J. Phys. Chem. 1992, 96, 8277-8282
8277
Electronic Structure, Bonding, Geometry, and Some Spectroscopic Properties of the Scandium-Nlckei Molecule Saba M. Mattar* and William D. Hamilton Department of Chemistry, University of New Brunswick, Bag Service No. 45222, Fredericton, New Brunswick, Canada E3B 6E2 (Received: May 6, 1992; In Final Form: June 16, 1992)
A set of LDF-LCAO computations that take into account electron-electron exchange and correlation are used to investigate the structure, bonding, and spectroscopic properties of the five lowest states (XzZ+,AZZ+,A'211, B'211, A"zA) of ScNi. Both compact and extended one-particleGaussian basis sets are employed in the calculations. The zZ+ground state arises from the 13at5r,25r;16~$16x; electronic configuration and is the same as that predicted by EPR spectroscopy. In both studies, the unpaired electron is suggested to reside mainly on the scandium atom, and the computed Sc s-character is in agreement with that determined from the experimental hyperfine splittings. A detailed description of the bonding and the valence one-electron molecular orbitals is presented. The we, w q e , Be, +e, ae,Be, spectroscopic constants, p(R)IRcand its derivatives are also computed for the five states. Vertical excitation energy computations predict that the experimental B'211 state observed electronic configuration. recently has the 12a25rxz5r~7rx1
Introduction The main difficulty encountered in the formation and detection of gas-phase transition-metal diatomics is their transient nature due to their high reactivity. This problem is minimized when they are isolated and prevented from further reaction. Consequently, a vast number of transition-metal diatomics were investigated after their isolation in inert gas matrices. These studies have been reviewed by Weltner and Van Zee.'J Homogeneous transition-metal diatomics are easier to prepare than heterogeneousones since this requires the generation of only a single metal atom species in the gas phase. In contrast, the preparation of mixed-metal diatomics requires the generation of two atomic elements which must react in sufficient quantities to form heterogeneous metal diatomics. In such cases,homogeneous diatomics are also inevitably formed which reduce the yield of the heterogeneous molecules.' Despite these extra experimental difficulties, it has recently been possible to generate and study a variety of heterogeneous metal diatomics in the gas phasea4 Electron paramagnetic resonance (EPR) spectroscopy has been used to characterize a number of matrix-isolated mixed-metal d i a t ~ m i c s . ~From - ~ the experimentally determined spin Hamiltonian parameters (fine, hyperfine, and g tensors), the ground state for these molecules is usually determined.',z-s-9 A large number of theoretical studies and electronic structure computations on homogeneous metal diatomics are now available. Several excellent reviews on the subject have been published, including those of Salahub,loShim," Walch et a1.lZand Koutecky and Fant~cci.'~ On the other hand, only a few computations on mixed-metal diatomics have been reported. The diatomics formed by the reaction of Fe with Mn, Co, Ni, and Cu have been investigated using the discrete-variational and X a (DV-Xa) approximation~'~ and HartreeFock self-consistent-field(HF-SCF) technique^.'^ The electronic structure of FeCr has been studied using the scattered-wave SCF-Xa method and compared with matrix-isolation results.I6 Results for NiFe and NiCu using HF-SCF and configuration-interaction (CI) methods are also available. 7 ~ 1 8 The local-density-functionallinear combination of atomic orbitals (LDF-LCAO) method has been used successfully to investigate homogeneous transition-metaldiatomics such as V2, Mnz, Crzrand M02.19,20This method has also been used previously to confirm the sextet ground state for VCO.z' In addition, TiV and VNi were investigatedu and found to give the same quartet ground states determined experimentally.6 In an ongoing effort to demonstrate the usefulness of the LDF-LCAO method?' it was felt that a Brewer-Engel diatomic with a doublet ground state should be tested. These molecules are formed by the combination of transition-metal atoms from the opposite sides of the periodic table and have strong multiple bonds that result in low-spin multiplicitie~.~~ The test molecule
