J . Phys. Chem. 1992, 96, 2479-2486 2479

2S state, augmented with a diffuse s function optimized24 for the IS state of the negative ion, and three diffuse p functions optim- i ~ e d ~ ~ for the 2P state of the neutral. The basis set is augmented with five even-tempered d functions with ao(d) = 0.0455 and with two uncontracted f functions (a(f) = 0.135 and 0.054). The basis set was contracted to [2s l p Id] using the A N 0 procedure based on a singles and doubles configuration-interaction calculation for the IS states of the negative ion. The outermost five s, five p, and three d functions were uncontracted. Explicitly, the basis set is of the form (20s 14p 5d 2f)/[7s 6p 4d 2fl.

The Mg primitive set is the (20s 12p) set augmented with three p functions optimized24 for the 3P state and supplemented with a seven-term 3d even-tempered set with ao(d) = 0.0592. The ANOs were determined as the average natural orbitals of the IS and 3P states of Mg where two electrons were correlated. The most diffuse s and p primitives are uncontracted to accurately describe the polarizability, giving a final contracted Mg Gaussian basis set of the form [6s 5p 2d]. This is the same basis set as used in our recent study5J4 of Mg+-ligand binding energies.

The hydrogen set is derived from an A N 0 set of the form (8s 6p 4d)/[4s 2p ld].I2 We uncontract the two s, two p, and one d primitive functions with the smallest exponents to improve the polarizability of H,; this results in a [6s 4p 2d] set. At 1.4 ao, our computed results for aI and 0 are 4.556 ao3 and 0.455 ao2, respectively. These values are in excellent agreement with those of Kolos and W o l n i e ~ i c z ~ ’ ~ ~ ~ (4.578 ao3 and 0.457 ao2). The

computed values are in good agreement with experiment’ (4.85 a: and 0.468 ao2). As shown by Kolos and Wolniewicz25 the difference between their a value at 1.4 a. and experiment is due to vibrational effects.

The nitrogen basis set is derived from the (13s 8p) primitive set of van D~ijneveldt.~’ The primitive polarization set used is a (6d 4f) even-tempered set; the a. values are aO(d) = 0.10 and ao(f) = 0.35. The (13s 8p 6d 4f) basis is contracted to [4s 3p 2d lfl based upon the natural orbitals from the 4S state. The outermost two s, two p, and one d primitives were uncontracted and an even-tempered diffuse s, p, and d function was added. The final basis set is of the form (14s 9p 6d 4f)/[7s 6p 4d If]. The quadrupole moment a t the MCPF level is 1.173 ao2 at 2.068 ao. Correcting this for vibrational effectsz8 yields a value of 1.16 ao2, which is a t the upper end of the experimental rangez1 (1.09 f 0.07 ao2). Note, however, that significantly increasing the size of the basis set reduces the quadrupole moment by less than 2% at the MCPF level. The parallel component of the polarizability a t the experimental re value is computed to be 14.76 a: a t the MCPF level compared with the experimental value9 of 14.78 ao3.

(25) Kolos, W.; Wolniewicz, L. J . Chem. Phys. 1965, 43, 2429. (26) Kolos, W.; Wolniewicz, L. J . Chem. Phys. 1967, 46, 1426. (27) van Duijneveldt, F. B. IBM Res. Rep. 1971, RJ945. (28) Cernusak, I.; Diercksen, G. H. F.; Sadlej, A. J. Chem. Phys. 1986,

108, 45.

Bond Strengths of Transition-Metal Dimers: TIV, V,, TiCo, and VNi

Eileen M. Spain and Michael D. Morse* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received: October 9, 1991)

The abrupt onset of predissociation in a severely congested electronic spectrum has been used to measure the bond strengths of jet-cooled TiV, V2, TiCo, and VNi by resonant two-photon ionization spectroscopy. The measured values are L#(TiV) = 2.068 * 0.001 eV, @(V2) = 2.753 f 0.001 eV, f$(TiCo) = 2.401 * 0.001 eV, and L#(VNi) = 2.100 f 0.001 eV. It is proposed that two criteria must be satisfied in order that bond strengths may be determined by this method: (1) the molecule must possess a sufficient density of electronic states near the lowest dissociation threshold, so that nonadiabatic couplings can readily induce predissociation, and (2) the lowest separated atom limit must generate repulsive potential energy curves, so that the potential curves are not nested and, as a result, poorly coupled. Finally, the bond strengths of TiV, V,, TiCo, VNi, Nil, NiPt, and Pt2 are compared to the corresponding filled d-subshell analogues, and the magnitude of d-orbital contributions to the chemical bonding in these molecules is evaluated.

I. Introduction The chemical bonding between transition-metal atoms is a

difficult and fascinating field of study, primarily because of the great complexity of the electronic structure of these species. In many examples it seems that the identity and nature of the ground state results from a delicate balance of large opposing effects. For example, the presence of open d subshells in these molecules leads to the possibility of multiple d-d bonds, while simultaneously providing a large exchange stabilization for high-spin states. Because of the very small size of the 3d orbitals, exchange effects favoring high-spin states are particularly important in the 3d transition-metal series. The interplay between the opposing effects of d-bonding (which favors spin pairing) and exchange (which favors high spin states) can be quite subtle. This contributes substantially to the inherent difficulties of theoretical treatments of the transition-metal molecules, particularly in the 3d series.

A similar difficulty is associated with the fact that the strongest chemical bonds often arise from the interaction of electronically excited atoms. An example is provided by transition-metal dimers composed of atoms with ground electronic configurations of dns2. In such systems a stronger chemical bond is certainly developed when excited atoms in their dn+lsl configuration are brought

OO22-3654/92/2096-2479$03 .OO/O

together. It is often unclear, however, whether the chemical energy released in forming such a bond is sufficient to overcome the energy required to prepare the atoms for bonding. Once again the ground state of the molecule is the result of a delicate balance between two opposing effects: the energetic costs associated with promoting the atoms, and the bond energy which is gained fol- lowing this preparation. It is a great challenge for both the experimentalist and the theoretician to understand the interplay between these effects and to establish the periodic trends which underlie the bonding in the homonuclear and heterocuclear transition metal diatomics.

Experimental contributions toward understanding the chemical bonding and electronic structure of transition-metal diatomics have involved many different techniques. Spectroscopic methods have included photoelectron spectroscopy of mass-selected metal cluster

resonant two-photon ionization spectroscopy (R2PI)

(1) Pettiette, C. L.; Yang, S. H.; Craycraft, M. J.; Conceicao, J.; Laak- sonen, R. T.; Cheshnovsky, 0.; Smalley, R. E. J . Chem. Phys. 1988,88,5377.

(2) Leopold, D. G.; Ho, J.; Lineberger, W. C. J . Chem. Phys. 1987, 86, 1715.

(3) Leopold, D. G.; Miller, T. M.; Lineberger, W. C. J . Am. Chem. SOC. 1986, 108, 178.

0 1992 American Chemical Society

2480

of diatomic and triatomic resonant two-photon ioni- zation photoelectron spectroscopy (R2PI-PES) of diatomic metals,,’ laser-induced fluorescence of metal dimers,28 direct absorption studies of metal dimer^,,^-^' and photodissociation spectroscopy of metal cluster cation^.^^-^^ Bond strength in- formation has been derived from photodissociation threshold measurements, collision-induced dissociation studies of metal cluster cation^,^^^^' and mass spectrometric studies of various high-temperature e q ~ i l i b r i a . ~ * . ~ ~ Work from this research group has concentrated on R2PI studies of diatomic transition metals, particularly the late-transition-metal dimers, including Pt2,’ NiCu,8-10 NiPt,” NiPd,I2 CrMo,13 NiAu,I4 CuPt,14 CuAg,I5 CuAu,I6 AgAu,” and Au2.I7 With results from this series of investigations, and prior work on Ni2,I8 V2,’9$20 Cr2,21.22*28929 and Mo2,23-30,31 some general features of the chemical bonding in the transition-metal diatomics are beginning to emerge.

