Determination of the bond dissociation energies of FeX and NiX (X = C, S, Se)

As one of its core elements, a key component of chemistry is the controlled breaking of chemical bonds, followed by the formation of new chemical bonds, allowing new compounds with potentially useful properties to be synthesized. Among the most fundamental goals of chemistry, therefore, is understanding the nature of the chemical bond, both in terms of its electronic structure and of its bond strength, or bond dissociation energy (BDE). In past work, a major focus of this group has been to understand the chemical bonding between transition metal atoms, including measurements of their BDEs. In those studies, we have measured the BDEs of more than 20 transition metal dimers,^1,2 including V₂, TiV, TiCo, VNi, Zr₂, YCo, YNi, ZrCo, ZrNi, NbCo, and NbNi by observing an abrupt onset of predissociation in a congested electronic spectrum. More recently, we have turned to the measurement of BDEs between transition metal atoms and main group atoms. We have recently reported precise measurements of the BDEs of VC, VN, VS, TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe, again using the onset of predissociation in a congested vibronic spectrum as the indicator of the BDE.^3,4 In this article, we report precise BDEs for the iron- and nickel-containing molecules, FeC, FeS, FeSe, NiC, NiS, and NiSe. The goal of our work is to provide precise and accurate values of the BDEs of a number of MX diatomic molecules in the gas phase, so that the chemical bonding in these systems may be better understood.

Because transition metals are of tremendous importance in catalyzing chemical transformations, precise knowledge of the BDEs between the transition metals and the main group elements is highly desired. Unfortunately, our knowledge of these quantities is compromised by the experimental limitations that have hampered previous investigations. Many chemical systems have received no study whatsoever, and when experimental measurements have been made, the results are frequently associated with large error limits. As an example, one of the most commonly used techniques to measure BDEs is Knudsen effusion mass spectrometry.⁵ In this technique, a gas-phase equilibrium such as

or

is mass spectrometrically measured, and the resulting equilibrium constant, as a function of temperature, is analyzed using statistical thermodynamics to deduce the BDE (or the difference in BDEs, in the case of reaction (1.2)).⁵ Because of the difficulty in controlling the high temperatures needed for these gas-phase reactions, as well as the assumptions required to evaluate the molecular partition functions, Knudsen effusion methods typically report uncertainties in the range of 0.1–0.4 eV.^6–9 For the FeS and NiS molecules investigated in this study, previous Knudsen effusion measurements provided error estimates of about 0.15 eV.¹⁰ 

In the present study, we recognize that near the ground separated atom limit, transition metal diatomics generally have an exceptionally high density of electronic and vibrational states, and nonadiabatic and spin-orbit interactions among these Born-Oppenheimer states allow an electronically excited molecule to hop from one potential energy curve to another. In the case of Fe + C/S/Se, the ground separated atom limit of 3d⁶4s², ⁵D + ³P gives 180 states; for Ni + C/S/Se, the 3d ⁹4s¹, ³D + ³P and 3d⁸4s², ³F + ³P separated atom limits are nearly degenerate, and generate 135 and 189 states, respectively. In this situation, it is fundamentally wrong to think of the molecule as moving on a single potential curve. When the energy of the ground separated atom limit is exceeded, the molecule finds a way to fall apart, probably on a sub-nanosecond time scale. By locating the predissociation threshold, we have found that it is generally possible to determine the bond dissociation energy of the molecule to a precision better than 0.01 eV.^3,4