is best investigated in the light of available experimental data. Van Zee and Weltner8 have used X-band EPR spectroscopy to study the matrix-isolated ScNi, ScPd, YNi, and YPd diatomics. In accordance with isovalent principle, all these Brewer-Engel molecules were found to have 2Z+ground states with the unpaired electron situated mainly on the lighter atom.8 Contrary to the experimental findings, the electronic structure of YPd was first computed and found to have a 2A ground statez5awhile recent HF-SCF-CI computations predict that all four diatomics have zZ+ ground states.25b Thus, it is quite important to check the ground states of these molecules by a different and complementary computational method such as the LDF-LCAO. Ideally, one would like to compute the electronic structure of all four diatomics. However, ScNi is the only one that does not require relativistic corrections to correlate theory and experiment. Consequently, only ScNi is reported in this paper. From its EPR spectra, Van Zee and Weltner8 proposed that its valence shell orbital configuration is 4saz3d~3ds43d~44su*'. Very recently, the gas-phase spectrum of ScNi has also been recorded.26 The ground state in the gas phase was found to be the same as the one encountered in a matrix. The preliminary analysis of the spectra shows an excited 211state lying approximately 10 107 cm-I above the XzZ+. Some of the spectroscopic constants for this 211 state were also measured.z6 Although EPR is an extremely powerful technique for the elucidation of the electronic structure of molecules, it cannot predict properties such as equilibrium bond lengths and binding energies. These properties may be computed using the LDFLCAO method. Charge distribution and spin densities at the nuclei may also be computed using this method and compared directly with those obtained by EPR spectroscopy. Other methods of computation, such as HF-SCF and HF-SCF-CI methods, have proven more difficult in handling transition-metal diatomics and clusters.'O MiedemaZ7has computed the binding energies for all the first-row mixed-transition-metal diatomics by extrapolating the binding energies from bulk metal data. Predicted dissociation energy values for diatomics composed of the 3d, 4d,and 5d metals were reported. The dissociation energy was estimated to be 3 16 kJ/mol (3.3 eV) for ScNiaZ7 Computational Details
The optimal bond distance and electronic structure of the ground and low-lying excited states of ScNi are determined using the LDF-LCAO method. Detailed descriptions of the method have been previously reported.21-z3a*28-z9 Two types of basis sets are used in this study. The larger one is derived from Wachters' original 14s/9p/Sd primitives contracted to [62111111/3312/32].30 The basis sets are further augmented by p and d functions. Their exponents are 0.0833 and 0.02778
0022-3654/92/2096-8277t03.00/0 0 1992 American Chemical Society
8278 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
Mattar and Hamilton
TABLE I: Spectroscopic Constants for Some Sekcted Diatodcs" in Their Ground States state Re (A) De (eV) w,b W&X, Be a,
8,
*C
PI&
lafi/8Rl2
ref
'602
x3z, 12C160
X'Z' '2C2 XlZ: 52Cr2 XlZ:
1.210 1.207 1.207
7.601 5.080 7.010
1569.2 1580.3 1610.0
14.720 12.073
1.359 1.446
4.1
71.0 158.0
13.13
c, d
1.130 1.128 1.127
13.022 11.108 11.980
2167.6 2170.2 2160.0
22.702 13.461
1.818 1.931
5.1
90.0 175.0
5.51
1.237 1.242 1.243
7.389 6.300 5.970
1837.9 1855.6 1920.0
30.240 14.080
1.733 1.821
6.2
98.6 183.0
9.76
c, d
1.667 1.680 1.680
2.820 1.600 2.600
569.0 470.0 520.0
10.114 9.000 6.000
0.220
13.0
5.1
1.97
C
e 40 4.226 -0.12241 4.240
2.983 2.75641 2.723
c, d
e 40
e 40
42 20a
"The units of we, w p , , and Be are in cm'l. a, is in lo4 cm-I, while a, and 8, are in cm-l. Those of fiI& and lap/aRI2 are debye and debye/bohr, respectively. bFor the simple diatomics the accuracy of we is =*15.0 cm-I, while for transition-metal diatomics" it is =&40.0 cm-I. 'This work. d13s/8p basis setg8contracted to 7 ~ / 4 p . )CReference ~ 34, Table 39.
