve as benchmarks for the development of more accurate computational methods. In recent publications, we have published new measurements of the bond dissociation energies of VC, VN, VS, TiSe, ZrSe, HfSe, VSe, NbSe, TaSe, FeC, NiC, FeS, NiS, FeSe, and NiSe.11–13 For several of these molecules, no previous BDE measurements existed in the literature. In many of the transition metal—main group diatomic molecules, the transition metal has a ground state with a Dg or Fg term, while the main group element has a ground 2 Pu or 0021-9606/2017/147(8)/084301/8/$30.00 term.14 This leads to a large number of potential energy curves arising from ground state atoms; further, the existence of low-lying excited terms for many transition metal atoms implies that a large number of additional electronic states arise from limits only slightly higher in energy. In such situations, the number of electronic states grows tremendously as one approaches the ground separated atom limit, leading to the observation of a dense quasi-continuous optical spectrum in this region. For all of the molecules listed above, the spectrum was recorded using the resonant two-photon ionization (R2PI) spectroscopic method, which detects the absorption of radiation by the subsequent ionization of the molecule from its excited electronic state using a second photon. Ionization is followed by mass spectrometric detection. At a well-defined threshold in energy, however, the spectrum abruptly ceased, leaving only a background signal at the mass of the molecule. This occurs because at this sharp threshold, the molecule dissociates too quickly to be ionized. In this high-energy region of multiple curve crossings and avoided curve crossings, nonadiabatic and spin-orbit couplings occur so readily that it is fundamentally wrong to think of the molecule as moving on a single Born-Oppenheimer potential surface. As a result, the molecule finds a way to dissociate rapidly as soon as the ground separated atom limit is exceeded. On this basis, we assign the observed predissociation threshold as the bond dissociation energy of the molecule. In the present investigation, the observation of predissociation thresholds has been used to measure the BDEs of the group 4 and 5 transition metal silicides, TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi. Strictly speaking, a predissociation threshold provides an upper limit to the BDE. However, if the molecule is cold, has a sufficient density of states, and has sufficient spin-orbit and g 147, 084301-1 Published by AIP Publishing. 084301-2 Sevy et al. J. Chem. Phys. 147, 084301 (2017) nonadiabatic coupling to allow it to hop from one potential curve to another, the predissociation threshold provides an accurate value of the thermochemical BDE. In the case of V2 , measurements of the atomic and molecular ionization energies have been combined with predissociation measurements of the BDEs of V2 and V2 + to verify, using the thermochemical cycle D0 (V2 ) + IE(V) = D0 (V+ − V) + IE(V2 ), (1.1) that the predissociation thresholds correspond to true thermochemical bond dissociation energies to an accuracy of ±0.002 eV.15–18 Accordingly, we believe that when a sharp predissociation threshold is observed in small transition metal molecules, it will generally correspond to the thermochemical BDE. This point has been discussed in a greater detail in our recent publication on the BDEs of FeC, NiC, FeS, NiS, FeSe, and NiSe.13 Thermochemical cycles analogous to (1.1) offer another use for BDEs. By definition, the energy required to separate the diatomic molecule AB into A+ + B + e is the same, regardless of whether the molecule is first dissociated into A + B and then the A fragment is ionized or if the molecule is ionized and then dissociated into A+ + B. Thus, D0 (A − B) + IE(A) = IE(AB) + D0 (A+ − B). (1.2) Ionization energies of the elements, IE(A), are well known,14 while the BDEs of many diatomic cations, D0 (A+ B), have been measured by methods such as guided ion beam mass spectrometry19,20 and mass-selected predissociation threshold studies.21–23 Likewise, the