This phenomenon is illustrated schematically in Figure 1, which displays potential energy curves of some of the electronic states of diatomic FeC. This figure is qualitatively based on the ab initio calculations of Tzeli and Mavridis¹¹ but displays only a few of the Λ-S potential curves of the molecule. The ground separated atom limit generates 27 Λ-S potential curves (not all shown), while there are 9 separated atom terms below a separated atom energy of 20 000 cm⁻¹, generating 254 Λ-S states altogether. Only three of these 9 separated atom limits are displayed in the figure. Some of the potential curves arising from the ground and excited separated atom limits (not shown) are repulsive. The density of potential energy curves becomes even greater when spin-orbit splitting is considered. When the molecule is excited below the ground separated atom limit (hν₁), the initially excited state can decay only by fluorescence and typically displays a lifetime in the few hundred nanosecond to microsecond range. This allows the excited molecule sufficient time to absorb a second photon (hν₂), ionizing the molecule and permitting detection by mass spectrometry. A spectrum may be recorded, although the high density of electronic states makes it nearly impossible to interpret the nearly continuous spectrum in the energy range just below the dissociation limit. When excited above the ground dissociation limit, however, spin-orbit and nonadiabatic couplings provide a means for the excited molecule to hop to a dissociative state and rapidly fall apart. In our experience, this process typically occurs on a subnanosecond time scale, too quickly to allow the initially excited molecule to be ionized. The result is an abrupt cessation of signal at the mass of the ion. The abrupt cessation of the spectrum provides an accurate measure of the separation between the ground vibronic level of the molecule and the ground separated atom limit, which is the bond dissociation energy.

Transition metal carbides, sulfides, and selenides have proven to be important or potentially important in a variety of fields. Their applications have been found in disciplines including catalysis, medicine, electrochemistry, and superconductors. The use of iron carbide materials, in particular, seems to have really blossomed in these areas. For example, iron carbide has been used for drug delivery through nanoparticle therapy, which can be used to target cancer cells.¹² It has also seen applications in catalytic processes, such as Fischer-Tropsch chemistry,¹³ as well as showing promise as a contrast agent in magnetic resonance imaging (MRI).¹⁴ Transition metal sulfides have also found a number of innovative uses, including acting as a catalyst for the carbonylation of ethylene,¹⁵ as a binder-free cathode in lithium-ion batteries,¹⁶ and even in cancer treatment as inhibitors of angiogenesis.¹⁷ As for the transition metal selenides, iron selenide has superconductive properties¹⁸ while nickel selenide nanoparticles have been shown to be effective in reducing nitroaromatic compounds to aromatic amines.¹⁹ 

Another area where precise bond dissociation energies are needed is in the testing of computational approximations, particularly for density functional theory (DFT). Chemical computations on transition metal-containing systems are notoriously difficult, particularly for larger systems where variationally based methods are out of the question. For such systems, DFT methods are the only practical alternative. Accordingly, computational chemists are testing various DFT methods against measured bond dissociation energies, to determine which functionals perform best.^20–26 Unfortunately, the large errors in experimental BDEs make such comparisons difficult at best. It is our hope that the precise BDEs reported in our previous work^3,4 and in this article will provide the benchmarks computational chemists need to test their methods.

In this study, diatomic FeC, NiC, FeS, NiS, FeSe, and NiSe were investigated to measure their bond dissociation energies by the observation of a sharp predissociation threshold in a congested electronic spectrum. For these investigations, the resonant two-photon ionization (R2PI) spectroscopic method was employed. While the R2PI method has been described in detailed previously,²⁷ some details pertinent to the present study are provided here.

For each of the molecules studied, the gaseous metal molecules were generated by laser ablation of a metal target disk. The metal target differed between the studies, but a nickel-containing alloy was used for the NiX studies while a pure iron sample was used for the FeX studies. Various alloys were used in the NiX studies in order to calibrate the optical spectra, as discussed in greater detail below. In all cases, the disk, which was rotated and translated continuously to allow for the uniform removal of material, was vaporized using the focused fundamental output of a pulsed Nd:YAG laser (1064 nm; approximately 10 mJ/pulse). The ablation took place during a pulse of carrier gas that flowed over the surface of the sample, picking up the ablated material. The carrier gas in all studies was ultra-high purity (UHP) helium seeded with a small percentage of reactive gas: 0.2% CH₄ for FeC and NiC, 0.7% H₂S for FeS and NiS, 0.25% H₂Se for NiSe, and 0.6% H₂Se for FeSe. Hydrogen selenide gas was synthesized from ZnSe as previously described.⁴ In all cases, the backing pressure of the carrier gas was in the range of 20–70 psi.