for Sc and 0.1531 and 0.05103 for NL3' The smaller basis sets of Andzelm et al.31(1 3s/8p/Sd contracted to [4333/431*/311']) are also used in separate computations. Due to the compact nature of the latter basis sets, basis set superposition error (BSSE) corrections are also performed. The counterpoise method of Boys and Bernardi is employed.32 The method requires that the total energy of the atoms be computed separately.20a The same C,, symmetry adapted basis sets used for the diatomic are also used for the Sc and Ni fragments. As expected for the larger basis set, no appreciable difference in the results is observed due to the BSSE corrections. The SCF iterations are continued until the relative change in both the charge density and exchange-correlation potential is less than A complete Mulliken population analysis is carried out for the molecule in its ground state. As stated previously,22these results may be used cautiously in conjunction with contour diagrams for the wave functions to provide a semiquantitative picture of the structure and bonding. In order to compute the molecular spectroscopicconstants, the total energy is expressed as a fourth-degree polynomial E,, = -De + f ( R - Re)2- g(R + j(R - Re)* (1) and the Levenberg-Marquardt nonlinear least-squares method33 is used to fit E,o, to 25 R values (in a 0.25 au range) around the minimum. This yields numerical estimates of Re, De,f, g, and j. These values are related to we and w g e by comparing the G term of an anharmonic oscillator G(v) = web
+ Y2) - %
+ Y2I2
d V
(2)
to the energy in eq 1. Thus, the vibrational wavenumber and anharmonicity are34 w, = (f/2*27C2)1/2
(3)
and 15h32 Oge
-
256u6w:g3$
3jh2 32ir4w,2g2r2
(4)
where 7 is the reduced mass of the diatomic. Similarly, the rotational constant of a vibrating rotator, B,, is computed from the expression34
+ f/z)
(5)
Be = h/8r2cgRe2
(6)
B, = Be - a,(u where and35
(7)
In addition, the rotational constant 0p36 which takes into account the effects of centrifugal distortion, is also computed from the equations3'
9,= @e + D e b + Y2)
(8)
0,= 4B,3/w,2
(9)
and De
=
32B,'(wje) ---20a3,2 w,3 w,Z
a,2 6we
(10)
An additional program was written to determine the dipole moment and its derivatives as a function of the internuclear distance
Thus the terms
that are proportional to the intensities of the infrared vibrational transitions are also computed. The programs used for the determination of these properties are tested, and the results for a standard set of diatomics are given in Table I.w3 Identical values for we and w j , were obtained when using the present program and that of Grein and co-workers."
Results and Discussion Scandium-nickel is found to have a 22+ground state with a 1 3 d 5 ~ 2 ~ 5 ~ ~ t116wt1 ~ 1 6 +electronic configuration. The potential energy curves for d e ground and four low-lying excited states are given in Figure 1. These states are all stable as indicated by the minima of each curve, as well as the binding energy values. The lowest two excited states for this molecule are the 211 and the 2A. The binding energies, equilibrium bond distances,dipole moments, and its first derivative are listed in Table 11. Figure 2 contains the valence molecular orbitals for the ScNi ground state. Results of the Mulliken population analysis for this state are given in Table 111. By examining the population and distribution of the component atomic orbitals, one may determine the extent of bonding or antibonding within a molecular orbital. Figure 3 shows the contour diagram for the 1l d orbital. This orbital is an sdp hybrid with the dp forming the major component.