molecular ionization energy, IE(AB), can be measured by pulsed field ionization-zero electron kinetic energy (PFI-ZEKE) spectroscopy or photoionization efficiency (PIE) curves.24–27 When all four values have been measured, Eq. (1.2) provides a check for how well the experiments agree, as in the case of V2 mentioned above. When two of the values are known, measuring a third provides a way to calculate the last. The values measured in this work provide the second or third piece of information for each of the MSi diatomics investigated. Similarly, when data are available concerning the electron affinity of the diatomic metal silicide, the analogous thermochemical cycle may be used to deduce the bond dissociation energy of anion, using D0 (M − Si− ) = D0 (MSi) + EA(MSi) − EA(Si). (1.3) Another key property that may be obtained from the bond dissociation energy is the 0 K enthalpy of formation, given by ∆f,0K H◦ (MX(g)) = ∆f,0K H◦ (M(g)) + ∆f,0K H◦ (X(g)) − D0 (MX(g)), (1.4) where ∆f,0K H°(M(g)) is the heat of formation for the gaseous metal, ∆f,0K H°(X(g)) is the heat of formation for the gaseous ligand atom, and D0 (MX(g)) represents the BDE of the MX molecule. It is fair to say that doped silicon forms the basis for modern electronics and information technology. Generally, transition metal silicides are of particular interest in the materials and electronics industries, due to their distinct semiconducting capabilities, superior oxidation resistance, stability under high temperatures, and low corrosion rates.28 The behavior of transition metal silicides can be tuned by the choice of the transition metal,29 and as silicon-based technology moves to smaller scale structures, the silicon-metal atomic interactions are predicted to become more important.28 Accordingly, there is presently a need for precise knowledge of the chemical bonding in metal-silicon systems.28 While the present work will not directly address solid-phase transition metal silicides, the precise values reported here may be used to test computational methods more generally. In this article, we report BDE values for diatomic MSi molecules (M = Ti, Zr, Hf, V, Nb, Ta), observed via the observation of predissociation thresholds in a dense manifold of states in an R2PI spectrum. The closely related properties of the enthalpy of formation, ∆f,0K H°(MSi(g)), ionization energy, IE(MSi), and the BDE of the molecular anions, D0 (M–Si ) and D0 (M –Si), are calculated from the available literature, when possible. It is hoped that these data will enhance our understanding of chemical bonding in these and related systems and assist computational chemists in the development of more accurate computational methods. II. EXPERIMENTAL Predissociation thresholds were measured using the same instrument that was employed in other recent BDE studies from this group.11–13 A metal sample (Ti, Zr, Hf, V:Mo 1:1, Nb, Ta) is laser ablated using the third harmonic output of a Nd:YAG laser (355 nm) to generate a plasma. The plasma is then carried down a 1.3 cm reaction channel by a pulse of seeded gas (0.13% SiH4 in He), terminating in a 2 mm expansion orifice. Upon exiting the orifice, the carrier gas and its molecular contents undergo supersonic expansion into vacuum (10 5 Torr). The expansion is skimmed into a beam 1 cm in diameter and passes into a second chamber (10 6 Torr), containing a Wiley-McLaren ion source at the base of a reflectron time-offlight mass spectrometer.30,31 Output radiation from an optical parametric oscillator (OPO) laser is counterpropagated along the molecular beam, exciting the molecules. A short time later (∼20 ns) a KrF excimer laser (5.00 eV) is fired at a right angle to the molecular beam, ionizing the molecules that have been excited. The resulting ions are then accelerated into the mass spectrometer and the time-of-flight mass spectrum is recorded. The experiment is repeated at 10 Hz, and 30 repetitions are averaged for each wavelength point. After the signal has been accumulated for each wavelength, the OPO laser is incremented to the next wavelength, allowing an optical spectrum