After entrainment in the carrier gas, the products of ablation flow down a reaction channel approximately 1.9 cm in length, during which time they react to form the molecule of interest and undergo collisional cooling with helium, probably reaching temperatures near room temperature. The resulting species then expand into the vacuum chamber through a 2 mm orifice, undergoing rapid cooling via supersonic expansion.²⁸ The operating pressure in this vacuum chamber varies depending on the backing pressure used for the carrier gas but is typically in the range of 8 × 10⁻⁶ to 4 × 10⁻⁵ Torr (calibrated for air, uncorrected for helium) as measured with an ionization gauge. The on-axis portion of the expansion is roughly collimated through a 1.3 cm diameter skimmer, after which it enters the Wiley-McLaren ion source of a linear time-of-flight mass spectrometer (TOFMS), located in a second chamber.²⁹ 

Within the ion source, the molecular beam is sequentially exposed to the radiation from two lasers. The first is a tunable OPO laser system that counterpropagates along the molecular beam axis. Approximately 50 ns after this laser is fired, the fifth harmonic output of a Nd:YAG laser (212.8 nm, 5.83 eV) intersects the molecular beam at right angles. Any ions that are created by these two laser pulses are then accelerated toward the chevron-oriented dual microchannel plate detector, after which the signal is amplified, digitized, and stored for analysis on the computer.

This ion signal is recorded as a function of the wavelength of the tunable laser. For each molecule investigated, the OPO was scanned red-to-blue, starting at an energy believed to be below the bond dissociation energy (BDE) of the molecule. The laser was then scanned until there was a complete depletion of ion signal for the molecule. Once the predissociation threshold was located, multiple spectra of that region were collected and summed, to improve the signal-to-noise ratio of the spectrum.

Since mass resolution is achieved in the TOFMS detection scheme, multiple masses can be concurrently monitored, allowing for simultaneous recording of their optical spectra. This proves to be very useful for calibration of the spectrum of the species of interest. In each case, the well-known wavenumbers of atomic transitions near the dissociation threshold were used to calibrate the spectrum.³⁰ 

For each of the FeX molecules studied, a pure iron sample was used as the ablation target. There were a large number of atomic iron transitions neighboring the dissociation threshold for each of the FeX molecules, so calibration was straightforward.

In the case of the NiX molecules, calibration was more difficult. When we began these studies, an alloy of 1:2 Fe:Ni was used in the hope that the BDEs of the NiX and FeX molecules could be simultaneously measured, without the need to change samples. While this alloy worked for measuring the BDE of NiS, it was not successful for NiC. Precisely in the vicinity of the dissociation threshold for NiC, there were a large number of extremely intense transitions in atomic iron, which lead to a decrease in the overall mass spectrum intensity due to what we believe was a Coulomb space-charge effect. Although the Fe atomic signals were huge, all other species in the mass spectrum showed a strong depletion at these wavelengths. This decrease in the signal precisely at the predissociation threshold made it difficult to determine its exact location. Changing to a pure nickel sample produced a similar but slightly less severe effect, due to strong transitions in atomic nickel. It was not until we changed to an alloy of Ni:Pd, which reduced the amount of atomic nickel in the mass spectrum, that a clean NiC spectrum could be observed. A small amount of iron was still present in the molecular beam, likely coming from the vaporization block; this produced a nice atomic spectrum that was suitable for calibration.

While studying NiSe, a different issue arose. Here, only a few widely spaced atomic transitions were observed in the vicinity of the predissociation threshold. In order to calibrate the spectrum, the ablation target was changed to a Ni:V alloy; the abundant atomic transitions of vanadium were then used for calibration.

