J. Phys. Chem. 1996, 100, 10121-10122
10121
Ab Initio Investigation of Vibrational Effects on Magnetic Hyperfine Coupling Constants in the X3Σg- State of B2H2 B. Engels,* H. U. Suter, and M. Peric´ † Institut fu¨ r Physikalische und Theoretische Chemie, UniVersita¨ t Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany ReceiVed: February 9, 1996X
The influence of the vibrational motion on the magnetic hyperfine coupling constants (hfcc’s) in the X3Σgof B2H2 is investigated by means of ab initio methods. The present study clearly shows that for the isotropic hfcc’s of the boron centers the incorporation of the vibrational effects is essential already for the vibrational ground state. For the boron center the isotropic hfcc’s calculated for the lowest vibrational state (Aiso(11B) ) -5.2 MHz) differ considerably from the value obtained at the equilibrium geometry (Aiso(11B) ) -14.0 MHz) but agrees excellently with the experimental value (Aiso(11B) ) -5.2 MHz) obtained previously. For the hydrogen centers and for all anisotropic hfcc’s the effects are found to be much smaller. In the present study the averaged values for various vibrational states and isotopic effects are given.
Binary boron species receive more and more attention1 because the process of their thermal decomposition is potentially important in the creation of thin metallic films involved in the manufacture of semiconductor devices. The HBBH molecule, which represents one of the simplest members of the family of binary boron species, was studied by various theoretical approaches.2 Very recently, in an excellent study Knight and co-workers3 described an experimental characterization of HBBH using electron spin resonance (ESR) in neon and argon matrices at 4 K. With the exception of Aiso(11B) the measured magnetic hyperfine coupling constants (hfcc’s) showed close agreement with ab initio theoretical calculations conducted as a part of their study. For Aiso(11B), however, a large discrepancy between the experimental (-5.2(4) MHz) and the theoretical value (-19.1 MHz) was found. In a previous ab initio investigation of the X2Πu state of B2H2+,4,5 we found that the isotropic hfcc’s of the boron center are largely affected by vibronic effects arising from the cis and the trans bending motion. Because the neutral and the ionic systems are very similar, analogous results are also expected for the B2H2 molecule. For the description of the vibrational effects we employ the potential energy surface obtained in a current study6 that uses the same method as employed in our B2H2+ study. To obtain the electronic hfcc’s as a function of the nuclear geometry we employed the AO basis set given by Chipman.7 The electronic hfcc’s are calculated using the MRD CI/BK method.8 In all calculations of the electronic hfcc’s the bond distances are kept fixed at the optimized values of the equilibrium geometry (B-H ) 2.231 bohr; B-B ) 2.869 bohr). At the equilibrium geometry (linear nuclear arrangement) we obtained Aiso(11B) ) -14.0 MHz and Aiso(H) ) -41.4 MHz. Both values are somewhat different from the theoretical values obtained by Knight and co-workers (Aiso(11B) ) -19.1 MHz; Aiso(H) ) -36.5 MHz). The deviation between the results of both theoretical works is presumably due to the improved treatment employed in the present work, but it cannot explain the difference in the experimental value of Aiso(11B). * To whom correspondence should be addressed. † Permanent address: University of Belgrade, Faculty of Physical Chemistry, Studentski trg 16, POB 137, 11001 Belgrade, Yugoslavia. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00409-1 CCC: $12.00
The dependence of the isotropic hfcc’s on the bending angles FT and FC are displayed in Figure 1. (FT and FC represent the angles between the B-B and B-H bonds at the trans and cis bending, respectively.) While Aiso(11B) strongly increases as a function of FT [Aiso(11B) (FT ) 60°) ) 167 MHz], a much smaller dependence is found with respect to FC [Aiso(11B))FC ) 60°) ) 21 MHz]. Furthermore, Aiso(H) shows very small changes with both bending motions. The geometry dependence of hfcc’s is similar to our findings for the 2Bu and 2A1 components of the 2-fold spatiallydegenerate X2Πu sate of B2H2+.5 The explanation for this behavior can be traced to the change in the character of one of the singly occupied πu orbitals which gains more and more σ character during the bending motion. Due to an increase of the direct contribution from this orbital, the calculated values of Aiso(11B) increase. For a detailed discussion of the various effects we refer to our previous paper.5 Due to the strong increase of Aiso(11B) upon bending large vibrational effects can be expected. To include these effects an vibrational averaging was performed in which both bending modes were included. The influence of other modes (stretch modes) and the interaction between the bending modes were neglected. The potential curve for the 3Bg state (trans bending) is fitted by a polynomial of the eigth order (because this curve was found to be fairly anharmonic) and that for the 3B1 state (cis bending) by a fourth-order polynomial in FT and FC, respectively. Employing as basis the eigenfunctions of the corresponding fourdimensional harmonic oscillator the vibrational energy levels and wave functions for each mode are computed variationally. The vibrational states are characterized by the quantum numbers VT, lT, VC, lC; lT and lC are the quantum numbers for the vibrational angular momenta arising at trans-cis bending (li ) Vi, Vi-2, ..., 1 or 0). The hfcc’s functions displayed in Figure 1 are fitted to the polynomials in FT2n, FC2n without cross terms, and the vibronic mean values are computed as described in detail elsewhere.9 The calculated frequencies (see Table 1) of the trans (Πg) and cis (Πu) bending modes are 597 and 623 cm-1, respectively. This results is in fair agreement with theoretical values given by Tague and Andrews (549 and 640 cm-1), which used the second-order Møller-Plesset perturbation theory and did not include anharmonic effects.10 © 1996 American Chemical Society
10122 J. Phys. Chem., Vol. 100, No. 24, 1996
Engels et al. TABLE 1: Energy Levels and Vibronic Mean Values of the Isotropic hfcc’s for Boron and Hydrogen Atoms in the X3Σg- State of H11B11BHa present work Πu VT lT
Πg VC lC
0 0 1 1 2 0
0 1 0 1 0 2
0 0 1 1 0 0
0 1 0 1 0 0
exp (ref 3)
Eb (cm-1)
Aiso(11B) (MHz)
Aiso(H) (MHz)
Aiso(11B) (MHz)
Aiso(H) (MHz)
0 599 623 1220 1241 1260
-5.2 17.0 -4.4 17.8 -3.4 8.3
-39.2 -38.3 -39.2 -38.3 -39.9 -38.1
-5.2(4)
-38.9(5)
a Couplings between the Πu and the Πg mode and effects resulting from other modes (stretch modes, etc.) are not taken into account in the theoretical treatment. The calculated values of the isotropic hfcc’s obtained at the equilibrium geometry (without considering vibrations) are as follows: Aiso(11B) ) -14.0 MHz and Aiso(H) ) -41.4 MHz. b Obtained as E VT,lT,VC,lC - EVT)lT)VC)lC)0.