to be recorded for the specific masses of interest. At least three scans over the predissociation threshold region are averaged to ensure reproducibility and improve the signal-to-noise ratio. III. COMPUTATIONS Calculations were performed using the Gaussian 09 software suite.32 The B3LYP density functional method33,34 was employed with the LANL2DZ basis set.35 This basis set uses an effective core potential that makes the computations much more tractable and includes mass-velocity and Darwin 084301-3 Sevy et al. relativistic effects on the core electrons. Unrestricted geometry optimization and frequency calculations were performed to attempt to determine the ground states for each MSi molecule. Spin-orbit coupling was neglected, and the calculations were performed in the C2v point group. All calculations were performed using a super-fine grid in order to insure that the integrations were sufficiently accurate; this was found to significantly affect the results. Alternative configurations were examined by altering the orbital occupations and running the calculation again. In several examples, these alternative configurations led to a revision in the calculated ground state. Singlet, triplet, and quintet spin states were considered for TiSi, ZrSi, and HfSi; doublet, quartet, and sextet states were computed for VSi, NbSi, and TaSi. For each calculated multiplicity, the electron configuration was assigned based on the apparent orbital symmetry, and possible term symbols were deduced. Finally, separate calculations on the ground state energies of the metal and silicon atoms were performed, in order to obtain computational estimates of the BDE by difference. IV. RESULTS A. Experimental results Figure 1 displays the R2PI spectrum of TiSi obtained by scanning over the observed predissociation threshold, identified as 17 755 cm 1 (2.201 eV). Also shown is the simultaneously recorded Ti+ signal that was used to calibrate the spectrum using the well-known atomic energy levels.14 Analogous atomic spectra were used to calibrate the predissociation thresholds for the other species reported here. At energies below the threshold, there is a nearly continuous spectrum with many absorption features; when the photon energy exceeds 17 755 cm 1 , however, the ion signal drops to baseline and no additional features are observed. A detailed discussion of the assignment of proposed error limits has been provided in our previous publication on the BDEs of TiSe, ZrSe, HfSe, FIG. 1. R2PI spectrum of titanium silicide (blue) and titanium signal used for calibration (red), showing the predissociation threshold at 17 755(25) cm 1 . The uncertainty range (±25 cm 1 ) is indicated by the horizontal bar above the arrow showing the location of the predissociation threshold. J. Chem. Phys. 147, 084301 (2017) FIG. 2. R2PI spectrum of zirconium silicide (blue) and zirconium signal used for calibration (red), showing predissociation threshold at 23 791(25) cm 1 . The horizontal bar at the top of the arrow indicates the ±25 cm 1 assigned error limit. VSe, NbSe, and TaSe.12 Sources of error that are considered include the finite laser linewidth, calibration errors, and the existence of rotationally or vibrationally excited molecules in the molecular beam. Following the rationale described in that article,12 the uncertainty assigned to the BDE of TiSi is 25 cm 1 (0.003 eV), giving D0 (TiSi) = 2.201(3) eV. Further considerations of possible errors of interpretation are provided in Sec. V A. Figures 2–6 show the analogous spectra for ZrSi, HfSi, VSi, NbSi, and TaSi, with predissociation thresholds assigned at 23 791(25), 23 158(25), 18 020(25), 24 845(25), and 24 190(25) cm 1 , respectively. B. Computational results Considering the valence nd and (n+1)s orbitals of the metal atom and the 3s and 3p orbitals of the silicon atom, 10 molecular orbitals may be formed. These consist of four FIG. 3. R2PI spectrum of hafnium silicide (blue) and hafnium signal used for calibration (red), showing predissociation threshold at 23 158(25) cm 1 . Both 176 Hf and 174 Hf isotopes were used for calibration because the signal was too intense in the former to easily measure peak locations of the more intense features. 