Figures 2–7 display the portion of the optical spectrum where the predissociation threshold is found for FeC, NiC, FeS, NiS, FeSe, and NiSe, respectively. In all cases, the arrow identifies the assigned predissociation threshold, which corresponds to the BDE; a horizontal bar on the tail of the arrow corresponds to the proposed error limit for D₀. The assignment of error limits has been discussed in detail in our previous article on the BDEs of TiSe, ZrSe, HfSe, VSe, NbSe, and TaSe.⁴ Figures 2–7 also display the atomic spectra that were used for calibration. Table I summarizes the measured BDE values for all six molecules. In both the figures and in Table I, the proposed error limit is reported in parentheses, in units of the last digits quoted.

The spectrum of FeC, displayed in Figure 2, shows discrete features with increasing intensity toward the blue until the spectrum drops to baseline near 31 890 cm⁻¹. Because the spectrum is relatively sparse, we have assigned a rather large uncertainty to our proposed value of the bond dissociation energy, D₀(FeC) = 3.961(19) eV. The magnitude of our assigned error was chosen to account for the relatively large spacing between adjacent vibronic levels.

Table II provides a comparison of our measured value of D₀(FeC) to the results of previous experiments and computations. The BDE of FeC has previously been estimated from the experimental data by two other methods. In the first, the thermochemical cycle

was used, in combination with the experimental values of D₀(Fe⁺–C), IE(Fe), and IE(FeC), to solve for D₀(FeC). In this cycle, the bond energy of Fe⁺–C was measured in an ion photodissociation experiment³¹ and the ionization energy of FeC was estimated in a resonant two-photon ionization experiment from our group,²⁷ resulting in D₀(FeC) = 3.9(3) eV.²⁷ Subsequently, a far more accurate measurement of IE(FeC) was made using the pulsed field ionization-zero electron kinetic energy (PFI-ZEKE) technique,³² leading to a revised value of D₀(FeC) = 3.8(3) eV. In a 1997 experiment, the appearance potential for production of FeC⁺ from Fe(CO)₅ was measured and combined with other data to obtain a somewhat lower value of D₀(Fe⁺–C),³³ leading to an estimate of D₀(FeC) = 3.34(18) eV. In the thermochemical cycle, the ionization energies IE(Fe) and IE(FeC) are now extremely well-known, so the weak link is the BDE of the FeC⁺ cation. In the ion photodissociation work,³¹ the study was limited by the low intensity of the excitation light and its poor spectral resolution. In the subsequent study on the appearance potential of FeC⁺ from Fe(CO)₅,³³ the indirect nature of the photochemical process, along with the gradual rise of the FeC⁺ signal from background, introduces significant error. For these reasons, we believe that our direct measurement of the predissociation threshold provides a more accurate result.

In a spectroscopic study conducted in high resolution, the vibrational levels of the ground X ³Δ state were fitted to a modified Morse potential, providing D₀(FeC) = 2.858 eV.³⁴ This result is obtained from the fitted vibrational constants ω_e = 867.32(15) cm⁻¹ and ω_ex_e = 7.9799(21) cm⁻¹. Using these two vibrational constants, the functional form

leads to a value of D₀ given as

This procedure is accurate if the higher anharmonic corrections are negligible, even at high vibrational levels. If higher-order anharmonicities are significant or if the fitted vibrational levels are systematically perturbed, however, the results can be seriously in error. The value obtained in the case of FeC is more than 1 eV smaller than our measurement, and is substantially less than the other experimental values. It seems that either the observed vibrational levels are perturbed or a larger number of vibrational levels are required to obtain a good extrapolation to D₀ for this example.

Also displayed in Table II are all of the computational results for D₀(FeC) that we could find in the literature. It is obvious that the calculation of the BDE of this molecule is a tremendous challenge for theory. As noted by Tzeli and Mavridis, FeC “is a genuine multireference system,” making it nearly impossible to tackle using a single reference method.¹¹ Even the most extensive calculation, the CCSDTQ(full)/CBS study by Lau et al., provides a value of D₀(FeC) that is about 0.2 eV below our result.³⁵ The molecule also provides a tremendous challenge for density functional methods, with different functionals giving values ranging from 0.86 eV to 6.75 eV.