In addition to the spectroscopic work of this group referenced above, we are also interested in the bond strengths of the tran- sition-metal molecules, and in identifying the important factors which determine these bond strengths. Of course, bond strengths are strongly affected by the extent of d-orbital contributions to the bond. These contributions are determined largely by the physical size of the d orbitals, which affects both the magnitude of the exchange effects and the ability of d orbitals on different

The Journal of Physical Chemistry, Vol. 96, No. 6 , 1992 Spain and Morse

centers to overlap to form bonds. In this latter regard it is the difference in size between the d orbitals and the outer s orbital which is most critical in determining whether significant overlap can be achieved. In mixed early-late transition metal dimers, yet another important effect may occur. These compounds contain a highly electropositive metal, with a low ionization potential, in combination with a late transition metal having a high electron affinity. This may lead to significant ionic character in the re- sulting chemical bond, which may strengthen it considerably. In addition to this purely ionic effect, a back-donation of d electrons from the late transition metal to the early, electropositive metal may occur as well. As a result it is possible that mixed early-late transition metal diatomics may be bound more strongly than either of their homonuclear counterparts.

At present, the bond strengths of VNi,25 V2,25 Ni2,18 NiPt,” Pt2,7 AlNi,26 and Cr2+40 have been determined by measuring the abrupt onset of predissociation in a congested optical spectrum. In this paper we add the bond strengths of the intermetallic molecules TiV and TiCo to this list. In addition, we discuss the criteria which must be met if bond strengths are to be safely inferred from the onset of predissociation in the transition-metal diatomic molecules. The d-orbital contributions to the bond strength are also derived for the molecules listed above by com- parison to their filled d-subshell coinage metal analogues. Finally, an examination of the periodic trends in the chemical bonding between transition metals is presented.

11. Experimental Section The pulsed laser vaporization-molecular beam apparatus used

in the present resonant two-photon ionization (R2PI) studies has been previously described.24 Diatomic metals are formed by laser vaporization of a metal target in the throat of a pulsed supersonic expansion of helium using the second harmonic radiation of a Q-switched Nd:YAG laser. Intermetallic alloys of the appropriate mole fractions were used as metal targets. In the present in- vestigations three alloys were used, formed by weighing out the component elements and subjecting them to an electric arc under an inert atmosphere of argon. After the arc was struck, the current was slowly increased until the sample melted and was thoroughly mixed by convection currents. The electrical current was then discontinued, and the molten alloy was allowed to cool. The resulting material was then ground to form a flat disk suitable for laser vaporization.

Diatomic vanadium and vanadium-nickel were studied using a sample composed of a 1:l molar ratio of vanadium to nickel. Since V, has a significantly greater bond strength than either VNi or Ni2, it was the most abundant diatomic species produced, and could be readily investigated using this alloy. Adequate quantities of VNi were produced as well. Diatomic TiCo was produced in copious amounts from an alloy consisting of a 1:1 molar ratio of titanium to cobalt. In this case the bond between titanium and cobalt is much stronger than that found in either Ti2 or Co2, making TiCo the most abundant diatomic molecule produced by far. Presumably this occurs because Ti2 and Co2 are readily converted to TiCo by the exothermic displacement reactions:

Ti2 + Co - Ti + TiCo (2.1)

Ti + Co, - TiCo + Co (2.2)

For the study of TiV, a 1: 1 molar ratio alloy was initially prepared as described above. The cluster distribution produced from this source, however, was dominated by V2 and very little TiV was produced. To overcome this problem, the titanium content of the alloy was increased (to approximately a 3:l Ti:V molar ratio) to reduce the rate of the displacement reaction

TiV + V - Ti + V, (2.3)

It was expected that this would increase the concentration of TiV in the final molecular beam. This strategy proved to be effective,

(4) Leopold, D. G.; Lineberger, W. C. J . Chem. Phys. 1986, 85, 5 1 . ( 5 ) Leopold, D. G.; Almholf, J.; Lineberger, W. C.; Taylor, P. R. J . Chem.

(6) Ervin, K. M.; Ho, J.; Lineberger, W. C. J . Chem. Phys. 1988,89,4514. (7) Taylor, S.; Lemire, G. W.; Hamrick, Y . ; Fu, Z.-W.; Morse, M. D. J .

(8) Fu, Z.-W.; Morse, M. D. J . Chem. Phys. 1989, 90, 3417. (9) Spain, E. M.; Morse, M. D., manuscript in preparation. (IO) Spain, E. M.; Morse, M. D., manuscript in preparation. ( 1 1) Taylor, S.; Spain, E. M.; Morse, M. D. J . Chem. Phys. 1990, 92,

(12) Taylor, S.; Spain, E. M.; Morse, M. D. J . Chem. Phys. 1990, 92,

(13) Spain, E. M.; Behm, J . M.; Morse, M. D. Chem. Phys. Lett. 1991,

(14) Spain, E. M.; Morse, M. D., manuscript in preparation. ( 1 5 ) Bishea, G. A.; Marak, N.; Morse, M. D. J . Chem. Phys. 1991, 95,

(16) Bishea, G. A,; Pinegar, J . C.; Morse, M. D. J . Chem. Phys. 1991,95,

(17) Bishea, G. A,; Morse, M. D. J . Chem. Phys. 1991, 95, 5646. (18) Morse, M. D.; Hansen, G. P.; Langridge-Smith, P. R. R.; Zheng,

L.-S.; Geusic, M. E.; Michalopoulos, D. L.; Smalley, R. E. J . Chem. Phys. 1984,80, 5400.

(19) Langridge-Smith, P. R. R.; Morse, M. D.; Hansen, G. P.; Smalley, R. E.; Merer, A. J . J . Chem. Phys. 1984, 80, 593.

(20) Spain, E. M.; Behm, J. M.; Morse, M. D. J . Chem. Phys., in press. (21) Michalopoulos, D. L.; Geusic, M. E.; Hansen, S. G.; Powers, D. E.;

Smalley, R. E. J . Phys. Chem. 1982, 86, 3914. (22) Riley, S. J.; Parks, E. K.; Pobo, L. G.; Wexler, S. J . Chem. Phys.

1983, 79, 2577. (23) Hopkins, J . B.; Langridge-Smith, P. R. R.; Morse, M. D.; Smalley,

R. E. J . Chem. Phys. 1983, 78, 1627. (24) Fu, Z.-W.; Lemire, G. W.; Hamrick, Y . ; Taylor, S.; Shui, J.-C.;

Morse, M. D. J . Chem. Phys. 1988, 88, 3524. (25) Spain, E. M.; Morse, M. D. In?. J . Mass Spectrom. Ion Processes

Phys. 1988, 88, 3780.

Chem. Phys. 1988, 89, 5517.

2698.

27 IO.

179, 411.

5618.

5630.

1990, 102, 183.

ration. (26) Behm, J. M.; Arrington, C. A,; Morse, M. D., manuscript in prepa-

(27) Sappey, A. D.; Harrington, J . E.; Weisshaar, J. C. J . Chem. Phys. 1988. 88. 5243: 1989. 91. 3854.

(28) Bondybey, V. E.; English, J . H. Chem. Phys. Lett. 1983, 94, 443. (29) Efremov, Y. M.; Samoilova, A. N.; Gurvich, L. V . Opt. Specfrosc.