084301-4 Sevy et al. FIG. 4. R2PI spectrum of vanadium silicide (blue) and vanadium signal used for calibration (red), showing predissociation threshold at 18 020(25) cm 1 . The horizontal bar at the top of the arrow indicates the ±25 cm 1 assigned error limit. σ orbitals, two pairs of π orbitals, and one pair of δ orbitals. To maintain consistent numbering across the MSi series, these are labeled as the 1σ, 2σ, 3σ, 4σ, 1π, 2π, and 1δ orbitals for all of the molecules considered. For all of the MSi molecules, the 1σ orbital lies far below the other orbitals and is composed primarily of the Si 3s atomic orbital. It is doubly occupied in all of the states considered, regardless of their spin multiplicity. Next comes the 2σ, 1π, 3σ, and 1δ orbitals that lie close in energy. The energy ordering of these orbitals varies from metal to metal and depends on the electronic state under consideration. The 2σ and 3σ orbitals are linear combinations of the metal ndσ, (n+1)sσ, and silicon 3pσ orbitals that are either FIG. 5. R2PI spectrum of niobium silicide (blue) and titanium atomic signal used for calibration (red), showing predissociation threshold at 24 845(25) cm 1 . The horizontal bar at the top of the arrow indicates the ±25 cm 1 assigned error limit. For this study, the niobium atomic transitions proved difficult to identify, so the sample was changed to titanium, which provided more readily identified atomic transitions for calibration. A small gap in the spectrum at 25 000 cm 1 occurs because the method the OPO laser uses to generate laser radiation changes between 400 nm and 399.9 nm. J. Chem. Phys. 147, 084301 (2017) FIG. 6. R2PI spectrum of tantalum silicide (blue) and tantalum signal used for calibration (red), showing predissociation threshold at 24 190(25) cm 1 . The horizontal bar at the top of the arrow indicates the ±25 cm 1 assigned error limit. bonding or nonbonding in character; the 1π orbitals are bonding combinations of the metal ndπ and silicon 3pπ orbitals, and the 1δ orbital is a nearly pure ndδ orbital localized on the metal atom. For the states considered here, either 6 (TiSi, ZrSi, and HfSi) or 7 (VSi, NbSi, and TaSi) electrons are distributed in the 2σ, 1π, 3σ, and 1δ orbitals. Above these orbitals lie the antibonding 2π and 4σ orbitals that remain empty in all of the low-lying states of the MSi molecules. The real question in the electronic structure of the group 4 and 5 monosilicides centers on the distribution of the remaining 6 or 7 electrons in the 2σ, 1π, 3σ, and 1δ orbitals. The various possible ways of distributing these electrons lead to a large number of low-lying electronic states. The calculated properties are presented in Table I. Both TiSi and ZrSi are calculated to have 1σ2 2σ2 1π2 1δ1 3σ1 , 5 ∆ ground terms, while HfSi is calculated to have a 1σ2 2σ2 1π3 3σ1 , 3 Π ground term. These ground terms are in agreement with the previous density functional theory (DFT) study of Wu and Su,36 which employed a very similar computational method. For TiSi, our calculated 5 ∆ ground term is also in agreement with multireference single and double excitation configuration interaction, with perturbative quadruple excitations (MRSDCI+Q) and multireference coupled-pair approximation (MRCPA) calculations.37 In the case of ZrSi, previous B3LYP investigations conducted by Gunaratne et al. find a ground term of quintet multiplicity, in agreement with our result; the unrestricted coupled-cluster singles and doubles (triples) [UCCSD(T)] method, however, yielded a ground state singlet or triplet, depending on the chosen basis set.28 In MP2 calculations, Gunaratne et al. find ZrSi to have a singlet ground state.38 Our own calculations find 5 ∆, 1 Σ+ , and 3 Σ+ terms to lie within 0.13 eV of the ground state in ZrSi. These results show that the determination of the ground state of ZrSi will require a much more sophisticated computational treatment than we have been able to provide. For the group 5 silicides, the situation is