Equation (4.1) may be used to combine our value of D₀(FeC) with the precisely known ionization energies, IE(Fe) = 7.902 467 8(12) eV³⁰ and IE(FeC)=7.59318(6) eV,³² to obtain an improved value of the FeC⁺ bond dissociation energy. The result is D₀(Fe⁺–C) = 4.270(19) eV.

The predissociation threshold in the spectrum of NiC (Figure 3) is more clearly defined than in FeC, allowing more restrictive error limits to be assigned: D₀(NiC) = 4.167(3) eV. Very limited experimental data exist for comparison to this value. The available experimental and computational points of comparison are presented in Table III. In our previous resonant two-photon ionization study of NiC, transitions were observed as far to the blue as 3.34 eV, placing D₀(NiC) ≥ 3.34 eV.³⁶ Although not very restrictive, this is in agreement with the present result. Subsequent to our initial study, Rao, Reddy, and Potukuchi examined our experimental data and fitted the results to a modified Lippincott potential, obtaining D₀(NiC) = 3.454 eV,³⁷ a value that is not very close to the present result. In our original article on the spectroscopy of NiC,³⁶ the vibrational intervals ΔG_1/2 and ΔG_3/2 were measured, and from these intervals the vibrational constants ω_e = 875.155 cm⁻¹ and ω_ex_e = 5.382 cm⁻¹ were deduced using Equation (4.2). Because only two vibrational intervals were used to deduce two parameters, no error limits could be assigned. Using these values in Equation (4.3) gives D₀(NiC) = 4.357 eV, about 0.2 eV higher than the present result. In a subsequent dispersed fluorescence study, ground state vibrational levels up to v = 10 were found, providing values of ω_e = 874.6(1.7) cm⁻¹ and ω_ex_e = 5.9(2) cm⁻¹.³⁸ Using these values in Equation (4.3) provides D₀(NiC) = 3.96(14) eV, about 0.2 eV less than the present result. For the example of NiC, it appears that extrapolation to the dissociation limit while ignoring the higher anharmonic terms leads to a reasonable result, in contrast to the behavior shown by FeC. It is possible that problems show up in the extrapolation for FeC due to spin-orbit perturbations between the ³Δ ground term and the low-lying isoconfigurational ¹Δ term. In NiC, the ¹Σ⁺ ground term is widely separated from other terms³⁹ and has no isoconfigurational spin-orbit interactions. As a result, it is not expected to be significantly perturbed.

Computational work on NiC has been nearly as extensive as work on FeC. Beginning in 1982,⁴⁰ a series of computational studies of ever-increasing accuracy have been performed. Of those based on wavefunction methods, the landmark studies of Tzeli and Mavridis³⁹ and Lau et al.⁴¹ are particularly noteworthy. The results obtained, D₀(NiC) = 3.95 and 4.048 eV, respectively, lie only 0.22 and 0.12 eV below our result, respectively. As was the case for FeC, the BDEs calculated using density functional methods depend very strongly on the particular functional that was used and vary over an extremely broad range. This illustrates the need for further development of density functionals so that transition metal systems may be accurately calculated.

As in the case of FeC, the ionization energy of NiC is extremely well-known based on a PFI-ZEKE spectroscopic study that provided IE(NiC) = 8.37205(6) eV.⁴² Combining our measurement of D₀(NiC) with this value and the ionization energy of atomic nickel, IE(Ni) = 7.639 877(17) eV,³⁰ Equation (4.1), modified for nickel, allows the BDE of NiC⁺ to be obtained: D₀(Ni⁺–C) = 3.435(3) eV.

Figures 4–7 display the predissociation thresholds of FeS, NiS, FeSe, and NiSe, respectively. The spectrum of FeS shows an abrupt and definitive drop to baseline, allowing D₀(FeS) to be assigned as 3.240(3) eV. For NiS, the drop to baseline is also abrupt, but occurs in a less intense portion of the overall spectrum, allowing D₀(NiS) to be assigned as 3.651(3) eV. The FeSe and NiSe molecules display more structured spectra, and the significant spacing between adjacent peaks in the spectrum of FeSe forces us to increase our assigned error limit, providing D₀(FeSe) = 2.739(6) eV. For NiSe, the vibronic features remain fairly closely spaced, providing D₀(NiSe) = 3.218(3) eV.

