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 Δf,0KH°(TiSi(g)) = 705(19) kJ mol−1, Δf,0KH°(ZrSi(g)) = 770(12) kJ mol−1, Δf,0KH°(HfSi(g)) = 787(10) kJ mol−1, Δf,0KH°(VSi(g)) = 743(11) kJ mol−1, Δf,0KH°(NbSi(g)) = 879(11) kJ mol−1, and Δf,0KH°(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.

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 2Pu or 3Pg 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 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(AB)+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(MSi)=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

Δf,0KH(MX(g))=Δf,0KH(M(g))+Δf,0KH(X(g))D0(MX(g)),
(1.4)

where Δf,0KH(M(g)) is the heat of formation for the gaseous metal, Δf,0KH(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, Δf,0KH°(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.

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-of-flight 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.

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 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.

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, 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.

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.

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.

Close modal
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.

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.

Close modal
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 176Hf and 174Hf isotopes were used for calibration because the signal was too intense in the former to easily measure peak locations of the more intense features.

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 176Hf and 174Hf isotopes were used for calibration because the signal was too intense in the former to easily measure peak locations of the more intense features.

Close modal
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.

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.

Close modal
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.

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.

Close modal
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.

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.

Close modal

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 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 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 1σ22211, 5Δ ground terms, while HfSi is calculated to have a 1σ2231, 3Π 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 5Δ 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 5Δ, 1Σ+, and 3Σ+ 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.

TABLE I.

Calculated electronic states of the MSi molecules.

Molecule D0(exp)aConfigurationbTermEnergy (T0, eV)Dipole moment (D)ωec (cm−1)rec (Å)D0c (eV)〈S〉d
TiSi 22211 5Δ 0.00 3.77 350.0 2.475 2.09 2.001 
2.201(3) 21311 5Π/5Φ 0.53 3.84 369.4 2.329 1.56 2.039 
 2231 3Π 0.71 3.43 327.6 2.406 1.39 1.164 
 2141 3Δ 0.71 5.01 309.7 2.330 1.38 1.278 
 224 1Σ+ 0.74 3.72 460.1 2.245 1.36 0.000 
 2141 3Σ+ 0.84 3.48 354.3 2.231 1.25 1.228 
ZrSi 22211 5Δ 0.00 3.80 348.9 2.570 2.51 2.001 
2.950(3) 224 1Σ+ 0.13 3.96 448.7 2.361 2.38 0.000 
 2141 3Σ+ 0.13 3.85 479.9 2.291 2.38 1.003 
 2231 3Π/3Φ 0.32 4.29 361.1 2.490 2.20 1.065 
 21311 5Π/5Φ 0.35 3.59 398.1 2.433 2.16 2.004 
 2141 3Δ 0.54 5.34 427.7 2.337 1.97 1.027 
HfSi 2231 3Π 0.00 3.02 388.4 2.416 2.39 1.025 
2.871(3) 224 1Σ+ 0.12 3.35 433.8 2.330 2.27 0.000 
 22211 5Δ 0.20 2.91 309.4 2.582 2.19 2.006 
 2141 3Σ+ 0.74 4.70 472.9 2.269 1.65 1.003 
 21311 5Π/5Φ 1.11 3.99 390.4 2.407 1.28 2.002 
VSie 22311 4Π/4Φ 0.00 3.28 309.3 2.433 2.54 1.691 
2.234(3) 22221 6Σ+ 0.03 3.47 354.8 2.436 2.51 2.504 
 2241 2Δ 0.36 4.70 230.1 2.345 2.18 1.168 
 2241 2Σ+ 1.50 3.47 354.8 2.436 1.03 0.940 
NbSie 22221 6Σ+ 0.00 2.90 362.6 2.496 2.42 2.502 
3.080(3) 22311 4Π/4Φ 0.03 3.18 367.8 2.391 2.38 1.547 
 2241 2Δ 0.16 4.23 419.7 2.249 2.24 0.961 
 2241 2Σ+ 0.59 3.18 473.5 2.258 1.83 0.513 
TaSi 22311 4Π/4Φ 0.00 2.83 399.4 2.375 2.68 1.515 
2.999(3) 2241 2Σ+ 0.10 2.39 473.6 2.260 2.58 0.504 
 22221 6Σ+ 0.26 2.50 349.8 2.497 2.43 2.501 
Molecule D0(exp)aConfigurationbTermEnergy (T0, eV)Dipole moment (D)ωec (cm−1)rec (Å)D0c (eV)〈S〉d
TiSi 22211 5Δ 0.00 3.77 350.0 2.475 2.09 2.001 
2.201(3) 21311 5Π/5Φ 0.53 3.84 369.4 2.329 1.56 2.039 
 2231 3Π 0.71 3.43 327.6 2.406 1.39 1.164 
 2141 3Δ 0.71 5.01 309.7 2.330 1.38 1.278 
 224 1Σ+ 0.74 3.72 460.1 2.245 1.36 0.000 
 2141 3Σ+ 0.84 3.48 354.3 2.231 1.25 1.228 
ZrSi 22211 5Δ 0.00 3.80 348.9 2.570 2.51 2.001 
2.950(3) 224 1Σ+ 0.13 3.96 448.7 2.361 2.38 0.000 
 2141 3Σ+ 0.13 3.85 479.9 2.291 2.38 1.003 
 2231 3Π/3Φ 0.32 4.29 361.1 2.490 2.20 1.065 
 21311 5Π/5Φ 0.35 3.59 398.1 2.433 2.16 2.004 
 2141 3Δ 0.54 5.34 427.7 2.337 1.97 1.027 
HfSi 2231 3Π 0.00 3.02 388.4 2.416 2.39 1.025 
2.871(3) 224 1Σ+ 0.12 3.35 433.8 2.330 2.27 0.000 
 22211 5Δ 0.20 2.91 309.4 2.582 2.19 2.006 
 2141 3Σ+ 0.74 4.70 472.9 2.269 1.65 1.003 
 21311 5Π/5Φ 1.11 3.99 390.4 2.407 1.28 2.002 
VSie 22311 4Π/4Φ 0.00 3.28 309.3 2.433 2.54 1.691 
2.234(3) 22221 6Σ+ 0.03 3.47 354.8 2.436 2.51 2.504 
 2241 2Δ 0.36 4.70 230.1 2.345 2.18 1.168 
 2241 2Σ+ 1.50 3.47 354.8 2.436 1.03 0.940 
NbSie 22221 6Σ+ 0.00 2.90 362.6 2.496 2.42 2.502 
3.080(3) 22311 4Π/4Φ 0.03 3.18 367.8 2.391 2.38 1.547 
 2241 2Δ 0.16 4.23 419.7 2.249 2.24 0.961 
 2241 2Σ+ 0.59 3.18 473.5 2.258 1.83 0.513 
TaSi 22311 4Π/4Φ 0.00 2.83 399.4 2.375 2.68 1.515 
2.999(3) 2241 2Σ+ 0.10 2.39 473.6 2.260 2.58 0.504 
 22221 6Σ+ 0.26 2.50 349.8 2.497 2.43 2.501 
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 ωe, re, and D0 refer to the harmonic vibrational frequency, the equilibrium bond length, and the energy 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 〈S〉. 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 1σ2241, 2Δ ground states on the basis of matrix isolation ESR studies in Ref. 39.