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8279
Electronic Structure of ScNi
TABLE II: Equilibrium DLst.accs, Binding Energies, lad Spectroscopic Coastratn for the ScNi Diatomic" state Re (A) De (eV) T, (cm-I) we W e 4 @e a, 8, X22+ 2.019 5.95 0.0 405.9 9.753 0.154 8.91 3.52 1.81 2.080 1.55 0.0 322.0 A22+ Aff2A
2.061 2.031 2.230 2.003 2.230 1.963
A'2l-I
B'2l-I Bf2l-I1/2 B%/2
4.92 5.27 5.35 4.54
8240.9 5386.8 6050.3 4797.5 7614.5 11331.3c 10222.0 10107.0
4% 1.802 0.400
l8d8Rl2 0.838
333.0 368.8 361.7
41.099 12.148
0.148 0.152
9.53 1.08
3.56 3.86
8.61 3.37
1.923 3.268
1.032 0.422
364.9
0.792
0.157
1.16
4.03
0.34
3.857
1.269
462.3 391.2 354.2
3.379 3.99 -9.70
0.163
8.11
3.45
0.56
1.715
0.632
ref
b 25b 26 b b 25b b 25b b 26 26
"Units are defined in Table I. bThis work. Obtained using Wachter's basis set.3o E D wnot ~ include splitting due to spin-orbit coupling. 4.0
4.5
-5.0
-5.5
1.8
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
R (4 Figure 1. Relative energy of ScNi states as a function of the internuclear bond distance, R. Basis sets are from ref 30. The energy scale is relative ) Ni("). to the sum of the ground-state energies of S C ( ~ Dand
Figure 3. Scandium-nickel contour diagram for the 1l a t orbital. Contour values are 0.04, 0.08, 0.12, and 0.16 for contours 1-4 and -0.04, -0.08, -0.12, and -0.16 for contours 5-8. The zero contour is denoted by a 0. Units are (e-/ad)1/2.
0.0
140
-3.0 v
-
130
Figure 4. Scandium-nickel contour diagram for the 12ut orbital. Contour values are listed in Figure 3.
Spin a
Spin 0
ScNi Figure 2. Spin-unrestricted valence molecular orbital diagram for the ground-state configuration of scandium-nickel. Core electrons occupy the 1s to 4% orbitals.
The contours show that the s and d9 atomic orbitals are in-phase and bonding in nature. Table I11 indicates that this orbital is mainly nickel character and arises from the donation of approximately 0.19 electron from the 3d,r(Ni) to the empty 3d,z(Sc) atomic orbital. However, the small sizes of the 3d,z(Ni) and 3d,a(Sc) result in small overlap values (0.02 for the spin-up component and 0.01 for the spin-down component). Thus, although donation occurs, the orbital may be classified as weakly bonding. Figure 4 depicts the contour diagram for the l2ot orbital. It is largely s in character, with only an 8% 3d9 contribution. This diagram, the large overlap values, and the almost q u a l contri-
Figure 5. Scandium-nickel contour diagram for the 1 3 d orbital. Contour values are listed in Figure 3.
butions from the 4s(Sc) and 4s(Ni) (Table 111) indicate that a strong covalent bond is formed.
Mattar and Hamilton
8280 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 TABLE 111: Mulliken Population Analysis for the ScNi Ground State orbital analysis orbital overlap llat 1la1 12at 12a4 13at 5?r+' 5x41 16t+
16'1 totals
0.02 0.01 0.32 0.33 -0.21 0.15 0.14 0.04 0.03
0.02 0.0 1 0.48 0.43 0.35
scandium P 0.00 0.00 0.01 0.02 0.15 0.01 0.01
1.29
0.20
S
d 0.19 0.17 0.00 0.0 1 0.24 0.32 0.28 0.09 0.06 1.36
nickel P
0.04 0.02 0.42 0.47 0.19
0.00
0.00 0.00 0.00 0.02 0.0 1 0.01
d 0.75 0.79 0.08 0.06 0.05 1.66 1.70 1.91 1.94
1.14
0.04
8.94
S
occupation no.
Figure 6. Scandium-nickel contour diagram for the 57rt orbital. Contour values are listed in Figure 3. The plane denoted is 1 8, above the molecular axis.