(30) Efremov, Y . M.; Samoilova, A. N.; Kozhukhovsky, V. B.; Gurvich,

(31) Samoilova, A. N.; Efremov, Y . M.; Zhuravlev, D. A,; Gurvich, L. V.

(32) Jarrold, M. F.; Creegan, K. M. Chem. Phys. Lett. 1990, 166, 116. (33) Lessen, D.; Brucat, P. J . Chem. Phys. Lelt. 1989, 160, 609. (34) Hettich, R. L.; Freiser, B. S . J . Am. Chem. SOC. 1987, 109, 3537. (35) Hettich, R. L.; Freiser. B. S. ACS Symp. Ser. 1987, 359, 155. (36) Loh, S. K.; Hales, D. A.; Lian, L.; Armentrout, P. B. J . Chem. Phys.

(37) Loh, S. K.; Lian. L.; Armentrout, P. B. J . Am. Chem. SOC 1989, 1 1 1 .

(38) Kant, A.; Lin, S.S . J . Chem. Phys. 1969, 51, 1644. (39) Cocke, D. L.; Gingerich, K. A. J . Chem. Phys. 1972, 60, 1958.

1974, 36, 381.

L. V. J. Mol. Spectrosc. 1978, 73, 430.

Khim. Vys. Energ. 1974, 8, 229.

1989, 90, 5466.

3167. (40) Lessen, D. E.; Asher, R. L.; Brucat, P. J . Chem. Phys. k i f . 1991,182,

412.

Bond Strengths of TiV, V,, TiCo, and VNi

since a weak but adequate TiV ion signal intensity was readily obtained using the titanium enriched alloy.

Following supersonic expansion into vacuum, the molecular beam was collimated and admitted into the ionization region of a reflectron time-of-flight mass spectrometer. Resonant two- photon ionization spectroscopic studies were then performed by directing a Nd:YAG pumped dye laser down the molecular beam axis. This was intersected at right angles by the output beam of a pulsed excimer laser operating on KrF (248 nm, 5.00 eV), which served to ionize molecules which had been excited by the dye laser radiation. Lifetimes of excited electronic states were measured by time-delayed resonant two-photon ionization methods. The resulting plot of ion signal as a function of delay time was fitted to an exponential decay using a nonlinear least-squares algorithm, which allowed the l / e lifetime of the excited electronic state to be extracted.

In all of the cases reported here, a calibration of the predis- sociation threshold energy was established by monitoring the precisely known41 transmission spectrum of I, under high resolution (0.04 cm-') at the predissociation threshold of the molecule. For V,, however, the predissociation threshold was beyond the range of the I, atlas,41 so the dye laser radiation was Raman shifted in high-pressure H2, and the 1, absorption spectrum was obtained using the first Stokes radiation. Since the Raman shifting process occurs in a stimulated manner, it takes place on the line with the highest Raman gain, which for room temperature H2 is Q(1). According to the constants of Huber and Herzberg,42 this implies that the first Stokes radiation emerging from the H2 Raman cell is shifted 4155.264 cm-' to the red of the fundamental. This precisely determined Raman shift allows the useful calibration range of the I, atlas to be extended about 4155 cm-' to the blue, as was necessary for precise measurement of the predissociation threshold of V,.

111. Results A. The Bond Strength of TiV. Titanium-vanadium provides

an example of chemical bonding between two early transition metals, where the 3d orbitals are relatively large, and almost certainly capable of bonding interactions. On the other hand, over 1 eV of energy is required to promote both atoms to the d"+'sl configuration which is most suitable for bonding. As a result, the net bond strength may be reduced considerably from what would otherwise be expected, and it is not immediately obvious whether the ground state of the TiV molecule will derive from the Ti d2s2, 3F + V d4s', 6D or Ti d3si, SF + V d4s1, 6D separated atom limits, which are located 0.25 and 1.06 eV above the ground state of the separated atoms (Ti d2s2, 3F + V d3s2, 4F), respectively. To investigate these effects and to determine the bond strength of TiV, the resonant two-photon ionization spectrum of TiV was scanned in the hope of locating a predissociation threshold.

Despite a rather poor TiV signal, as mentioned in section 11, a weak, nearly continuous absorption spectrum was nevertheless observed using the R2PI method. This is displayed in Figure 1, which also indicates an abrupt termination of the continuum absorption at 16 678 cm-l. As is discussed in more detail below, we interpret this abrupt drop in signal as a predissociation threshold and use it to derive a bond strength of TiV as Dt(TiV) = 2.068 f 0.001 eV. In the present work our intention was only to locate this threshold, so only a limited range of frequencies was scanned. Although it is possible that discrete vibronic bands may be found to the red of 16 000 cm-I where we have not scanned, as of yet no discrete vibronic spectra have been found for TiV. Accordingly, no spectroscopic information has been obtained except for the predissociation threshold shown in Figure 1.

It would be absurd for TiV, or any transition-metal dimer, to possess an extremely large density of optically allowed states below

(41) Gerstenkorn, S.; Luc, P. Atlas du Spectre #Absorption de la Mole- cule d'lode; CRNS: Paris, 1978. Gerstenkorn, s.; Luc, P. Rev. Phys. Appl. 1979, 14, 791.

(42) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979.

The Journal of Physical Chemistry, Vol. 96, No. 6, 1992 2481

6 0 0

- B i7~ 4 0 0

I

200

n r 6 4 0 0 1 6 5 0 0 1 6 6 0 0 1 6 7 0 0 1 6 8 0 0

Frequency (cm.1)

Figure 1. Predissociation threshold in TiV, observed by resonant two- photon ionization using a dye laser operating on a mixture of rhodamines 610 and 640, in conjunction with KrF excimer radiation, which provided the second, ionizing photon. The dense continuum of transitions ter- minates abruptly at 16678 cm-', allowing the bond strength of TiV to be determined as l$(TiV) = 2.068 f 0.001 eV.

16 678 cm-I and not have any optically allowed states above this frequency. Rather, it seems certain that TiV possesses optically accessible electronic states both above and below 16 678 cm-I but that a rapid decay mechanism prohibits us from observing tran- sitions above this threshold. Given our dye and excimer laser pulse durations, transitions above 16 678 cm-' should have been detected had the upper-state lifetime exceeded 5 ns. On the other hand, timedelayed resonant two-photon ionization measurements provide an excited-state lifetime of approximately 60 bus for states which are reached by excitation of the apparent continuum of Figure 1. From these data, we conclude that the excited-state lifetime drops by 4 orders of magnitude promptly at 16 678 cm-I.

Perhaps one or several of the TiV excited states might have a radiative lifetime of 5 ns (or less) above 16 678 cm-'. Although this would require a combined oscillator strength for all emission systems off = 1.0, the possibility is conceivable. It is difficult to understand how all of the excited states above the 16 678-cm-l frequency threshold could be such superb radiators, however. A more plausible explanation is that this threshold marks the onset of predissociation and that all states above this limit are predis- sociated on a subnanosecond time scale, making them invisible to the resonant two-photon ionization method.

In addition to being a predissociation threshold, we suggest that 16 678 cm-' is the true dissociation limit of TiV. As is evident in the apparent continuum of Figure 1, TiV possesses a severe congestion of states below 16678 cm-I. This tremendous density of states will cause the Bom4ppenheimer approximation to break down so that it becomes incorrect to think of the molecule as vibrating on a single potential energy surface. If photoexcitation of TiV places it above the lowest dissociation limit, and the Born-Oppenheimer approximation has broken down, then motion may occur on one of the potential energy surfaces correlating to the ground-state atoms, and dissociation will result. Of course, good quantum numbers such as Q must be preserved in the process, but this presents few restrictions in the case of TiV since the combination of a ground-state titanium atom (3F2) and a ground-state vanadium atom (4F3,2) results in all values of Q from 0.5 to 3.5. Hence, unless a state of TiV is excited with R I 4.5, dissociation to ground-state atoms will be possible. The ground state of TiV is known43 to be 4X1,2, so transitions from this 0'' = 0.5 component can only populate excited states with Q I 1.5, and these excited states can predissociate to ground-state atoms. With this argument, a bond strength of Dt(Ti-V) = 2.068 f 0.001 eV is assigned to TiV, where the error limit reflects the uncertainty in locating the threshold in Figure 1.