The results of previous measurements and calculations on FeS, NiS, FeSe, and NiSe are presented in Table IV. Both FeS and NiS have been investigated by Knudsen effusion mass spectrometry, where the equilibrium constant of the displacement reaction

was evaluated by the third-law method to obtain the BDEs of FeS and NiS, relative to the BDE of MnS. As the BDE of MnS had been previously measured, values of D₀(FeS) = 3.31(17) eV and D₀(NiS) = 3.53(15) eV were obtained. The BDE of FeS has also been estimated as D₀(FeS) ≤ 3.34 eV in a previous mass spectrometric study.⁴³ All of the Knudsen effusion results are in good agreement with our result, which is considerably more precise.

We have also considered the most accurate spectroscopic data for FeS and NiS to determine whether the Morse potential extrapolation given in Equation (4.3) provides reliable results. As was found for FeC, this procedure gives significant errors for FeS and NiS compared to all other methods for these molecules. This may again be related to the fact that FeS and NiS are open-shell molecules that are subjected to spin-orbit perturbations from nearby states.

Diatomic FeS, in particular, has been the subject of a number of computational studies. This is largely a result of the importance of iron-sulfur clusters in biological chemistry. For FeS, recent calculations have been in reasonably good agreement with our BDE, particularly those performed with the B3LYP method,^44,45 or the CASPT2 method.⁴⁶ An exception is the diffusion Monte Carlo/pseudopotential method, which predicts a BDE that is too low by about 0.5 eV.⁴⁷ Fewer computational studies have been performed on NiS, providing BDEs ranging from 3.12 to 3.68 eV.^45,48–50

To our knowledge, the present investigation is the first to provide bond dissociation energies of FeSe and NiSe. As might be expected through comparison to other MS/MSe species,⁷ the M–Se bond is weaker than the M–S bond. Our value of D₀(FeSe) = 2.739(6) eV is in reasonably good agreement with the DFT B3LYP computation of this quantity, 2.83 eV.⁴⁵ The same method, however, gives a value for D₀(NiSe) that is 0.35 eV less than our result.⁴⁵ 

Accurate bond dissociation energies are known for FeS⁺ and NiS⁺, D₀(Fe⁺–S) = 3.08(4) eV and D₀(Ni⁺–S) = 2.47(4) eV, respectively.^51,52 Combining these results with our values of D₀(FeS) and D₀(NiS), and the well-known ionization energies IE(Fe) = 7.902 467 8(12) eV and IE(Ni) = 7.639 877(17) eV,³⁰ the analogues of Equation (4.1) may be solved for the ionization energies of the metal sulfides. The results are IE(FeS) = 8.06(4) eV and IE(NiS) = 8.82(4) eV. This value of IE(FeS) compares to a previously obtained experimental value of IE(FeS) = 8.3 eV, with an error listed as either 0.2, 0.3, or 0.6 eV in three different places in the article.⁵³ Our result is in agreement but provides a reduction in the error limit by a factor of 5 or more.

The electron affinity of FeS has been determined in two different experiments, resulting in values of 1.76(10) and 1.725(10) eV.^54,55 The anionic analogue of the thermochemical cycle given in Equation (4.1)

then allows the value of D₀(Fe–S⁻) to be derived using our value of D₀(FeS) and the well-known electron affinity of sulfur, EA(S) = 2.077 120(1) eV.⁵⁶ The result is D₀(Fe–S⁻) = 2.92(10) eV or 2.89(10) eV. These values are much greater than the electron affinity of FeS, indicating that FeS⁻ will photodetach at lower energies than it will photodissociate.