The highest occupied molecular orbital (HOMO) is the 1307 orbital. Its contour is shown in Figure 5. It has larger dZ2 character than the 12at orbital. Table I11 shows that the scandium atom constitutes 74% of this orbital's character. The large scandium character is illustrated in Figure 5 by the zero contour between the atoms being "bent" toward the nickel. This orbital is clearly antibonding in nature and is confirmed by the overlap value of -0.21 listed in Table 111. The 57r orbitals are predominantly due to 3d-type interactions. Fi re 6 shows typical d7r bonding between the two atoms for the 57r$.' . It is largely nickel in character, which may be noted by the higher contour values on the nickel. The orbital population in Table I11 shows that the 3dx,(Ni) and 3d,,,(Ni) orbitals donate 0.60 of an electron to the empty 3dx,(Sc) and 3dJSc). The overlap values of 0.15 and 0.14 indicate that the resulting 57r molecular orbitals are bonding and that significant delocalization of charge has occurred. Figure 7a exhibits the 161 orbital. The contours indicate that it is also mainly Ni in character. Table I11 shows a scandium population of only 0.15 electron while that of the nickel constitutes 3.85. Thus, donation also occurs from the 3d+2(Ni)and 3d (Ni) to the corresponding Sc atomic orbitals. Overlap values oy0.04 and 0.03 and the wave function contour diagram show that there is little delocalization of the nickel charge to the internuclear region, indicating a weaker &bond than the corresponding 57r. This is illustrated in Figure 7b. The total populations listed in Table I11 reveal that scandium has a valence population of d1.36s1*29 while the nickel has a d8.94s1.14 valence orbital occupation. One may qualitatively conclude that the d9s1state of Ni participates in the bonding of the ground-state molecule. Assignment for the scandium is more difficult due to the nearly equal occupations for the d and s valence orbitals. The gross atomic charges show that approximately 0.1 5 of an electron is transferred from the scandium to the nickel. The overall analysis indicates that the ScNi diatomic has one strong a-bond, two weaker 7r-bonds, and two very weak 6-bonds. These bonds are further weakened by the antibonding nature of the 13a SOMO. An electron configuration of
Figure 7. Scandium-nickel contour diagrams for the lat orbital. (a, top) Top view. Contour values are listed in Figure 3. (b, bottom) Corresponding three-dimensional view. The planes are 1 8, above the molecular axis.
was proposed.8 The oneelectron MO and contour diagrams of Figures 2-7 closely support this configuration. From the EPR hyperfine splittings, Van Zee and Weltner8 found that the unpaired electron has 35.2% s character on the scandium center. This is in excellent agreement with the value listed in Table 111. The isotropic hyperfine splitting constants may also be computed from net spin densities at the appropriate nuclei. For a given nucleus B 87r
A'""@) = - g 8 g N @ N { c I x m , a ( B ) 1 2 3 m
- clxm'.B(B)12} m'
( l 3,
where xm,,(B) and X ~ , , ~ ( Brepresent ) the occupied spin-up and spin-down orbitals, respectively, g N is the gyromagnetic ratio of the nucleus B, and BN is its nuclear m a g n e t r ~ n .In ~ ~eq 13, the expression in brackets is the net spin density at the nucleus. In the present computations, the ground-statewave function is a single Slater determinant and may be contaminated with states of higher multiplicity. However, the contamination is expected to be small because the diatomic has no low-lying quartet states.25bOnly the isotropic hyperfine splitting constant for the Sc center was determined from EPR spectroscopy.8 The reported value was 994
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8281
Electronic Structure of ScNi
from HF-SCF-CI computations.2sb In addition, the amount of 4s(Sc) character of the HOMO predicted by the LDF method is in excellent agreement with that found experimentally.* There are few computations for heterogeneous metal diatomics that predict their ground states, bond lengths, and bond energies. The present ScNi and previous VNi and TiV results2*suggest that the LDF-LCAO method may adequately predict the geometry, electronic structure, and charge distributions of mixed-metal diatomics. In addition, from the computations it is also possible to carry out a detailed analysis of the structure and bonding in terms of the diatomic one-electron molecular orbitals.
1 Figure 8. Scandium-nickel contour diagram for the 77rt orbital. Contour values are 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06 for contours 1-6 and -0.01, -0.02, -0.03, -0.04, -0.05, and -0.06 for contours 7-12. The contour plane is 1 A above the molecular z axis.