no clearer. Our results on VSi and NbSi indicate that the 1σ2 2σ2 1π3 1δ1 3σ1 , 4 Π/4 Φ term (Π or Φ cannot be determined from the 084301-5 Sevy et al. J. Chem. Phys. 147, 084301 (2017) TABLE I. Calculated electronic states of the MSi molecules. Molecule D0 (exp)a TiSi 2.201(3) ZrSi 2.950(3) HfSi 2.871(3) VSie 2.234(3) NbSie 3.080(3) TaSi 2.999(3) Configurationb 1σ2 2σ2 1π2 1δ1 3σ1 1σ2 2σ1 1π3 1δ1 3σ1 1σ2 2σ2 1π3 3σ1 1σ2 2σ1 1π4 1δ1 1σ2 2σ2 1π4 1σ2 2σ1 1π4 3σ1 1σ2 2σ2 1π2 1δ1 3σ1 1σ2 2σ2 1π4 1σ2 2σ1 1π4 3σ1 1σ2 2σ2 1π3 1δ1 1σ2 2σ1 1π3 1δ1 3σ1 1σ2 2σ1 1π4 1δ1 1σ2 2σ2 1π3 3σ1 1σ2 2σ2 1π4 1σ2 2σ2 1π2 1δ1 3σ1 1σ2 2σ1 1π4 3σ1 1σ2 2σ1 1π3 1δ1 3σ1 1σ2 2σ2 1π3 1δ1 3σ1 1σ2 2σ2 1π2 1δ2 3σ1 1σ2 2σ2 1π4 1δ1 1σ2 2σ2 1π4 3σ1 1σ2 2σ2 1π2 1δ2 3σ1 1σ2 2σ2 1π3 1δ1 3σ1 1σ2 2σ2 1π4 1δ1 1σ2 2σ2 1π4 3σ1 1σ2 2σ2 1π3 1δ1 3σ1 1σ2 2σ2 1π4 3σ1 1σ2 2σ2 1π2 1δ2 3σ1 Term 5∆ 5 Π/5 Φ 3Π 3∆ 1 Σ+ 3 Σ+ 5∆ 1 Σ+ 3 Σ+ 3 Π/3 Φ 5 Π/5 Φ 3∆ 3Π 1 Σ+ 5∆ 3 Σ+ 5 Π/5 Φ 4 Π/4 Φ 6 Σ+ 2∆ 2 Σ+ 6 Σ+ 4 Π/4 Φ 2∆ 2 Σ+ 4 Π/4 Φ 2 Σ+ 6 Σ+ Energy (T0 , eV) Dipole moment (D) ωe c (cm 1 ) re c (Å) D0 c (eV) 0.00 0.53 0.71 0.71 0.74 0.84 3.77 3.84 3.43 5.01 3.72 3.48 350.0 369.4 327.6 309.7 460.1 354.3 2.475 2.329 2.406 2.330 2.245 2.231 2.09 1.56 1.39 1.38 1.36 1.25 2.001 2.039 1.164 1.278 0.000 1.228 0.00 0.13 0.13 0.32 0.35 0.54 3.80 3.96 3.85 4.29 3.59 5.34 348.9 448.7 479.9 361.1 398.1 427.7 2.570 2.361 2.291 2.490 2.433 2.337 2.51 2.38 2.38 2.20 2.16 1.97 2.001 0.000 1.003 1.065 2.004 1.027 0.00 0.12 0.20 0.74 1.11 3.02 3.35 2.91 4.70 3.99 388.4 433.8 309.4 472.9 390.4 2.416 2.330 2.582 2.269 2.407 2.39 2.27 2.19 1.65 1.28 1.025 0.000 2.006 1.003 2.002 0.00 0.03 0.36 1.50 3.28 3.47 4.70 3.47 309.3 354.8 230.1 354.8 2.433 2.436 2.345 2.436 2.54 2.51 2.18 1.03 1.691 2.504 1.168 0.940 0.00 0.03 0.16 0.59 2.90 3.18 4.23 3.18 362.6 367.8 419.7 473.5 2.496 2.391 2.249 2.258 2.42 2.38 2.24 1.83 2.502 1.547 0.961 0.513 0.00 0.10 0.26 2.83 2.39 2.50 399.4 473.6 349.8 2.375 2.260 2.497 2.68 2.58 2.43 1.515 0.504 2.501 hSid a For comparison, the bond dissociation energy measured in the present study is listed below the molecule for each species, in units of eV. b Orbitals are listed in a uniform order within a configuration for comparison purposes. c The computed quantities ω , r , and D refer to the harmonic vibrational frequency, the equilibrium bond length, and the energy e e 0 difference between the v = 0 vibrational level and the ground separated atom limit, omitting spin-orbit effects, respectively. d Calculations were done using the unrestricted B3LYP method, and expectation values of Ŝ2 were equated to S(S + 1) and solved for S. This is listed here as hSi. Values that differ significantly from the expected values of S = 0, 1, 2 (for TiSi, ZrSi, and HfSi) or S = 0.5, 1.5, 2.5 (for VSi, NbSi, and TaSi) are indicative of problems with the computational method. e VSi and NbSi have been suggested to have 1σ2 2σ2 1π4 1δ1 , 2 ∆ ground states on the basis of matrix isolation ESR studies in Ref. 39. calculation) and the 1σ2 2σ2 1π2 1δ2 3σ1 , 6 Σ+ term lie within 0.03 eV, with 4 Π/4 Φ emerging as the ground term in VSi but 6 Σ + the ground term in NbSi. These two terms are also calculated to lie similarly close in energy in the previous DFT studies of Wu and Su (VSi and NbSi) and Gunaratne et al. (NbSi only).28,36 The quartet and sextet states of NbSi are also found to lie very close in energy in UCCSD(T) calculations, with the ground state depending on the basis set employed.28 To complicate matters further, the 1σ2 2σ2 1π4 1δ1 , 2 ∆ term lies only slightly higher in energy in both VSi and NbSi. This 2 ∆ term has been suggested to be the ground state of VSi and NbSi, based on ESR experiments, but this work appears to begin with the assumption that the ground states of these species have 2 ∆ symmetry, rather than deducing this in a definitive manner from the observed spectra.39 In TaSi, the three terms (4 Π/4 Φ, 2 Σ + , and 6 Σ + ) are also calculated to lie quite close in energy (within 0.26 eV), but our calculation along with two other DFT studies all predict 4 Π/4 Φ to lie lowest in energy.36,40 These ambiguous