Automated calculation of anharmonic vibrational contributions to first hyperpolarizabilities: quadratic response functions from vibrational configuration interaction wave functions.

Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H(2)O, CH(2)O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.

[1]  O. Christiansen.  Response theory for vibrational wave functions. , 2005, The Journal of chemical physics.

[2]  D. M. Bishop,et al.  Differences between the exact sum-over-states and the canonical approximation for the calculation of static and dynamic hyperpolarizabilities , 1997 .

[3]  J. Gauss,et al.  Frequency-dependent polarizabilities and first hyperpolarizabilities of CO and H2O from coupled cluster calculations , 1999 .

[4]  Jerzy Leszczynski,et al.  Non-linear optical properties of matter : from molecules to condensed phases , 2006 .

[5]  William H. Press,et al.  Numerical recipes , 1990 .

[6]  V. Kellö,et al.  Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties , 1991 .

[7]  Ove Christiansen,et al.  INVITED ARTICLE www.rsc.org/pccp | Physical Chemistry Chemical Physics , 2006 .

[8]  P. Jørgensen,et al.  Cauchy moments of Ne, Ar, and Kr atoms calculated using the approximate coupled cluster triples model CC3 , 2005 .

[9]  B. Kirtman,et al.  Variational calculation of vibrational linear and nonlinear optical properties. , 2005, The Journal of chemical physics.

[10]  P. Prasad,et al.  Multiphoton absorbing materials: molecular designs, characterizations, and applications. , 2008, Chemical Reviews.

[11]  J. Bertrán,et al.  Molecular electric properties and nuclear and vibrational relaxation , 1993 .

[12]  J. Kongsted,et al.  Linear response functions for a vibrational configuration interaction state. , 2006, The Journal of chemical physics.

[13]  F. Aiga,et al.  Higher‐order response theory based on the quasienergy derivatives: The derivation of the frequency‐dependent polarizabilities and hyperpolarizabilities , 1993 .

[14]  Ove Christiansen,et al.  Cauchy moments and dispersion coefficients using coupled cluster linear response theory , 1997 .

[15]  D. M. Bishop,et al.  ADDITIONAL COMPACT FORMULAS FOR VIBRATIONAL DYNAMIC DIPOLE POLARIZABILITIES AND HYPERPOLARIZABILITIES , 1998 .

[16]  E. Dalgaard.  Quadratic response functions within the time-dependent Hartree-Fock approximation , 1982 .

[17]  D. M. Bishop,et al.  Nonlinear response theory with relaxation: the first-order hyperpolarizability. , 2005, The Journal of chemical physics.

[18]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[19]  S. Naguleswaran,et al.  PHENOMENOLOGICAL DAMPING OF NONLINEAR-OPTICAL RESPONSE TENSORS , 1998 .

[20]  J. Kongsted,et al.  Automatic generation of potential energy and property surfaces of polyatomic molecules in normal coordinates. , 2007, The Journal of chemical physics.

[21]  K. Ruud,et al.  Analytic calculations of vibrational hyperpolarizabilities in the atomic orbital basis. , 2008, The journal of physical chemistry. A.

[22]  O. Christiansen,et al.  Variational calculation of static and dynamic vibrational nonlinear optical properties. , 2007, The Journal of chemical physics.

[23]  J. Ward,et al.  Measurements of nonlinear optical polarizabilities for twelve small molecules , 1979 .

[24]  Evert Jan Baerends,et al.  A density-functional theory study of frequency-dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules , 1995 .

[25]  Efficient treatment of the effect of vibrations on electrical, magnetic, and spectroscopic properties , 2000 .

[26]  J. Olsen,et al.  Polarizabilities and first hyperpolarizabilities of HF, Ne, and BH from full configuration interaction and coupled cluster calculations , 1999 .

[27]  D. M. Bishop,et al.  A simple method for determining approximate static and dynamic vibrational hyperpolarizabilities , 1995 .

[28]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[29]  Jacob Kongsted,et al.  Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties. , 2006, The Journal of chemical physics.

[30]  E. Donley,et al.  A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements , 1998 .

[31]  M G Papadopoulos,et al.  Linear and nonlinear optical properties of [60]fullerene derivatives. , 2009, The journal of physical chemistry. A.

[32]  J. Olsen,et al.  Linear and nonlinear response functions for an exact state and for an MCSCF state , 1985 .

[33]  Evert Jan Baerends,et al.  Calculating frequency-dependent hyperpolarizabilities using time-dependent density functional theory , 1998 .

[34]  J. J. Sakurai,et al.  Modern Quantum Mechanics , 1986 .

[35]  Reply to ''Comment on 'Phenomenological damping in optical response tensors' '' , 2001 .

[36]  J. Ward,et al.  Measurements of second‐ and third‐order nonlinear polarizabilities for HF and HCl , 1985 .

[37]  P. N. Butcher,et al.  The Elements of Nonlinear Optics , 1990 .

[38]  M. Papadopoulos,et al.  Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study. , 2006, The journal of physical chemistry. A.

[39]  Poul Jørgensen,et al.  Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy , 1998 .

[40]  T. Carrington,et al.  Variational quantum approaches for computing vibrational energies of polyatomic molecules , 2008 .

[41]  J. Olsen,et al.  TIME-DEPENDENT RESPONSE THEORY WITH APPLICATIONS TO SELF-CONSISTENT FIELD AND MULTICONFIGURATIONAL SELF-CONSISTENT FIELD WAVE FUNCTIONS , 1995 .

[42]  P. W. Langhoff,et al.  Padé Summation of the Cauchy Dispersion Equation , 1969 .

[43]  P. Jørgensen,et al.  Frequency-dependent first hyperpolarizabilities using coupled cluster quadratic response theory , 1997 .

[44]  D. M. Bishop,et al.  A perturbation method for calculating vibrational dynamic dipole polarizabilities and hyperpolarizabilities , 1991 .

[45]  D. M. Bishop,et al.  Compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities , 1992 .

[46]  Paweł Sałek,et al.  Density-functional theory of linear and nonlinear time-dependent molecular properties , 2002 .

[47]  Derek A. Long,et al.  The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules , 2001 .

[48]  Bernard Kirtman,et al.  Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6 , 1998 .

[49]  David P. Shelton,et al.  Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase , 1994 .

[50]  M. Duran,et al.  A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules , 1997 .

[51]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[52]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[53]  P. Fischer,et al.  Phenomenological damping in optical response tensors , 2000 .