MHz. The net spin densities at the Sc and Ni nuclei are computed and found to be 0.933 and 1.601 a ~ - respectively. ~, The use of eq 13 leads to a value of 1015 MHz for the Sc center. Thus, the Sc isotropic hyperfine constants determined from theory and experiment are in good agreement. The binding energies and equilibrium bond lengths are listed in Table 11. Ovemtimation of the binding energies is a well-known consequence of the LDF a p p r o ~ i m a t i o n . ~This ~ ~ -overbinding, ~-~~ in some cam,may be as large as several electronvolts. A post-SCF nonlocal correction method46v48-5’ to the LDF-LCAO program, which helps reduce these values, is now being tested. Not surprisingly, our computed binding energy for the ground state is larger than that previously predicted by Miedema.27 It is difficult to compare the binding energies obtained by the two methods. The present method relies on the total energies obtained by a quantum mechanical technique while that of Miedema is independent of the diatomic ground state and derived from the classical macroscopic AH/‘of the pure bulk metals.27 The binding energy corrected for nonlocal effects should eventually be compared with the experimental binding energy as it becomes available. The spectroscopic constants Re,we, w& and Be are computed for the five lowest states. Only a few experimentalvalues for these constants are available for comparison. Theoretical we values, computed using LDF methods, are usually larger than the corresponding experimental ne^.^^^,^^ Table I1 shows that the computed we for the X22+and B’211 states are approximately 70 cm-‘ larger than preliminary experimental values determined by Morse et a1.26 This is probably due to the overbinding caused by the LDF approximation. The experimental and computed anharmonicities, coge,for the B’211 and B’211112are reasonable. However, the calculated values are dependent on the number of energy points used in fitting eq 1 and at least 20 points are needed for consistent results. The experimental B’2111/2 X22+ and B’2113 X2Z+ transitions occur around 10222 and 10 107 cm-I. $he present excited state computations predict a similar transition around 11 331 cm-’due to the promotion of the 13u electron to the empty 7?r orbital. The population analysis of the 7r orbital indicates that it is 82.0% 4p(Sc), 1.9% 3d(Sc), and 16.0% 4p(Ni). The 77 contour plot is given in Figure 8. From this figure it is clear that the predominant 4p(Sc) and the 4p(Ni) are bonding in nature and result in a typical ?r-bond. The residual 1.9% 3d(Sc) character is also apparent in the contour plot.
-
-
Conclusions In conclusion, the LDF-LCAO results predict that ScNi has a bound 2Z+ ground state similar to the experimentally observed diatomic. The HOMO is antibonding and the unpaired electron resides mainly on the Sc atom. This is in accord with the EPR results of Weltner and Van Zee where the unpaired electron was found to be mainly situated on the lighter metal.8 The LDFLCAO electronic structure description is similar to that obtained
Acknowledgment. S.M.M. acknowledges the financial assistance of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the allocation of computer time from the Computer Services Department of the University of New Brunswick. We are also grateful to Professor M. D. Morse for the preliminary ScNi gas-phase results and Professor F. Grein for providing us with his &, we, wg,, and De computation program. Registry No. ScNi, 12035-54-0.