Having measured the bond dissociation energies of these molecules, the enthalpies of formation are calculated according to the following equation at 0 K in the gas phase:

The calculated enthalpies of formation for the FeX and NiX molecules are reported in Table V. The 0 K enthalpies of formation for Fe(g), Ni(g), C(g), and S(g) were taken from Ref. 57; that of Se(g) was taken from Ref. 58. These values are listed in boldface around the perimeter of the table, while the $ΔHf,0K°(MX)$ values are presented in the appropriate row and column. The large errors in the calculated $ΔHf,0K°(MX)$ values, particularly for the nickel-containing molecules, are primarily due to the large errors in the $ΔHf,0K°(MX)$ values. Our calculated values for $ΔHf,0K°(FeS)$ and $ΔHf,0K°(NiS)$ agree very well with the previous values of 370(16) and 357(17) kJ/mol, respectively.⁵⁹ For both molecules, our values fall well within the quoted error limits; further, our results reduce the uncertainties in these quantities by factors of roughly 10 and 2, respectively.

To place these bond dissociation energies in perspective, it is useful to consider the molecular orbitals that are formed from the valence 3d and 4s orbitals of Fe and Ni in combination with the valence ns and np orbitals of C, S, and Se. A schematic molecular orbital diagram for these molecules is presented in Figure 8. Numbering the molecular orbitals so that only those deriving from the atomic valence orbitals are considered, at the lowest energy lies the 1σ orbital, which is primarily C 2s, S 3s, or Se 4s in character. Although the 1σ orbital may have some bonding character, it is best considered to be core-like. Next are the 2σ and 1π orbitals which are bonding combinations of the metal 3dσ and 3dπ orbitals with the nonmetal npσ and npπ orbitals, respectively. Above these lie the 1δ and 3σ orbitals, which are mainly nonbonding in character and are composed primarily of the metal 3dδ and 4sσ atomic orbitals. Finally at the highest energy are the 2π and 4σ orbitals which are antibonding combinations of the metal 3dπ and 3dσ orbitals with the nonmetal npπ and npσ orbitals, respectively. Although the relative energies of these orbitals vary among the six molecules considered here to some degree, the overall trends are well-understood through this generic diagram.

In all of the molecules considered here, the 1σ, 2σ, and 1π orbitals are filled. The FeC molecule has 12 valence electrons, while FeS, FeSe, and NiC have 14 valence electrons. Finally, NiS and NiSe have 16 valence electrons. Rotationally resolved spectroscopy,^60,61 as well as quantum chemical computations,^11,35 has determined that the ground configuration and term of FeC is 1σ² 2σ² 1π⁴ 1δ³ 3σ¹, ³Δ₃, a triply bonded molecule.¹¹ In moving to NiC, the two additional electrons fill the 3δ and 4σ orbitals, giving a 1σ² 2σ² 1π⁴ 1δ⁴ 3σ², ¹Σ⁺ state, again demonstrated by rotationally resolved spectroscopy and quantum chemistry.^36,39,41,62 As is the case for FeC, NiC has a triple bond that arises from the presence of 6 electrons in the 2σ and 1π bonding orbitals.³⁹ The existence of a triple bond in both molecules accounts for the strong bonds in these species.

Although FeO, FeS, and FeSe have the same number of valence electrons as NiC, the ground states of FeO and FeS, which have been experimentally determined, are quite different from that of NiC. Both FeO^63,64 and FeS^65–67 place the two additional electrons in the 2π antibonding orbital, rather than filling the 1δ and 3σ nonbonding orbitals, leading to a ground term of 1σ² 2σ² 1π⁴ 1δ³ 3σ¹ 2π², ⁵Δ₄. Although ⁵Δ is apparently the ground state of FeS, the 1σ² 2σ² 1π⁴ 1δ² 3σ² 2π², ⁵Σ⁺ state lies very low in energy and has been obtained as the ground state in some computations.^45,46,68 In the one computational study available, FeSe is also calculated to have a ground state of ⁵Σ⁺.⁴⁵ Whether the ground state arises from a 1δ³ 3σ¹ or a 1δ² 3σ² occupation of the nonbonding orbitals is of little importance as far as the bond dissociation energy is concerned. These differences amount to rearrangements of electrons within the nonbonding orbitals and are not expected to significantly change the BDE.