results regarding the ground electronic states of the MSi molecules may be contrasted with what is known for the isovalent MC molecules. The ground terms of TiC and ZrC are known to be 1σ2 2σ1 1π4 3σ1 , 3 Σ+ ,41–43 while VC and NbC have 1σ2 2σ2 1π4 1δ1 , 2 ∆ ground terms.44,45 In the case of HfC, the ground term remains experimentally unknown, while TaC has a 1σ2 2σ2 1π4 3σ1 , 2 Σ+ ground term.46 As has been stressed by Simard et al., the electronic structure of the transition metal carbides differs from that of fluorides, oxides, and nitrides because the 2p orbitals lie much higher in energy in carbon, leading to greater mixing with the nd and (n+1)s orbitals of the transition metal.45 This reduces the energy separation between primarily ligand-based and primarily metal-based orbitals, making the identity of the MC ground 084301-6 Sevy et al. state difficult to predict without detailed computations, particularly as compared to the other MX (X = F, O, N) molecules. This problem is exacerbated in the MSi molecules because the valence orbitals of Si lie even closer to the valence orbitals of the metal atom. A related complication results from the fact that the MSi bond is typically 1 to 2 eV weaker than the MC bond, leading to smaller separations between the bound states in the MSi species than in the MC species. Because the states are more closely spaced in the MSi molecules, identification of the ground state becomes more difficult. It is also worth pointing out that computational results obtained at the B3LYP/LANL2DZ level consistently underestimate the bond dissociation energy of the MSi molecules, with the exception of VSi. Further, because the spin-orbit stabilization of the ground levels of the separated atoms is typically larger than the stabilization in the molecule, this error would be exacerbated if spin-orbit corrections to the computed D0 (MSi) values were included. We have addressed this issue in our previous paper on the MSe molecules, M = Ti, Zr, Hf, V, Nb, Ta, where spin-orbit corrections to the computed D0 values were estimated to range from 0.13 to 0.56 eV.12 It is more difficult to estimate the magnitude of this correction for the MSi molecules, simply because we are less certain of the identity of the ground state. V. DISCUSSION A. Possible errors of interpretation It is assumed that the molecular excited states reached by photon absorption predissociate as soon as the ground separated atom limit is reached and that no barrier to predissociation exists apart from the centrifugal barrier. This assumption may be justified by considering the long-range interactions between the atoms. These are governed by the interaction between the ns orbital of the metal atom (doubly occupied in the ground states of Ti, Zr, Hf, V, and Ta; singly occupied in Nb)14 and the 3pσ orbital of Si (either singly occupied or empty in the 3s2 3p2 , 3 Pg ground state of Si, depending on the orientation of approach). Interactions between the metal ns and silicon 3pσ orbitals lead to a σ bonding and a σ* antibonding orbital at long range, and the number of electrons in each of these determines whether a long-range attraction or repulsion occurs. Configurations that are attractive at long range, and therefore lack a barrier to dissociation, are σ1 , σ2 , and σ2 σ* . In contrast, σ1 σ* and σ2 σ*2 configurations are expected to be repulsive at long distance and may have a barrier to dissociation, even if they become attractive at shorter distances. The ns2 metal atoms (Ti, Zr, Hf, V, and Ta) combine with Si to give σ2 and σ2 σ* configurations at long range, depending on the orientation of the approaching Si atom. Both are attractive. Thus, we anticipate no barriers to dissociation in the cases of TiSi, ZrSi, HfSi, VSi, and TaSi. For Nb, the interaction of the 5s1 configuration with the Si atom leads to σ1 , σ2 , or σ1 σ* configuration at long range, depending on the orientation of the approaching Si atom and the details of how the spins on the two atoms are coupled. The σ1 and σ2 curves are attractive at long range, so a pathway to predissociation that