(43) Van Zee, R. J.; Weltner, W., Jr. Chem. Phys. Lett. 1984, 107, 173.

2482 The Journal of Physical Chemistry, Vol. 96, No. 6, I99

2500 A 2000 c

I I I I I 0 20OO 4000 6000 8000

Energy above ground state atoms (cm-1)

Figure 2. Integrated density of states for Til, TiV, and V,. This figure presents the number of distinct Hund's case (c) electronic states, N ( E ) , arising from separated atom limits within an energy E of ground-state atoms. It is evident that all three species possess a vast number of electronic states which are accessible at the lowest dissociation threshold, since many of the states arising from excited-separated-atom limits are attractive, and will dip below the ground-separated-atom limit. Ac- cordingly, an abrupt predissociation threshold is expected for all three species as soon as the molecule is excited above its lowest dissociation limit.

In order to comprehend the enormous number of excited states which exist for open d-subshell transition-metal dimers such as those studied in this work, it is helpful to consider the molecular states which arise when the titanium and vanadium atoms combine to form a chemical bond. Ground-state titanium (3d24s2, 3F2) and vanadium (3d34s2, 4F3/2) atoms correlate diabatically to re- pulsive dtid$u2u*2 states of the TiV molecule, resulting in four Q = 0.5 states, three Q = 1.5 states, two Q = 2.5 states, and one state with Q = 3.5, giving a total of 10 doubly degenerate Hund's case (c) electronic states. Even in Hund's case (a) (which cannot be appropriate near the dissociation limit for TiV) the Ti(3F) + V(4F) separated atom limit generates 84 potential curves labeled by A and S. When spin-orbit interactions are included, these 84 Hund's case (a) states split to give 294 distinct Hund's case (c) potential energy curves. Undoubtedly, a huge number of states are available near the lowest dissociation limit in TiV. Moreover, excited states of the separated atoms, such as Ti(3d34s', SF) and V(3d44s', 6D), lie quite low in energy, and molecular states arising from these limits almost certainly drop below the lowest disso- ciation threshold, adding to the congestion of electronic states accessible a t energies near the dissociation limit.

It is straightforward to calculate the number of Hund's case (c) potential curves arising from each separated atom limit of a diatomic molecule. From a separated atomic limit corresponding to a titanium atom with total (spin plus orbital) angular mo- mentum JTi interacting with a vanadium atom with total angular momentum Jv , a total of (2JTi + 1)(2Jv + 1)/2 relativistic adiabatic (Hund's case (c)) potential curves arise. Since the atomic energy levels are well known,44 it is a simple matter to count the number of molecular curves arising from separated atom limits within an energy E of the ground-separated atom limit. The resulting integrated density of states, N ( E ) , is a useful measure of the expected state density in the molecule. Figure 2 provides the integrated density of states within an energy E of the ground state separated atom limit, N(E), for Ti2, TiV, and V2. The results are astounding when compared to diatomic molecules composed of first-, second-, and third-row atoms. Within 10000 cm-l of the ground-state-separated atom energy over 2500 molecular states arise for V,, over 2000 molecular states arise for TiV, and over 1400 molecular states arise for Ti2. For comparison, analogous calculations for C2, CN, and N2 give only 50, 18, and 10 molecular states arising within 10 000 cm-l of ground-state atoms, respec- tively. Given such state densities in the transition-metal dimers, it should be no surprise that predissociation occurs for many

(44) Moore, C. E. Nafl. Bur. Stand. (US.) Circ. No. 467, 1971; Vol. 1-111.

'2 Spain and Morse

21700 21XoO 21900 2 2 h 22;00 Frequency (cm-I)

Figure 3. Resonant two-photon ionization spectrum of V,, near its dis- sociation limit, obtained using a dye laser operating on coumarin 440 in conjunction with KrF excimer radiation, which provided the second, ionizing photon. An intense continuum of transitions terminates at 22 201 cmP, allowing the bond strength of V, to be determined as Doq(V,) = 2.753 f 0.001 eV. A weaker, nearly continuous set of transitions, extending to 22338 cm-' occurs because rotationally cold 0: states ex- cited by optical transitions from the ground X 3ZJO''=Oi) level cannot predissociate to ground-state atoms, but can dissociate at the first ex- cited-separated-atomic limit, which lies 137.38 cm-' above ground state atoms.

molecules as soon as the lowest dissociation limit is exceeded. Cases in which abrupt predissociation thresholds fail to appear will be discussed in section IV below. B. The Bond Strength of V2. Since the integrated density of

states shown in Figure 2 for V2 exceeds that of TiV it should be possible to measure the bond strength of V2 by finding its pre- dissociation threshold as well. The ground electronic state of V2 is known to be 3Z&Q=O:),19 so optical transitions can populate excited states with Q = 0; or Q = 1,. Combination of two ground-state (3d34s2, 4F3,2) vanadium atoms results in molecular states given in Hund's case (c) nomenclature as 3,, 2,, 2,, 1, (2 states), I,, 0; (2 states), and 0; (2 states), so photoexcitation to 1, excited states can lead to prompt predissociation. On the other hand, 0: excited states cannot predissociate to ground-state atoms unless a heterogeneous (rotationally induced) perturbation is present, since no 0: excited states correlate to ground-state atoms. The 0: excited states which may be produced by optical excitation of ground-state V2 can predissociate to the first excited separated atom limit, V(3d34s2, 4F3j2) + V(3d34s2, 4FSi2), however, since two 0: states correlate to this limit. This limit lies 137.38 cm-' above ground-state vanadium atoms.

Figure 3 displays the spectrum of V2 near the dissociation threshold. Toward the red, an intense near-continuum absorption occurs, which abruptly drops at a frequency of approximately 22 201 cm-'. To the blue of this limit, a much weaker, structured near-continuum absorption persists to 22 338 cm-I, beyond which no spectral features are observed. These observations are very much in line with the expectations described in the previous paragraph. It appears that the 1, excited states (and rotationally excited 0: states) predissociate as soon as the lowest dissociation threshold (22201 cm-I) is exceeded, while rotationally cold 0: states cannot predissociate rapidly until the first excited separated limit is reached. The difference between the two thresholds (22 338-22 201 cm-l = 137 cm-') should correspond to the 4Fsi2 - 4F3,2 excitation energy in the vanadium atom (137.38 cm-I)." The close correspondence between these two values further sub- stantiates the idea that predissociation in this molecule occurs promptly as soon as the lowest dissociation limit is exceeded. On this basis we assign D:(V,) = 2.753 f 0.001 eV. Excited-state lifetimes, measured in the V, absorption continuum between 22 139 and 22 198 cm-' ranged from 1.4 to 3.5 ps, while the lack of spectral features to the blue of 22 338 cm-' implied a lifetime below 5 ns in this energy region, again consistent with rapid predisso- ciation above this limit.

