J . Phys. Chem. 1992, 96, 2479-2486
2Sstate, augmented with a diffuse s function optimized24for the
IS state of the negative ion, and three diffuse p functions optimi ~ e for
d ~the~ 2Pstate 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 optimized24for 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 study5J4of 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 ao3and 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
2479
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 at the MCPF level is 1.173 ao2at 2.068 ao.
Correcting this for vibrational effectsz8yields a value of 1.16 ao2,
which is at 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 at the
experimental re value is computed to be 14.76 a: at 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 following 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.; Laaksonen, 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 The Journal of Physical Chemistry, Vol. 96, No. 6 , 1992
of diatomic and triatomic
resonant two-photon ionization 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 information 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,8-10NiPt,” 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,I8V2,’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 transition-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
(4) Leopold, D. G.; Lineberger, W. C. J . Chem. Phys. 1986, 85, 51.
( 5 ) Leopold, D. G.; Almholf, J.; Lineberger, W. C.; Taylor, P. R. J . Chem.
Phys. 1988, 88, 3780.
(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 .
Chem. Phys. 1988, 89, 5517.
(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,
2698.
(12) Taylor, S.; Spain, E. M.; Morse, M. D. J . Chem. Phys. 1990, 92,
27 IO.
(13) Spain, E. M.; Behm, J. M.; Morse, M. D. Chem. Phys. Lett. 1991,
179, 411.
(14) Spain, E. M.; Morse, M. D., manuscript in preparation.
(15) Bishea, G. A.; Marak, N.; Morse, M. D. J . Chem. Phys. 1991, 95,
5618.
(16) Bishea, G. A,; Pinegar, J . C.; Morse, M. D. J . Chem. Phys. 1991,95,
5630.
(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
1990, 102, 183.
(26) Behm, J. M.; Arrington, C. A,; Morse, M. D., manuscript in preparation.
(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.
1974, 36, 381.
(30) Efremov, Y . M.; Samoilova, A. N.; Kozhukhovsky, V. B.; Gurvich,
L. V. J. Mol. Spectrosc. 1978, 73, 430.
(31) Samoilova, A. N.; Efremov, Y . M.; Zhuravlev, D. A,; Gurvich, L. V.
Khim. Vys. Energ. 1974, 8, 229.
(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 . A m . 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.
1989, 90, 5466.
(37) Loh, S. K.; Lian. L.; Armentrout, P. B. J . Am. Chem. SOC 1989, 1 1 1 .
3167.
(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.
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 resulting 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,25V2,25Ni2,18NiPt,”
Pt2,7AlNi,26and Cr2+40have 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 comparison 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 investigations 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
+ Co,
-
-
+ TiCo
TiCo + Co
Ti
(2.1)
(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,
(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 twophoton 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 predissociation threshold energy was established by monitoring the
precisely known41transmission 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,41so 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 Molecule 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
600
-
B
i
7
~
400
I
200
n
r6400
16500
16600
16700
16800
Frequency (cm.1)
Figure 1. Predissociation threshold in TiV, observed by resonant twophoton 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 terminates 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 transitions 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 predissociated 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 I4.5,
dissociation to ground-state atoms will be possible. The ground
state of TiV is known43to be 4X1,2, so transitions from this 0''
= 0.5 component can only populate excited states with Q I1.5,
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, I99'2
2500
2000
Spain and Morse
A
c
21700
21XoO
21900 2 2 h 22;00
Frequency (cm-I)
I
I
I
I
I
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-atomlimits are
attractive, and will dip below the ground-separated-atom limit. Accordingly, an abrupt predissociation threshold is expected for all three
species as soon as the molecule is excited above its lowest dissociation
limit.
0
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 repulsive dtid$u2u*2states 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 dissociation 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 momentum JTiinteracting 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,44it 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 N2give only 50, 18, and 10 molecular
states arising within 10 000 cm-l of ground-state atoms, respectively. 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.
Figure 3. Resonant two-photon ionization spectrum of V,, near its dissociation 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 excited by optical transitions from the ground X 3ZJO''=Oi) level cannot
predissociate to ground-state atoms, but can dissociate at the first excited-separated-atomiclimit, 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 predissociation 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
4F3,2excitation energy in the vanadium atom (137.38 cm-I)."
The close correspondence between these two values further substantiates 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 predissociation 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 yprovided
~~
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
+
-
*
The Journal of Physical Chemistry, V O ~96,
. No. 6,1992 2483
Bond Strengths of TiV, V,, TiCo, and VNi
J
I---
5w
1500
16750
16850
16950
17050
17150
Frequency (cm.1)
I
19000
19200
19400
19600
Frequency (cm
19800
20000
’)
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 termination 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 Lin38assumed 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 dissociation 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 collisioninduced dissociation and resonant two-photon ionization studies
are not clear at 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 titanium, resulting in a strong interaction of the type envisioned
by Brewer and E ~ ~ g e lWith
. ~ ~ 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 at
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)4xor 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.