References and Notes (1) Weltner, W., Jr.; Van Zee, R. J. Annu. Rev. Phys. Chem. 1984, 35, 291-327. (2) Weltner, W., Jr.; Van Zee, R. J. In The Challenge of the d and f Electrons, Theory and Computations; Salahub, D. R., Zerner, M. C., Eds.; ACS Symposium Series 394; ACS: Washington, DC, 1989; pp 213-227. (3) Morse, M. D. Chem. Rev. 1986, 86, 1049. (4) Fu, Z.; Morse, M. D. J . Chem. Phys. 1989, 90,3417-3426. Bishea, G. A.; Morse, M. D. Chem. Phys. Lett. 1990,171,430-432. Lemire, G. W.; Bishea, G. A.; Heidecke, S. A.; Morse, M. D. J . Chem. Phys. 1990, 92, 121-132. Taylor, S.; Spain, E. M.; Morse, M. D. J . Chem. Phys. 1990, 92, 2698-2709. Taylor, S.; Spain, E. M.; Morse, M. D. J. Chem. Phys. 1990, 92, 2710-2720. Spain, E. M.; Morse, M. D. Int. J. Mass Spectrosc. Ion Processes 1990, 102, 183-197. Bishea, G. A.; Marak, N.; Morse, M.D. J . Chem. Phys. 1991,95,5618-5629. Bishea, G . A.; Pinegar, J. C.; Morse, M. D. J . Chem. Phys. 1991, 95, 5630-5645. Bishea, G. A.; Morse, M. D. J . Chem. Phys. 1991, 95, 5646-5659. Spain, E. M.; Behm, J. M.; Morse, M. D. Chem. Phys. Lett. 1991, 179, 411-416. (5) Baumann, C. A.; Van Zee, R. J.; Weltner, W., Jr. J . Chem. Phys. 1983, 79, 5272. (6) Van Zee, R. J.; Weltner, W., Jr. Chem. Phys. Lett. 1984, 107, 173-1 77. (7) Cheeseman, M.; Van Zee, R. J.; Weltner, W., Jr. High Temp. Sei. 1988, 25, 143-52. (8) Van Zee, R. J.; Weltner, W., Jr. Chem. Phys. Lett. 1988, 150, 329-333. (9) Cheeseman, M.; Van Zee, R. J.; Flanagan, H. L.; Weltner, W., Jr. J. Chem. Phys. 1990, 92, 1553-1559. (10) Salahub, D. R. Adu. Chem. Phys. 1987,69 (Ab Initio Methods in Quantum Chemistry Part II), 447-520. Salahub, D. R. In Applied Quantum Chemistry; Smith, V. H., Jr., Schaefer, H. F., 111, Morokuma, K., Jr., Eds.; Reidel: Dordrecht, 1986; pp 185-212. Salahub, D. R. Contribution of Cluster Physics to Material Science and Technology; Davenas, J., Rabette, P., Eds.; Nijhoff The Hague, 1986; pp 143-194. (1 1) Shim, I. Ten Papers in the Exact Sciences and Geology;Royal Danish Academy of Sciences and Letters: Copenhagen, 1985; pp 147-208. (12) Walch, S. P.; Bauschlicher, C. W. Comparison of Ablnitio Quantum Chemistry With Experiment For Small Molecules; Bartlett, R. J., Ed.; Reidel: Dordrecht, 1985; pp 17-53. (13) Koutecky, J.; Fantucci, P. Chem. Rev. 1986, 86, 539. (14) Guenzburger, D.; Baggio-Saitovitch, E. M. Phys. Reu. E 1981, 24, 2368-2379. (15) Goldstein, E.; Flora, C.; Hsia, Y . P. J. Mol. Struct. (THEOCHEM) 1985. 124. 191-200. (16) Nagarathna, H. M.; Montano, P. A.; Naik, V. M.J. Am. Chem. Soc. 1983, 105, 2938-2943. (17) Shim, I. Theor. Chim. Acta 1981, 59,413-421. (18) Shim, I. Theor. Chim. Acta 1980, 54, 113-122. (19) Salahub. D. R.; Bavkara. N. A. Surf. Sci. 1985. 156.605. (20) (a) Radzio, E.; Andklm, J.; Salahub,-D. R. J. Compur. Chem. 1985, 6,533-537. (b) Baykara, N. A.; McMaster, B. N.; Salahub, D. R. Mol. Phys. 1984, 52, 891. (21) Mattar, S. M.; Hamilton, W. J . Mol. Strucr. (THEOCHEM) 1991, 226, 147-155. (22) Mattar, S. M.; Hamilton, W. D. J . Phys. Chem. 1992,96, 16061610. (23) (a) Ziegler, T. Chem. Reu. 1991, 91,651-667. (b) Salahub, D. R.; Zerner, M. C. In The Challenge of the d and f Electrons, Theory and Computations; Salahub, D. R., Zerner, M. C., Eds.; ACS Symposium Series 394; Washington, DC, 1989; pp 1-16. (24) Brewer, L. Science 1968,161,115. Engel, N. Kem. Maanedsbl. 1949, 30, 53,75,97, 105, 113. Engel, N. Powder Merall. Bull. 1964, 7,8. Engel, N. Am. SOC.Metals, Trans. Q.1964, 57, 610. (25) (a) Shim, I.; Gingerich, K. A. Chem. Phys. Let?. 1983,101, 109. (b) Faegri, K., Jr.; Bauschlicher, C. W., Jr. Chem. Phys. 1991, 153, 399.