A previous investigation of the V2 bond strength by Knudsen effusion mass s p e c t r ~ m e t r y ~ ~ provided a value of D:(V2) of 2.49 * 0.13 eV using the second-law method. A third-law value of Dt(V,) = 2.47 f 0.22 eV was derived assuming a nondegenerate ground electronic state with o, = 325 cm-I, and re = 2.45 These values differ considerably from the values subsequently

Bond Strengths of TiV, V,, TiCo, and VNi

1500 ---I

The Journal of Physical Chemistry, V O ~ . 96, No. 6, 1992 2483

5w J

1 6 7 5 0 1 6 8 5 0 16950 17050 1 7 1 5 0

I

19000 19200 19400 19600 19800 20000

Frequency (cm ’)

Figure 4. Resonant two-photon ionization spectrum of TiCo, showing a predissociation threshold at 19 363 cm-l. This spectrum was obtained using coumarin 500 laser dye in conjunction with KrF excimer laser radiation, which provided the second, ionizing photon. The abrupt ter- mination of the dense spectral continuum allows the bond strength of TiCo to be determined as D:(TiCo) = 2.401 f 0.001 eV.

m e a s ~ r e d , ’ ~ * ~ ~ which are we = 537.1 cm-’ and re = 1.774 A. The errors in these parameters suggest that the diatomic V, partition function used by Knut and L i d x in the third-law method should be multiplied by a factor of about 0.32. This almost exactly cancels the error in estimating the electronic degeneracy of the V2 ground state, however, since Kant and Lin38 assumed a nondegenerate ground state, while the 3Z; ground state of V, has an electronic degeneracy of 3. Thus, it appears that errors in calculating the partition function of V2 cannot explain the discrepancy between the Knudsen effusion mass spectrometric measurement of Dt(V2) and that reported here.

Hales and Armentrout have performed collision-induced dis- sociation experiments on jet-cooled V,+ cluster cations. They measured the bond strength of V2+, and have used the atomic and neutral diatomic ionization potentials to derive the bond strength Dt(V2) = 2.76 f 0.22 eV,45 in excellent agreement with our measurement. The reasons for the discrepancy between the Knudsen cell measurements and the results from the collision- induced dissociation and resonant two-photon ionization studies are not clear a t this time.

C. The Bond Strength of TiCo. In contrast to these early transition-metal diatomics, TiCo provides an example of a mixed early-late transition metal diatomic which may have a significant amount of ionic character. In addition to the possibility of 4s electron transfer from the titanium to the cobalt, there is also a possibility of 3d-orbital backbonding from the cobalt to the ti- tanium, resulting in a strong interaction of the type envisioned by Brewer and E ~ ~ g e l . ~ ~ With this in mind an investigation of the bond strength of TiCo was undertaken.

The ground state of TiCo is known from ESR investigations to be 2Z in symmetry,4’ which gives an Q = 0.5 ground state. From this Q = 0.5 level, transitions to excited states described by Q = 0.5 and 1.5 are possible. In either case predissociation to ground-state atoms (Ti 3F2 + Co 4F9,2) is possible, since this separated atom limit generates five states with Q = 0.5 and five states with Q = 1.5 (in addition to five states described by Q = 2.5, four states with Q = 3.5, three with Q = 4.5, two with Q = 5.5, and one with 0 = 6.5). Figure 4 demonstrates that the expected prompt predissociation is indeed observed to occur a t 19 363 cm-I. From this predissociation threshold a bond strength of Dt = 2.401 f 0.001 eV is derived. It is interesting that this bond strength is much greater than that of either Ti2 (1.23 f 0.1 7 eV)4x or Co2 (0.95 f 0.26 eV),48 as is discussed further below.

(45) Hales, D. Ph.D. Thesis, University of California, Berkeley, 1990. (46) Brewer, L. Science 1968, 161, 115. Engel, N. Kem. Maanedsbl. 1949,

30, 5 3 , 75, 97, 105, 1 1 3 . Engel, N. Powder Metall. Bull. 1964, 7 , 8. Engel, N. Am. Soc. Metals, Trans. Q. 1964, 57, 610.

(47) Van Zee, R. J.; Weltner, W., Jr. High Temp. Sci. 1984, 17, 181. (48) Morse, M. D. Chem. Reo. 1986, 86, 1049.

Frequency (cm.1)

Figure 5. Predissociation threshold in VNi, observed by resonant two- photon ionization using a dye laser operating on rhodamine 610 in con- junction with KrF excimer radiation, which provided the second, ionizing photon. The dense continuum of transitions terminates at 16 940 cm-I, allowing the bond strength of VNi to be determined as D:(VNi) = 2.100 f 0.001 eV.

This fact was primarily responsible for the high concentration of TiCo in the molecular beam and helped to provide the excellent signal-to-noise ratio found in Figure 4.

In addition to locating the predissociation threshold, the dye laser was from 12 100 to 20000 cm-l in the hope of finding a more or less isolated band system. Unfortunately, no discrete vibronic transitions were observed, and this prevented a mea- surement of the ground-state bond length by rotationally resolved spectroscopy.

D. The Bond Strength of VNi. The resonant two-photon ionization spectrum of diatomic VNi is severely congested. No discrete vibronic bands could be found in the spectral range from 11 500 to 16 940 cm-’, even though the resonant two-photon ionization process was enhanced by dye laser light throughout this entire range. This unfortunate lack of discrete vibronic features precluded us from obtaining any detailed spectroscopic infor- mation. However, an abrupt drop in the enhanced VNi+ signal was observed at 16 940 cm-I, as displayed in Figure 5. Above 16940 cm-’, no spectral features were detected, while below this frequency a dense spectral continuum was recorded. Lifetimes of excited states measured in the continuum of Figure 5 (16 908-16 937 cm-I) fall in the range of 40-55 ps, while the lack of observed features to the blue of 16 940 cm-’ implies excited-state lifetimes shorter than 5 ns. From these data, we conclude that the excited-state lifetime drops by at least 4 orders of magnitude promptly at 16 940 cm-I, supporting the assignment of this energy as a predissociation threshold.

The ground state of VNi is to be 42, so transitions from the Q” = 0.5 or 0’’ = 1.5 components can only populate excited states with Q 5 2.5. Moreover, the ground states of the vanadium and nickel atoms are 3d34s2, 4F3j2 and 3d84s2, 3F4, respectively, which can combine to generate molecular states with all values off? from 0.5 to 5 .5 . Hence there should be no symmetry-based restrictions in the predissociation of excited electronic states of VNi with Q I 2.5 to ground-state atoms. Accordingly, the ob- served predissociation threshold at 16 940 cm-’ is assigned as the dissociation energy of VNi, giving D:(V-Ni) = 2.100 f 0.001 eV, where the error limit reflects the uncertainty in locating the threshold in Figure 5.

IV. Discussion A. Criteria for Measurement of Bond Strengths by Predisso-

ciation. By monitoring the onset of predissociation in a severely congested optical spectrum, we have measured the bond strengths of VNi,25 V2,25 TiCo, and TiV. These four molecules join Ni2,Ix NiPt,” Pt2,’ AlNi,26 and Cr2+@ as species for which bond strengths have been determined by this method. It would appear that this method will be generally useful for the open d-subshell transi- tion-metal dimers, where vast numbers of excited-electronic states are accessible a t the lowest dissociation limit. This expectation has not been borne out in the cases of NiPdt2 and PdPt,I2 however. It is important to understand why these particular molecules fail to exhibit a prompt predissociation threshold, so that the generality of this method of measuring bond strengths may be understood.