For the group 5 silicides, the situation is no clearer. Our results on VSi and NbSi indicate that the 1σ22311, 4Π/4Φ term (Π or Φ cannot be determined from the calculation) and the 1σ22221, 6Σ+ term lie within 0.03 eV, with 4Π/4Φ emerging as the ground term in VSi but 6Σ+ 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 1σ2241, 2Δ term lies only slightly higher in energy in both VSi and NbSi. This 2Δ 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 2Δ symmetry, rather than deducing this in a definitive manner from the observed spectra.39 In TaSi, the three terms (4Π/4Φ, 2Σ+, and 6Σ+) are also calculated to lie quite close in energy (within 0.26 eV), but our calculation along with two other DFT studies all predict 4Π/4Φ 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 1σ2141, 3Σ+,41–43 while VC and NbC have 1σ2241, 2Δ ground terms.44,45 In the case of HfC, the ground term remains experimentally unknown, while TaC has a 1σ2241, 2Σ+ 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 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.

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, 3Pg 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 σ2σ*. In contrast, σ1σ* and σ2σ*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 σ2σ* 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 σ1σ* 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 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, 3P1g 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 Ω=0g+, which may be excited to Ω=0u+or1u. The ground separated atom limit in each case generates molecular states with Ω=0g+,0u,1g,and1u, along with higher values of Ω. Notably, molecular states with Ω=0u+ are unable to dissociate to ground state atoms while preserving the Ω quantum number. Any molecular states that are photoexcited with Ω=0u+ in rotational levels with J′ = 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.

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, Δf,0KH°(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 uncertainties in the enthalpies of formation of the gaseous atoms, which are in the range of 2.1–16.7 kJ/mol.

TABLE II.

Summary of results of this work.a

MoleculeD0D0(M–Si)D0(M–Si)Δf, 0KH° (MSi(g))IE(MSi)
TiSi 2.201(3)   705(19) 6.49(17) 
ZrSi 2.950(3) ≤3.149(15) ≤4.108(20) 770(12)  
HfSi 2.871(3)   787(10)  
VSi 2.234(3)   743(11) 6.61(15) 
NbSi 3.080(3) ≤3.526(33) ≤4.018(41) 879(11)  
TaSi 2.999(3)   938(8)  
MoleculeD0D0(M–Si)D0(M–Si)Δf, 0KH° (MSi(g))IE(MSi)
TiSi 2.201(3)   705(19) 6.49(17) 
ZrSi 2.950(3) ≤3.149(15) ≤4.108(20) 770(12)  
HfSi 2.871(3)   787(10)  
VSi 2.234(3)   743(11) 6.61(15) 
NbSi 3.080(3) ≤3.526(33) ≤4.018(41) 879(11)  
TaSi 2.999(3)   938(8)  
a

Values are given in eV, except for Δf, 0KH°(MSi(g)), which is provided in kJ mol−1.

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.

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 2Δ 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 2Δ ground terms.44,45 In the cases of VSi and NbSi, no experimental proof of 2Δ 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 1σ2141, 3Σ+ for ZrSi and 1σ21411, 4Δ 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 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.

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. Additional work is planned for a number of diatomic molecules containing transition metals, and results for the bond dissociation energies of TiC, TiN, TiS, and WSi are in hand and will be submitted for publication in the near future.

The authors thank the National Science Foundation for support of this research under Grant No. CHE-1362152.

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