avoids a barrier is anticipated in the case of NbSi as well. Accordingly, for all of the investigated molecules, we believe the observed J. Chem. Phys. 147, 084301 (2017) predissociation threshold corresponds to the true bond dissociation energy. A second possible concern centers on the question of whether the initially excited spin-orbit substates, characterized by Ω, can predissociate to ground state atoms while preserving Ω. In previous work on V2 and Zr2 , we have found that a subset of the excited states reached by photon absorption fails to predissociate at the ground separated atom limit, dissociating only when the first excited separated atom level is reached.17,47,48 Is it possible that a similar difficulty could be introducing errors here? We think that this is very unlikely. First and foremost, none of the spectra displayed in Figs. 1–6 exhibit a clear double threshold, as was observed in the spectra of V2 and Zr2 . For all of the species considered here, the first excited separated atom limit places the Si atom in its 3p2 , 3 P1g level, 77.15 cm 1 above the ground separated atom limit.14 Thus, if dissociation to ground state atoms were problematic, a second threshold, 77 cm 1 higher in energy, would be expected. There is no evidence of a second threshold at this energy in any of the recorded spectra. The cases of the diatomic metals, V2 and Zr2 , are anomalous and are not expected to be replicated for the transition metal silicides. For both V2 and Zr2 , the ground Ω levels are Ω00 = 0g+ , which may be excited to Ω0 = 0u+ or 1u . The ground separated atom limit in each case generates molecular states with Ω = 0g+ , 0u− , 1g , and 1u , along with higher values of Ω. Notably, molecular states with Ω0 = 0u+ are unable to dissociate to ground state atoms while preserving the Ω quantum number. Any molecular states that are photoexcited with Ω0 = 0u+ in rotational levels with J0 = 0 are rigorously immune to predissociation at the ground state limit in these species. Even the Ω-destroying perturbations induced by the S- and L-uncoupling operators cannot connect these J = 0, Ω = 0u+ levels to electronic states that dissociate to ground state atoms.49 The existence of excited states that are rigorously immune to predissociation is not expected for the molecules investigated here. Accordingly, we are confident that the measured predissociation thresholds represent the true BDEs of these MSi molecules. B. Bond dissociation energies and related quantities The assigned bond dissociation energies of all six MSi molecules are provided in Table II. In addition, Eq. (1.4) has been used to calculate the 0 K enthalpies of formation, ∆f,0K H°(MSi(g)) using the standard enthalpies of formation for the gaseous atoms taken from the JANAF tables.50 The errors in the enthalpies of formation are dominated by the TABLE II. Summary of results of this work.a Molecule TiSi ZrSi HfSi VSi NbSi TaSi a Values D0 2.201(3) 2.950(3) 2.871(3) 2.234(3) 3.080(3) 2.999(3) D0 (M–Si ) D0 (M –Si) ≤3.149(15) ≤4.108(20) ≤3.526(33) ≤4.018(41) ∆f, 0K H° (MSi(g)) 705(19) 770(12) 787(10) 743(11) 879(11) 938(8) IE(MSi) 6.49(17) 6.61(15) are given in eV, except for ∆f, 0K H°(MSi(g)), which is provided in kJ mol 1 . 084301-7 Sevy et al. uncertainties in the enthalpies of formation of the gaseous atoms, which are in the range of 2.1–16.7 kJ/mol. Previously measured values of D0 (Ti+ –Si) = 2.54(17) eV and D0 (V+ –Si) = 2.37(15) eV,51 along with the atomic ionization energies IE(Ti) = 6.828 12(1) eV52 and IE(V) = 6.746 19(2) eV,15 have also been employed in Eq. (1.2) to deduce the ionization energies of the metal silicides, giving IE(TiSi) = 6.49(17) eV and IE(VSi) = 6.61(15) eV. Photoelectron spectra have been recorded for the mass selected anions ZrSi and NbSi ,28,38 and the resulting vertical detachment energies, 1.584(14) and 1.830(30) eV, respectively, may be combined with the electron affinity of atomic silicon, EA(Si) = 1.385(5) eV,53 using Eq. (1.3) to obtain upper limits on the bond dissociation energies of D0 (Zr–Si ) ≤ 3.149(15) eV and D0 (Nb–Si ) ≤ 3.525(31) eV. Similarly, the