Spain and Morse 2484 The Journal of Physical Chemistry, Vol. 96, No. 6, I992

TABLE I: Bond Strengths of Selected Transition-Metal Diatomics

measured bond intrinsic bond modified intrinsic coinage analogue (r"d),c A measured bond molecule strength, eV strength,' eV bond strength! eV bond &ength;eV A, eV atom A atom B sum length, A

TiV 2.068d 3.119 2.313 2 .03(C~, )~ 1.09 (0.28) 0.793 0.720 1.513 v2 2.753d3e 3.243 i 2.03 (Cui)' 1.21 0.720 0.720 1.440 1.766O

VNi 2.1 004.' 2.345 2.345 2.03 (Cu2)' 0.32 0.720 0.514 1.234 Ni2 2.068' 2.068' 2.068' 2.03 (Cu2)' 0.04 0.514 0.514 1.028 2.206 NiPt 2.7989 2.798' 2.798' 2.34 (CuAu)' 0.46 0.514 0.874 1.388 2.2088 Pt2 3.14h 3.14 3.14 2.29 (Au# 0.85 0.874 0.874 1.748

Defined as the measured bond strength plus the amount of energy required to promote both atoms to d"+ls' configurations. The promotion energy was calculated as the difference in the degeneracy-weighted averages of the spin-orbit levels of the lowest energy d"s2 and d"+lsI terms. bDefined as the measured bond strength plus the amount of energy required to promote the most easily excited atom to the dn+'sl configuration, as described in footnote a. CFrom the Dirac-Fock SCF calculations of Desclaux (ref 51), erroneously given in Bohr radii rather than in A in ref 25. dThis work. CFrom ref 25. /From ref 18. gFrom ref 11. *From ref 7. ' V 2 is known to have an su;du:d~:d6;,~2, ground state, and therefore correlates to a doubly-promoted separated atom limit of 3d44s',6D + 3d44s',6D. 'The level averaged ground states of Ni and Pt are d9s','D, so no promotion is required, and the promotion energies are zero. ' From ref 50. 'From ref 16. "From ref 17. "From ref 19.

TiCo 2.4Old 3.624 2.818 2.03 (CU~)' 1.59 (0.79) 0.793 0.544 1.337

In the examples of NiPd and PdPt, the interaction of a ground-state 4d105s0, 'So palladium atom with either nickel or platinum probably results in an attractive potential energy curve, owing to the possibility of a Lewis acid-Lewis base interaction between the empty 5 s orbital of palladium (a u acid) and the full or half-full 4s orbital of nickel (3d94s1 or 3d84s2) or 6s orbital of platinum (5d96s1 or 5d86s2) (a u base). These outer s electrons in Ni or Pt can act as u donors into the empty 5s orbital of palladium, making all states deriving from the interaction of a ground-state palladium atom (4dI05s0, ISo) and an S I or s2 nickel or platinum atom attractive. As a result, the first repulsive po- tential curves in the molecular electronic manifold probably do not arise until the 3d94s1, 3D3 (Ni) + 4d95s1, 3D3 (Pd) or the 4dI05s0, 'So (Pd) + 5dI06s0, 'So (PI) separated atom limits are reached, a t 6768.9 and 6140.0 cm-I, respectively. This lack of repulsive curves originating from the lowest separated atom limits may explain the absence of an abrupt predissociation threshold in NiPd and PdPt.',

In contrast, the diatomic molecules V,, VNi, TiCo, TiV, Ni,, and Pt, all possess ground-state-separated atom limits which must diabatically correlate to repulsive molecular states. For example, the ground levels of atomic titanium (3d24s2, 3F2), vanadium (3d34s2, 4F3/2), cobalt (3d74s2, 4F9i2), and nickel (3d84s2, 3F4) all contain filled 4s2 subs hell^,^^ resulting in repulsive Ti-Ti, Ti-V, Ti-Co, Ti-Ni, V-V, V-Co, V-Ni, Co-Co, Co-Ni, and Ni-Ni interactions. Likewise, the ground level of atomic platinum is 5d96s1, 3D3, so combination of two ground-state platinum atoms leads to attractive states if the 6s electrons are spin-paired (S = 0), and to repulsive states if the 6s electrons are coupled to give a net spin of S = 1 (5di5diuu* states). Thus the lowest separated atom limits of V,, VNi, TiCo, TiV, Ni,, and Pt, all generate repulsive curves, in marked contrast to what occurs in the pal- ladium-containing species NiPd and PdPt.

The remaining examples of transition-metal-containing dia- tomics exhibiting sharp predissociation thresholds are NiPt and AINi. For NiPt the lowest separated atom limit is Ni(3d84s2, 3F4) + Pt(5d94s1, 3D3). Diabatically this correlates to molecular states described as 3 d ~ i 5 d ~ , a 2 u * , which are expected to be attractive. However, the Ni(3d94s1, 3D3) + Pt(5d94s1, 3D3) separated atom limit lies only 204.8 cm-' above ground-state atoms, and this limit will generate repulsive potential curves diabatically correlating to molecular states described as 3dki5d~ua*, where the Ni 4s and Pt 6s electrons have been coupled to give a net spin, S = 1. Thus it is possible (perhaps even likely) that predissociation in NiPt fails to set in until the lowest dissociation limit is exceeded by 204.8 cm-' (or 0.025 eV). Likewise, the combination of a ground-state aluminum atom (3s23p', ,PI/,) with a ground-state nickel atom (3dx4s2, 3F4) is expected to give potential curves correlating to 3 d ~ i 3 s ~ l u 2 u * ' and 3dki3sk1u2d, depending upon whether the 3p electron of aluminum approaches the nickel atom in a u or 7~ orientation. In either case, these states may be expected to be attractive, having bond orders greater than zero. However, once again the Ni(3d94s1, 3D3) + Al(3s23p', ,PI/,) separated atom limit lies only 204.8 cm-' above ground-state atoms, and this will

generate potential curves correlating to 3 d & 3 ~ ~ ~ u l u * ~ if the 4s electron of nickel and the 3pu electron of aluminum are triplet- coupled, and these states will surely be repulsive. As in NiPt, it is likely that the measured predissociation threshold of AlNi will exceed the true bond strength of the molecule by approximately 204.8 cm-I.

From these considerations, we may conclude that there are two criteria which a transition-metal molecule must satisfy if its bond strength is to be measured by the location of a sharp predissociation threshold. First, the molecule must have a sufficient density of electronic states in the neighborhood of its lowest dissociation threshold to make motion on a single Bom-oppenheimer potential energy surface untenable. Second, the lowest separated atom limit must generate repulsive potential energy curves. Fortunately, most neutral transition-metal dimers will satisfy both criteria. The requirement of a large electronic state density is automatically fulfilled by the open d-subshell transition-metal dimers, while the second requirement is fulfilled whenever a d"s2 atom is combined with a dms2 atom, or when a d"sl atom combines with a dmsl atom. Excluding the closed d-subshell elements Cu, Ag, Au, Zn, Cd, and Hg, 174 of the 300 possible transition-metal dimers fall into the dns2-dms2 or dnsl-dmsl categories and should predissociate promptly when the lowest dissociation limit is exceeded. A possible caveat here is that the repulsive curves originating from the ground-state-separated atoms should not be too repulsive. Such a scenario could result in a curve crossing somewhat above the lowest dissociation limit, resulting in an artificially high measured value for the bond strength. B. Chemical Boading in TiV, Vz, Tic4 and VNi. Consideration

of the chemical bonding in the open d-subshell transition-metal molecules is now in order. Table I provides a comparison of the bond strengths of TiV, V,, TiCo, VNi, Ni,, NiPt, and Pt,. We have listed the measured bond strengths in the first column and the intrinric bond strengths in the second column. For the purposes of this discussion we define the intrinsic bond strength as the measured bond strength plus the amount of energy required to excite both constituent atoms to the d"sl states which are ideally set up for chemical bonding. It is therefore the bond strength that the molecule would be expected to possess if it were not necessary to promote the atoms to an appropriate electronic configuration for bonding. In addition, the third column of Table I presents the modified intrinsic bond strength, which is defined as the measured bond strength plus the promotion energy required to excite the more easily excited atom to the dnsl state which is appropriate for bonding. This would be the appropriate diabatic bond strength to consider if it could be determined that the ground state of the molecule correlates to a d"s' + dms2 separated atom limit. The fourth column of Table I lists the bond strength of the filled d-subshell analogue of each transition-metal diatomic, which is selected from the coinage metal diatomics Cu2, CuAg, CuAu, Ag,, AgAu, and Au, according to whether the constituent atoms are taken from the 3d, 4d, or 5d transition-metal series. These coinage metal molecules are formed from atoms with ground configurations of d'Os', 2S,12, which are ideally set up for formation