The weakened chemical bonds in FeS and FeSe, compared to FeC, may result from the placement of the additional electrons in the 2π antibonding orbital, which reduces the bond order from 3 to 2. However, this invites the question: Why does the molecule place these electrons in the antibonding 2π orbital, rather than in the nonbonding orbitals? The triple-bonded ¹Σ⁺ ground state that is found in the 14 valence electron NiC molecule correlates to the ground states of the atoms: Ni, ³D and C, ³P. It is not possible, however, to form the corresponding ¹Σ⁺ state in the isovalent FeS and FeSe molecules from the ground separated atom limit of Fe, ⁵D + S/Se, ³P, which generates only triplets, quintets, and septets (S = 1, 2, or 3). The lowest energy separated atom limit that can form the triply bonded ¹Σ⁺ state in either FeS or FeSe is the Fe, ³F + S/Se, ³P limit, near 12 000 cm⁻¹.³⁰ This triply bonded ¹Σ⁺ state originates from too high an energy to emerge as the ground state.

Finally, the 16 electron species NiO^69,70 and NiS^71–73 are also spectroscopically known, with ground states of 1σ² 2σ² 1π⁴ 1δ⁴ 4σ² 2π², ³Σ⁻. Diatomic NiSe is also calculated to have the same ground state.⁴⁵ As these states differ from those of FeS and FeSe only by the addition of two electrons to the nonbonding orbitals, they are also doubly bonded molecules that are expected to have smaller BDEs than the corresponding carbide, NiC.

It is not unexpected that the MSe molecules have weaker bonds than the MS molecules, owing to the reduced capacity of heavier elements in a group to form strong bonds. Going down a column in the p or s blocks invariably results in weaker bonds as the orbitals become larger, giving reduced orbital overlap. A more surprising result is that the chemical bonding of Ni to C, S, and Se is uniformly stronger than the bonding of Fe to these atoms. At present, we do not have a good explanation of this phenomenon.

By the observation of a sharp predissociation threshold in a congested electronic spectrum, the bond dissociation energies of FeC, NiC, FeS, NiS, FeSe, and NiSe have been measured. The results generally lie within the expected range, compared to the results available from previous experiments, but the proposed error limits are greatly reduced. From these data and other high-quality data in the literature, improved values of D₀(Fe⁺–C), D₀(Ni⁺–C), IE(FeS), IE(NiS), and D₀(Fe–S⁻) have been derived. Finally, by combining the measured bond dissociation energies with the enthalpies of formation of the gaseous elements, enthalpies of formation of the gaseous FeC, NiC, FeS, NiS, FeSe, and NiSe molecules at 0 K have also been derived.

In previous work, we have shown that the high density of vibronic states near the ground separated atom limit has permitted successful measurements of the BDEs of VC,³ VN,³ VS,³ TiSe,⁴ ZrSe,⁴ HfSe,⁴ VSe,⁴ NbSe,⁴ and TaSe.⁴ A related investigation of the BDEs of the transition metal silicides TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi is forthcoming.⁷⁴ In the present study, we have demonstrated that the technique of measuring BDEs by observing the onset of predissociation in a highly congested spectrum is not limited to the transition metals belonging to groups 3 and 4 but is also successful when applied to iron- and nickel-containing molecules. High densities of vibronic states are expected at the ground separated atom limit for molecules formed from a transition metal having a ground term with L = 2 or 3 (D or F terms) in combination with a main group element having L = 1 (P term), so we anticipate that this method may be extended to a large fraction of the transition metal MX molecules.

The authors thank the National Science Foundation for support of this research under Grant No. CHE-1362152. We also thank Jason Sorensen and Andrew Sevy for their assistance in the synthesis of gaseous H₂Se.