TABLE 2: Isotopic Effects on the Vibronic Mean Values of the Isotropic hfcc’s (All Values in MHz) isotopomere H11B11BH H10B10BH D11B11BD a
Figure 1. Dependence of the electronic isotropic hfcc’s for the boron center (dotted line) and the hydrogen center (solid line) for the X3Σgstate of B2H2 on the trans- (right side) and cis-bending (left side) coordinates FT and FC, respectively (see text). The bond distances are kept fixed at the values of B-H ) 2.231 bohr and B-B ) 2.869 bohr.
The results are given in Table 1, which contains the mean values of Aiso(11B) and Aiso(H) for the lowest vibrational states, and in Table 2 in which calculated isotopic shifts are given. It can be seen that for Aiso(11B) the inclusion of vibrational effects is essential for the vibrational ground state. The isotropic hfcc calculated for the lowest vibrational state (Aiso(11B) ) -5.2 MHz) differs considerably from the electronic value obtained at the equilibrium geometry (Aiso(11B) ) -14.0 MHz) and agrees excellently with the experimental value (Aiso(11B) ) -5.2 MHz) given by Knight and co-workers.3 For Aiso(H) the effect is much smaller, but the vibrational averaging shifts the calculated value toward the experimental value. Also, for Aiso(H) the difference between experiment and theory is smaller than the experimental error bar. As expected, the main effect arises due to the trans bending mode (90%), while the cis bending mode is less important. Table 1 also shows a strong dependence of Aiso(11B) on the vibrational quantum numbers. A similar treatment as performed for the isotropic hfcc’s was made for the anisotropic hfcc’s, but only small vibrational effects were found. The calculated values can be obtained upon request. Summarizing, two essential results are seen: (1) An agreement between experimental and theoretical values for Aiso(11B) is only possible if not only electronic but also large
Aiso(xB)
Aiso(xH)
-5.2 -1.7 (-5.0)a -7.5
-39.2 -40.1 -6.0 (-39.1)b
Multiplied by gn(11B)/gn(10B). b Multiplied by gn(H)/gn(D).
vibrational effects are taken into account. For Aiso(H) a much smaller influence of the nuclear motion is found. This explains the deviations found in the previous work of Knight et al.3 (2) Our calculations, in which only the two bending modes are taken into account, are sufficiently accurate to describe all main effects arising from the nuclear motion; i.e., our results obtained for the B2H2+ ion (for which no experimental results are available thus far) are expected to possess an accuracy similar to those obtained in the present work for the neutral B2H2 system. Acknowledgment. This work wsa financially supported by the Deutsche Forschungsgemeinschaft (DFG). References and Notes (1) Greenwood, N. N. Chem. Soc. ReV. 1992, 21, 19. (2) (a) Dill, J. D.; Schleyer, P. v. R.; Pople, J. A. J. Am. Chem. Soc. 1975, 97, 3402. (b) Treboux, G.; Barthelat, J. C. J. Am. Chem. Soc. 1993, 115, 4870. (c) Jouany, c.; Barthelat, J. C.; Daudey, J. P. Chem. Phys. Lett. 1987, 136, 52. (3) Knight, L. B., Jr.; Kerr, K.; Miller, P. K.; Arrington, C. A. J. Phys. Chem. 1995, 99, 16842. (4) Peric´, M.; Engels, B.; Peyerimhoff, S. D. J. Mol. Spectrosc. 1995, 171, 494. (5) Peric´, M.; Engels, B. J. Mol. Spectrosc. 1995, 174, 334. (6) Ostojic´, B.; Peric´, M.; Engels, B. To be published. (7) Chipman, D. Theor. Chim. Acta 1989, 76, 73. (8) Engels, B. Chem. Phys. Lett. 1991, 179, 398. Engels, B. J. Chem. Phys. 1994, 100, 1380. (9) Peric´, M.; Engels, B.; Peyerimhoff, S. D. In Understanding Chemical ReactiVity; Langhoff, S. R., Ed.; Kluwor Academic Publishers: Dordrecht, The Netherlands, 1995; Vol. 13. (10) Tague, J. T., Jr.; Andrews, L. J. Am. Chem. Soc. 1994, 116, 4970.
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