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Infrared Intensities: Cyciobutene. A NormaCCoordinate Analysis and Comparison with Cyciopropene Kenneth B. Wiberg* and Robert E. Rosenberg Department of Chemistry, Yale University, New Haven, Connecticut 0651 1 (Received: May 6, 1992; In Final Form: July 13, 1992)
The infrared and Raman spectra of cyclobutene and of its 1,2-d2and 3,3,4,4-d4isotopomers were determined, and the intensities of the infrared bands were measured. A new vibrational assignment was made with the help of the spectrum calculated using the 6-31G* basis set. A normal-coordinate analysis was carried out, and the infrared intensities were converted to atomic polar tensors and to dipole moment derivatives with respect to symmetry coordinates. The results of this investigation are compared with similar data obtained previously for cyclopropene and with corresponding data for cyclopropane, ethylene, and propane. Introduction Several years ago we reported a complete normal-coordinate analysis and infrared intensity study of cyclopropene.' At the time we hoped to explain the unusual charge distribution in cyclopropene which leads to a large dipole moment pointing away from the double bonda2 We felt that a similar analysis of cyclobutene would allow a direct comparison with a structurally similar molecule which has a normal small dipole moment directed toward the double bond. A study of cyclobutene would also extend our library of compounds whose infrared intensities have been analyzed. A long-term goal is to make a firm connection between observed infrared intensity and molecular charge distribution. Lord and Rea have reported a vibrational assignment and a normal-coordinate analysis for cyclobutene (l).3Subsequently, some assignments were changed by Suzuki and Nibler.4 However, they must be considered as a first approximation since the spectra used for the assignments were of low resolution, making band assignments difficult. Also only two isotopomers, do and d6 were used in the original study, making it Wicult to separate vibrations due to vinyl versus aliphatic hydrogens. In addition, it now seems clear that a unique force field usually cannot be obtained for a polyatomic molecule using only observed vibrational freq~encies.~ The off-diagonal elements of the force constant matrix are often coupled to the diagonal terms so that changes in one may be compensated by changes in the other without sisnifcantly altering the calculated frequencies. Therefore, we have prepared and have obtained the infrared and gas-phase Raman spectra of cyclobutene-l ,2-d2 and cyclobutene-3,3,4,4,-d4.The force field for 1 was reinvestigated with the aid of theoretical calculations. In addition, we have measured the intensities of the infrared bands so that the changes in dipole moment resulting from molecular distortions could be determined. These data make possible a detailed comparison of cyclopropene and cyclobutene.
TABLE I: Comparison of Ohsened and Calculated Structures for Cyclobutene'
parameter
T(CI-CI) r(Cl-4) r(C3-G) r(C1-Hd r(C4-H7) LC4-C 1 x
2
LH5ClC2
LC,-C,-C, LHT-Cd-Hs LC 1C4-H7 Cz-CI-C4-H7
obsd' 1.342 1.517 1.566 1.083 1.094 94.2 133.5 85.8 109.2 115.7 -64.8
6-31G' 1.322 1.515 1.562 1.075 1.086 94.5 133.5 85.5 108.6 115.8 -64.5
calcd MP2/6-31G* 1.346 1.512 1.564 1.087 1.095 94.1 133.6 85.9 108.6 115.9 -64.5
Distances in angstroms and angles in degrees. Bak, B.; Led,J. J.; Nygaard, L.; Rastrup-Andersen, J.; Sorensen, G. 0. J . Mol. Struct. 1969, 3, 369.
Vibrational Spectrum of Cyclobutene The two main problems with cyclobutene are those of making a satisfactoryvibrational assignment of the spectrum and of fmding a unique solution to the normalcoordinate problem. A calculation of the vibrational spectrum using ab initio MO theory provides useful information.6 First, after appropriate scaling, the calculated frequencies and intensities should be a good guide to what might be found for each symmetry block.' Second, the calculated force
0022-3654/92/2096-8282$03.00/00 1992 American Chemical Society