Figure 5. Predissociation threshold in VNi, observed by resonant twophoton ionization using a dye laser operating on rhodamine 610 in conjunction 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 measurement 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 information. 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 3d34s2,4F3j2and 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 I2.5 to ground-state atoms. Accordingly, the observed 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 Predissociation. By monitoring the onset of predissociation in a severely
congested optical spectrum, we have measured the bond strengths
of VNi,25 V2,25TiCo, and TiV. These four molecules join Ni2,Ix
NiPt,” Pt2,’ AlNi,26and 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 transition-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 NiPdt2and 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.
2484
The Journal of Physical Chemistry, Vol. 96, No. 6, I992
Spain and Morse
TABLE I: Bond Strengths of Selected Transition-Metal Diatomics
molecule
TiV
v2
TiCo
VNi
measured bond intrinsic bond modified intrinsic coinage analogue
strength, eV strength,' eV bond strength! eV bond &ength;eV
2.068d
2.753d3e
2.4Old
2.1 004.'
2.068'
2.7989
3.14h
3.119
3.243
3.624
2.345
2.068'
2.798'
3.14
2.313
i
2.818
2.345
2.068'
2.798'
3.14
2.03(C~,)~
2.03 (Cui)'
2.03 (CU~)'
2.03 (Cu2)'
2.03 (Cu2)'
2.34 (CuAu)'
2.29 (Au#
(r"d),c
A, eV
1.09 (0.28)
1.21
1.59 (0.79)
0.32
0.04
0.46
0.85
A
atom A atom B
0.793
0.720
0.793
0.720
0.514
0.514
0.874
0.720
0.720
0.544
0.514
0.514
0.874
0.874
sum
1.513
1.440
1.337
1.234
1.028
1.388
1.748
measured bond
length, A
1.766O
2.206
Ni2
2.2088
NiPt
Pt2
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. CFromthe Dirac-Fock SCF calculations of Desclaux (ref 51), erroneously given in Bohr radii rather than in A in ref 25. dThis work.
CFromref 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.
'
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 (3d94s1or 3d84s2)or 6s orbital
of platinum (5d96s1or 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 SI or s2 nickel
or platinum atom attractive. As a result, the first repulsive potential 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 palladium-containing species NiPd and PdPt.
The remaining examples of transition-metal-containing diatomics 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 uwhich
* , 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 and
u * ' 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 ~ ~ ~ uifl uthe
* ~4s
electron of nickel and the 3pu electron of aluminum are tripletcoupled, 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 dms2atom, or when a d"sl atom combines with a dmslatom.
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-dms2or dnsl-dmslcategories 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' + dms2separated 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)48and 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,c0character 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,E+
~ s umolecule,
*,
and this is
consistent with the great bond strength observed in our work.
the
In further confirmation of the Brewer-Engel
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,39again much greater than that of either Ti, (1.23 f
0.17 eV)48or Rh2 (2.92 f 0.22 eV),39suggesting a strongly bound
s ~ ~ d u ~ d r ~ d 62Z+
~ s ground
u * , 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)48or Irz (estimated at 3.7 f 0.7 eV),48
again suggesting a strongly bound s ~ ~ d u ~ d r ~ d 6 ~ s ground
u*,
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
+
(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 investigationshave determined that VNi possesses
a 42ground state, with the unpaired spin having approximately
10% 4s character on vanadium. A small, negative dipolar hyperfine 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 6configuration
*~du*'
would be expected as well,
thereby allowing du-su hybridization to occur.
Assuming this s ~ ~ d $ d r ~ d 6 ~ d 6 * ~configuration
su*'
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 47Tinuclei, 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 con~d6~
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,, particularly 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 intrinsic 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 Pt2in 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,.
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 at its lowest dissociation limit. Second, the lowest dissociation limit must generate repulsive electronic states since predissociation 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"dmsu2states
which characterize the coinage metal diatomics, but correspond
instead to d"dmsu2su*1states. Nevertheless, the d-orbital contributions 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.
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
moleculesjoin
NiPt,18 and Pt2I4as transition-metal diatomics
for which an abrupt predissociation threshold in an extremely
congested electronic spectrum has been used to measure bond
Acknowledgment. We thank Jeff Bright for his expert preparation 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 spectrum 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 Parameter 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%03.00/00 1992 American Chemical Society