Bond Strengths of TiV, V,, TiCo, and VNi

of a u2 bond using the s orbitals, but for which the d orbitals are filled and behave nearly as an inert core. As a result, the coinage metal bond strengths represent what might be expected if the d orbitals made no contribution to the chemical bonding. Finally, we also compute A, which we define as the difference between the intrinsic bond strength of the transition-metal diatomic (or modified intrinsic bond strength, given in parentheses) and the bond strength of the corresponding coinage metal analogue. This is a direct measure of the magnitude of the d-orbital contributions to the bond strength.

Based on Table I, it is clear that TiCo has the greatest intrinsic bond strength, but the required promotion energy of 1.2 eV greatly weakens the bond. Still, the measured bond strength of TiCo is large, and it greatly exceeds the estimated bond strength of both Ti, (1.23 f 0.17 eV)48 and Co2 (0.95 f 0.26 eV).48 In addition, the intrinsic bond strength of TiCo (3.63 eV) also greatly exceeds the estimated intrinsic bond strengths of Ti, (2.85 eV) and CO, (1.79 eV). Based on this result, it would appear that TiCo is likely to be an example of the Brewer-Engel bonding in which s-electron density is transferred from the early transition metal (titanium) to the late transition metal (cobalt). In this model d-electron density is in turn transferred from the late transition metal (cobalt) back to the early transition metal (titanium), resulting in very significant d-orbital contributions to the bond.

In confirmation of the Engel-Brewer bonding model for TiCo, Van Zee and Weltner have determined the ground electronic state of matrix-isolated TiCo4' to be by electron spin resonance (ESR) spectroscopy. Their analysis of the hyperfine coupling in this system shows the unpaired spin to have 33% character of 4s on titanium, 33% 3d on titanium, 25% 4s on cobalt, and 8% unidentified. The presence of so much 4sTi,c0 character in the unpaired spin suggests that the ground state of this molecule does not correlate to the doubly promoted 3d34s1, SF (Ti) + 3d84s', 4F (Co) separated atom limit, since a strongly bound state deriving from this limit would be expected to spin-pair the 4s electrons of titanium and cobalt, resulting in rather little spin density in the 4s-based orbitals. Instead, the ground state probably derives from the lowest singly promoted separated atom limit of 3d24s2, 3F (Ti) + 3d84s', 4F (Co). From this limit the net total of 10 d electrons can lead to a u2r464, 'E+ angular momentum coupling of the d electrons, which then couple to a u2u* configuration of the 4s electrons to give the observed ,E+ ground state. The small value of the total electron spin of the molecule (S = I / , ) implies that the d electrons are all spin-paired, which in turn implies that the d orbitals are strongly split into bonding and antibonding orbitals. Of course, some hybridization of the d and s orbitals is certain to occur, as is evident in the ESR results. Nevertheless, a nominal d-electron bond order of 5, along with an s bond order of '/, is expected for this ~ u ~ d u ~ d ? r ~ d 6 ~ s u * , ,E+ molecule, and this is consistent with the great bond strength observed in our work.

the isovalent TiRh molecule has been determined by Knudsen effusion mass spectrometry to possess a very large bond strength of 4.01 f 0.15 eV,39 again much greater than that of either Ti, (1.23 f 0.17 eV)48 or Rh2 (2.92 f 0.22 eV),39 suggesting a strongly bound s ~ ~ d u ~ d r ~ d 6 ~ s u * , 2Z+ ground state as well. Likewise, the bond energy of the isovalent TiIr molecule has recently been measured to be 4.37 f 0.28 eV by the second law method and 4.31 f 0.02 eV by the third law method, giving a selected value of 4.33 f 0.14 eV.49 This, too, is significantly greater than the bond strength of Ti, (1.23 f 0.17 eV)48 or Irz (estimated at 3.7 f 0.7 eV),48 again suggesting a strongly bound s ~ ~ d u ~ d r ~ d 6 ~ s u * , ground state for TiIr.

The VNi molecule also consists of a combination of an early and a late transition metal, and might also be expected to follow the Brewer-Engel bonding model.46 However, the intrinsic bond strength of this species, 2.35 eV, is only 0.32 eV greater than the bond strength of its coinage metal analogue, Cu, (2.03 f 0.02 eV).50 This would indicate smaller contributions from d-electron

In further confirmation of the Brewer-Engel

(49) Pelino, M.; Gingerich, K. A.; Gupta, S. K. J . Chem. Phys. 1989, 90, 1286.

The Journal of Physical Chemistry, Vol. 96, No. 6, 1992 2485

bonding in VNi than was found for TiCo. As was the case for TiCo, the ESR spectroscopic results of Van Zee and W e l t r ~ e r ~ ~ are extremely helpful in understanding the bonding in this molecule. These investigations have determined that VNi possesses a 42 ground state, with the unpaired spin having approximately 10% 4s character on vanadium. A small, negative dipolar hy- perfine component associated with 5'V implies that the remaining electron spin associated with vanadium is primarily 3d6 in character. Based on these observations Van Zee and Weltner suggest the s$d~?dr~d6~d6*~su*~ configuration as the ground state of VNi. Unlike TiCo, where hyperfine interactions with both nuclei could be observed, in VNi it was only possible to observe hyperfine interactions with the 5'V nucleus. Accordingly, the proposed electronic configuration is not as definite as it was for TiCo. On the other hand, this configuration makes physical sense, since it would correlate to the 3d34s2, 4F (V) + 3d94s1, 3D (Ni) separated atom limit, the lowest level of which lies only 204.786 cm-l above ground-state atoms [3d34s2, 4F (V) + 3d84s2, 3F (Ni)].M Presumably, the du, d r , and d6 orbitals would have large amplitude on the nickel atom, because of its larger nuclear charge; accordingly the d6* orbital would have large amplitude on the vanadium atom. Of course, some contribution from the s ~ ~ d u ~ d r ~ d 6 ~ d 6 * ~ d u * ' configuration would be expected as well, thereby allowing du-su hybridization to occur.

Assuming this s ~ ~ d $ d r ~ d 6 ~ d 6 * ~ s u * ' configuration is essentially correct, the electronic configuration of VNi is very similar to that of TiCo, differing only by the addition of two d6* electrons. Although this reduces the formal d electron bond order to 4 and preserves the s bond order of I/, , it is difficult to rationalize the reduced bond strength in VNi as compared to TiCo, since the d6* electrons which distinguish the two molecules are generally thought to be rather nonbonding in character. A likely contributor to the reduced bond strength of VNi results from the reduced size of the 3d orbitals in V as compared to Ti, and in Ni as compared to Co. Table I also provides a list of the radial expectation values ( r3d) for the two atoms making up each of the transition-metal diatomics listed, as obtained by numerical Dirac-Fock calculations on the at0ms.j' For TiCo the sum of these two radii, which gives some indication of the internuclear distance at which the 3d orbitals of the two atoms interact most strongly, is 1.337 A. For VNi this value is reduced to 1.234 A, while in Ni, it drops to 1.028 A. From previous work8,'8,48*so it is known that the bond length and bond strength of Ni, are essentially identical with those of NiCu and Cu,, demonstrating that the d9 cores on the nickel atoms are uninvolved in the chemical bonding. While some d-orbital contributions to the bonding are still retained in VNi, it seems likely that the smaller size of the orbitals in VNi as compared to TiCo is the root cause of the observed reduction in bond strength.

