Quantum chemical calculation of vibrational spectra of large molecules—Raman and IR spectra for Buckminsterfullerene

In this work we demonstrate how different modern quantum chemical methods can be efficiently combined and applied for the calculation of the vibrational modes and spectra of large molecules. We are aiming at harmonic force fields, and infrared as well as Raman intensities within the double harmonic approximation, because consideration of higher order terms is only feasible for small molecules. In particular, density functional methods have evolved to a powerful quantum chemical tool for the determination of the electronic structure of molecules in the last decade. Underlying theoretical concepts for the calculation of intensities are reviewed, emphasizing necessary approximations and formal aspects of the introduced quantities, which are often not explicated in detail in elementary treatments of this topic. It is shown how complex quantum chemistry program packages can be interfaced to new programs in order to calculate IR and Raman spectra. The advantages of numerical differentiation of analytical gradients, dipole moments, and static, as well as dynamic polarizabilities, are pointed out. We carefully investigate the influence of the basis set size on polarizabilities and their spatial derivatives. This leads us to the construction of a hybrid basis set, which is equally well suited for the calculation of vibrational frequencies and Raman intensities. The efficiency is demonstrated for the highly symmetric C60, for which we present the first all‐electron density functional calculation of its Raman spectrum. © 2002 Wiley Periodicals, Inc. J Comput Chem 9: 895–910, 2002

[1]  V. B. Berestet͡skiĭ,et al.  Quantum Electrodynamics , 2021, Introduction to Quantum Mechanics.

[2]  H. Schaefer,et al.  Analytic Raman intensities from molecular electronic wave functions , 1986 .

[3]  Hans W. Horn,et al.  ELECTRONIC STRUCTURE CALCULATIONS ON WORKSTATION COMPUTERS: THE PROGRAM SYSTEM TURBOMOLE , 1989 .

[4]  M. Halls,et al.  COMPARISON STUDY OF THE PREDICTION OF RAMAN INTENSITIES USING ELECTRONIC STRUCTURE METHODS , 1999 .

[5]  A. Komornicki,et al.  An efficient ab initio method for computing infrared and Raman intensities: Application to ethylene , 1979 .

[6]  Herman Vanherzeele,et al.  Dispersion of the third-order optical nonlinearity of C60. A third-harmonic generation study , 1992 .

[7]  A. J. Sadlej,et al.  Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties , 1991 .

[8]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

[9]  P. Atkins,et al.  Molecular Quantum Mechanics. 3rd edition , 2003 .

[10]  H. Schaefer,et al.  Erratum: Analytic evaluation and basis set dependence of intensities of infrared spectra [J. Chem. Phys. 84, 2262 (1986)] , 1986 .

[11]  D. Bermejo,et al.  Absolute Raman intensities of CH4, CH3D, CH2D2, CHD3, and CD4 , 1977 .

[12]  Alan K. Burnham,et al.  Measurement of the dispersion in polarizability anisotropies , 1975 .

[13]  Jerzy Cioslowski,et al.  A new population analysis based on atomic polar tensors , 1989 .

[14]  Roger D. Amos,et al.  Raman intensities using time dependent density functional theory , 2000 .

[15]  Yi Luo,et al.  Ab initio calculations of the polarizability and the hyperpolarizability of C60 , 1997 .

[16]  A. Einstein.  On the Quantum Theory of Radiation , 1983 .

[17]  Poul Jørgensen,et al.  Ground and excited state polarizabilities and dipole transition properties of benzene from coupled cluster response theory , 1999 .

[18]  H. W. Schrötter,et al.  Raman Scattering Cross Sections in Gases and Liquids , 1979 .

[19]  K. Rao,et al.  Molecular Spectroscopy: Modern Research , 1972 .

[20]  T. Thirunamachandran,et al.  Molecular Quantum Electrodynamics , 1984 .

[21]  M. Verheijen,et al.  Raman scattering in single crystal Cbo , 2017 .

[22]  M. E. Rose.  Elementary Theory of Angular Momentum , 1957 .

[23]  Sean A. C. McDowell,et al.  Molecular polarisabilities - a comparison of density functional theory with standard ab initio methods , 1995 .

[24]  L. Schiff,et al.  Quantum Mechanics, 3rd ed. , 1973 .

[25]  H. Schaefer,et al.  Analytic evaluation and basis set dependence of intensities of infrared spectra , 1986 .

[26]  S. Brodersen,et al.  Raman spectroscopy of gases and liquids , 1979 .

[27]  Hal J. Rosen,et al.  Vibrational Raman and infrared spectra of chromatographically separated C60 and C70 fullerene clusters , 1991 .

[28]  A. Schäfer,et al.  Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr , 1994 .

[29]  A. C. Albrecht.  On the Theory of Raman Intensities , 1961 .

[30]  R. Amos,et al.  Time-dependent density functional theory applied to Raman scattering from methane , 1997 .

[31]  WM. CHAPPELL,et al.  Molecular Vibrations , 1879, Nature.

[32]  R. Bartlett,et al.  Coupled-cluster calculations of Raman intensities and their application to N4 and N5− , 1999 .

[33]  P. Atkins,et al.  Molecular Quantum Mechanics , 1970 .

[34]  Henrik Koch,et al.  Calculation of frequency-dependent polarizabilities using coupled-cluster response theory , 1994 .

[35]  B. Chase,et al.  Substituted C60 molecules: a study in symmetry reduction , 1992 .

[36]  G. Herzberg,et al.  Infrared and Raman spectra of polyatomic molecules , 1946 .

[37]  P. Taylor,et al.  On the calculation of dipole moment and polarizability derivatives by the analytical energy gradient method: Application to the formaldehyde molecule , 1984 .

[38]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.