dissociation energies of the anions to form M + Si are readily derived from the atomic electron affinities EA(Zr) = 0.426(14) eV and EA(Nb) = 0.893(25) eV,53 giving D0 (Zr –Si) ≤ 4.108(20) eV and D0 (Nb –Si) ≤ 4.017(39) eV. These results only provide upper limits on the anionic bond dissociation energies, however, because the vertical detachment energies of the anions only provide upper limits on the adiabatic detachment energies. In any case, a lower energy process for the anions is the loss of an electron, rather than dissociation. C. Comparison to previous work and trends in bond dissociation energies Very little previous work exists for the molecules reported here. To our knowledge, no measurements of the BDEs of any of these MSi molecules have been previously reported. The ESR spectra of VC, VSi, NbC, and NbSi isolated in rare gas matrices have been investigated and have been explained by assuming that all four molecules have 2 ∆ ground terms, with the orbital angular momentum quenched by a particularly strong ligand field arising from the rare gas atoms.39 This suggestion is bolstered by rotationally resolved optical studies of VC and NbC, which unequivocally demonstrate that these carbide species have 2 ∆ ground terms.44,45 In the cases of VSi and NbSi, no experimental proof of 2 ∆ ground states is yet available and the computations reported here and elsewhere do not support this assignment. The only remaining experimental work on the transition metal silicides investigated here is photoelectron spectroscopic studies of mass-selected ZrSi and NbSi anions.28,38 These studies have led the authors to propose ground electronic states of 1σ2 2σ1 1π4 3σ1 , 3 Σ+ for ZrSi and 1σ2 2σ1 1π4 3σ1 1δ1 , 4 ∆ for NbSi. More work is required before these tentative assignments can be confirmed, however. The results obtained in this study show that the 3d metals, Ti and V, exhibit similar bond energies to silicon, as was found in our previous study of the group 4 and 5 MSe molecules, where TiSe and VSe also have similar bond energies.12 Also as was found in that study, the BDEs increase substantially in moving to the 4d and 5d metals, but the corresponding 4d and 5d metals have similar bond energies. For the MSi molecules, the BDE increases by 0.76 eV, on average, in moving from the 3d metal to either the 4d or 5d metal; for the MSe molecules, the same change in metal atom increases the BDE on average by 0.96 eV. This increase in BDE among the 4d and 5d J. Chem. Phys. 147, 084301 (2017) metals reflects the larger size of the d-orbitals of the metal, allowing better interaction with the nonmetallic element. A point of contrast between the MSe and MSi molecules is that the BDE decreases in moving from group 4 to group 5 in the MSe molecules, by 0.21 eV on average, while it increases in moving from group 4 to group 5 in the MSi molecules, by 0.10 eV on average. It seems reasonable that the high electronegativity of Se would favor bonding to the slightly more electropositive group 4 elements over the group 5 elements. Because the bonding in the MSi species is expected to be more covalent in character, this effect is diminished and even reversed. VI. CONCLUSION Predissociation thresholds were observed for TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi using resonant two-photon ionization spectroscopy. These thresholds were used to obtain bond dissociation energies and enthalpies of formation for the respective molecules. Using thermochemical cycles, ionization energies of TiSi and VSi were estimated, along with bond dissociation energies of ZrSi and NbSi . Along with previous work on VC, VN, VS,11 TiSe, ZrSe, HfSe, VSe, NbSe, TaSe,12 FeC, FeS, FeSe, NiC, NiS, and NiSe,13 these data show that the observation of a sharp predissociation threshold in a dense vibronic spectrum provides a powerful means of estimating the bond dissociation energy for transition metals bonded to p-block elements. The uncertainties obtained using this technique are greatly reduced compared to those obtained by other methods. 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