Van Zee and Weltner have also reported ESR results on the TiV molecule, which is thereby determined to have a 4Z ground state.43 On the basis of observation of hyperfine interactions between the electron spin and both the s'V and 47Ti nuclei, these investigators conclude that the wave function of the unpaired spins contains about 8% su character on V and 7% su character on Ti, with the remainder of the spin distributed in the 3d orbitals in such a way that the dipolar hyperfine coupling constants are small and negative. This in turn implies that the remainder of the spin is primarily in d6 orbitals. Accordingly, the s ~ ~ d u ' d r ~ d 6 ~ con- figuration is proposed for the ground state, with the implication that a certain amount of su-du hybridization is occurring. This is very similar to the su:du:dr:d6:, 3E; ground state of V,, par- ticularly since the ground-state configurations of both molecules correlate to doubly promoted separated atom limits. The lack of one da-bonding electron in TiV as compared to V, is expected to reduce its bond strength, although some compensation for this effect should result from the larger size of the 3d orbitals in

(50) Morse, M. D. Chemical Bonding in the Late Transition Metals: The Nickel and Copper Group Dimers. Advances in Metal and Semiconductor Clusters, Vol. I . Spectroscopy and Dynamics; JAI Press: Greenwich, CT, in press.

( 5 I ) Desclaux, J . P. At. Dura Nucl. Data 1973, 12, 3 11.

2486 J . Phys. Chem. 1992, 96, 2486-2490

titanium as compared to vanadium. With this in mind, the in- trinsic bond strengths of TiV and V2 are expected to be similar, with V, somewhat more strongly bound. This is indeed found to be the case, with the two molecules having intrinsic bond strengths of 3.13 eV (TiV) and 3.25 eV (V?). In this case, the great difference in measured bond strengths for the two molecules (0.68 eV) results primarily from the increased promotion energy which is required to prepare the titanium atom for bonding (0.8 1 eV, as compared to 0.25 eV for vanadium).

The remaining species listed in Table I (Ni,, NiPt, and Pt,) are all late-transition-metal diatomics for which the nd orbitals are quite contracted. In Ni, this contraction is so severe that 3d contributions to the chemical bond are essentially absent. In Pt,, however, relativistic contractions of the ns orbitals lead to better shielding of the 5d orbitals from the nuclear charge, causing the 5d orbitals to expand and become more accessible for chemical bonding. As a result, the intrinsic bond strength of Pt, is 0.85 eV greater than that of its coinage group congener, Au,. This implies a very strong interaction between the 5d orbitals on platinum, and suggests s~~du:d?~~d6:d6:~d?r;4 as the primary electronic configuration of fit,, giving a net bond order of 2 for the Pt, molecule. The NiPt molecule falls midway between Ni, and Pt2 in its bond strength, undoubtedly because the combination of a very small 3d orbital on nickel with a large, accessible 5d orbital on Pt gives a 3d-5d bond intermediate in strength between those found in Ni, and Pt,.

V. Conclusions Abrupt predissociation thresholds have been observed in the

resonant two-photon ionization spectra of TiV, V2, TiCo, and VNi, permitting the bond strengths of these molecules to be determined as D,(TiV) = 2.068 f 0.001, D0(V2) = 2.753 f 0.001, Do(TiCo) = 2.401 f 0.001, and D,(VNi) = 2.100 f 0.001 eV. These molecules join NiPt,18 and Pt2I4 as transition-metal diatomics for which an abrupt predissociation threshold in an extremely congested electronic spectrum has been used to measure bond

strengths. An argument for the requirements needed to determine the bond

strength by the onset of p r e d i i a t i o n has been presented, yielding two criteria which must be fulfilled for the method to be suocessful. First, the molecule must possess a very large density of electronic states a t its lowest dissociation limit. Second, the lowest disso- ciation limit must generate repulsive electronic states since pre- dissociation in a set of nested potential energy curves may not be efficient.

The chemical bonding in TiV, V,, TiCo, VNi, Ni,, NiPt, and Pt, has been discussed in relation to the electronic configurations of the ground-state molecules (in so far as they are known). The contribution of the d orbitals to the measured bond strength has also been considered by taking into account the promotion energy required to prepare the atoms for bonding and by comparison with the filled d-subshell coinage metal diatomics. The d-orbital contributions to the chemical bond in TiV, V2, Ni2, NiPt, and Pt, are found to be 1.10, 1.22,0.04, 0.46, and 0.85 eV, respectively. In the cases of TiCo and VNi it is somewhat more difficult to estimate the d-orbital contributions to the bonding, since the molecular ground states do not correlate to the d"dmsu2 states which characterize the coinage metal diatomics, but correspond instead to d"dmsu2su*1 states. Nevertheless, the d-orbital con- tributions to the bonding in TiCo are 0.47 eV greater than in VNi, and it is argued that this is primarily a result of the larger size of the 3d orbitals in Ti and Co than in V and Ni, respectively.

Acknowledgment. We thank Jeff Bright for his expert prep- aration of the TiV, TiCo, and VNi alloys, and Professor William H. Breckenridge for the use of the intracavity etalon employed in high-resolution studies, which allowed the predissociation thresholds to be accurately measured using the absorption spec- trum of I,. We gratefully acknowledge research support from the National Science Foundation under Grant CHE-8912673. Acknowledgment is also made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research.

Zero-Fieid Splitting of the First Excited Triplet State of Dlbenzocycioheptadienyiidene. A Carbene to Biradical Transformation upon Electronic Excitation

A. Despres, V. Lejeune, E. Migirdicyan,* Laboratoire de Photophysique MolPculaire du CNRS, B6timent 21 3, UniversitP de Paris-Sud, 91405 Orsay Cedex, France

and M. S. Platz Department of Chemistry, The Ohio State University, Columbus, Ohio 43210 (Received: October 15, 1991)

The quasi-line fluorescence and excitation spectra of dibenzocycloheptadienylidene (DBC) in n-hexane at 20 K, obtained by site-selective laser experiments, do not present mirror-image symmetry. The fluorescence decay of matrix-isolated DBC is nonexponential and attributed to the emission from different sublevels of the first excited triplet state. In the presence of a magnetic field, the lifetime of the slow component decreases. Its dependence as a function of a weak magnetic field can be calculated for different values of the zero-field splitting parameter D. The best fitting value is ID1 = 0.02 cm-I. The D value in the first excited triplet state is significantly smaller than in the ground state where ID/ is known to be 0.3932 cm-I. The decrease of the D value is interpreted with very simple molecular orbital theory. The excitation of DBC takes electron density off the carbene center and delocalizes it into the aromatic rings.

Introduction Conventional electron paramagnetic resonance (EPR) and the

optically detected magnetic resonance (ODMR) methods have been commonly used to determine the zero-field splitting (ZFS) parameters D and E of triplet states having lifetimes longer than milliseconds. These techniques are, however, more difficult to apply to excited species having shorter triplet lifetimes since their

steady-state concentration is very low. In a recent paper,l we Presented a method that allows one to determine the ZFS Pa- rameter D Of excited triplet states Of m-xylylene biradicals having lifetimes Of the order Of microseconds or shorter. The method

(1) Lejeune, V.; Despres, A.; Migirdicyan, E. J . Phys. Chem. 1990, 94, 8861

0022-3654/92/2096-2486%03.00/0 0 1992 American Chemical Society