Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann)Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2 n q 1 and 2 n q 2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self- consistent field, and second-order Moller)Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state

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

[2]  Thomas Bondo Pedersen,et al.  Coupled cluster response functions revisited , 1997 .

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

[4]  J. Gauss,et al.  Analytic Evaluation of Second Derivatives of the Energy: Computational Strategies for the CCSD and CCSD(T) Approximations , 1997 .

[5]  Patrick Norman,et al.  CUBIC RESPONSE FUNCTIONS IN THE MULTICONFIGURATION SELF-CONSISTENT FIELD APPROXIMATION , 1996 .

[6]  Poul Jørgensen,et al.  Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies , 1996 .

[7]  Ove Christiansen,et al.  Response functions in the CC3 iterative triple excitation model , 1995 .

[8]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[9]  H. Ågren,et al.  Cubic response functions in the random phase approximation , 1995 .

[10]  P. Szalay,et al.  Analytic energy derivatives for coupled‐cluster methods describing excited states: General formulas and comparison of computational costs , 1995 .

[11]  P. Piecuch,et al.  Orthogonally spin‐adapted single‐reference coupled‐cluster formalism: Linear response calculation of static properties , 1995 .

[12]  D. Mukherjee,et al.  Coupled-Cluster Based Linear Response Approach to Property Calculations: Dynamic Polarizability and Its Static Limit , 1995 .

[13]  C. Hättig,et al.  Correlated frequency-dependent polarizabilities and dispersion coefficients in the time-dependent second-order Møller-Plesset approximation , 1995 .

[14]  F. Aiga,et al.  Frequency-dependent hyperpolarizabilities in the brueckner coupled-cluster theory , 1994 .

[15]  Yngve Öhrn,et al.  Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems , 1994 .

[16]  H. Koch,et al.  Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function , 1994 .

[17]  P. Jørgensen,et al.  Brueckner coupled cluster response functions , 1994 .

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

[19]  John F. Stanton,et al.  Many‐body methods for excited state potential energy surfaces. I. General theory of energy gradients for the equation‐of‐motion coupled‐cluster method , 1993 .

[20]  Fumihiko Aiga,et al.  Frequency‐dependent hyperpolarizabilities in the Mo/ller–Plesset perturbation theory , 1993 .

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

[22]  J. Olsen,et al.  Multiconfigurational quadratic response functions for singlet and triplet perturbations: The phosphorescence lifetime of formaldehyde , 1992 .

[23]  J. Olsen,et al.  Quadratic response functions for a multiconfigurational self‐consistent field wave function , 1992 .

[24]  W. Kutzelnigg.  Stationary perturbation theory , 1992 .

[25]  S. Karna,et al.  Frequency dependent nonlinear optical properties of molecules: Formulation and implementation in the HONDO program , 1991 .

[26]  N. Handy,et al.  Frequency dependent hyperpolarizabilities with application to formaldehyde and methyl fluoride , 1990 .

[27]  Henrik Koch,et al.  Coupled cluster response functions , 1990 .

[28]  Trygve Helgaker,et al.  Excitation energies from the coupled cluster singles and doubles linear response function (CCSDLR). Applications to Be, CH+, CO, and H2O , 1990 .

[29]  D. M. Bishop,et al.  Molecular vibrational and rotational motion in static and dynamic electric fields , 1990 .

[30]  Trygve Helgaker,et al.  Configuration-interaction energy derivatives in a fully variational formulation , 1989 .

[31]  J. Broeckhove,et al.  On the equivalence of time-dependent variational-principles , 1988 .

[32]  H. Sellers.  Analytical force constant calculation as a minimization problem , 1986 .

[33]  Hideo Sekino,et al.  Frequency dependent nonlinear optical properties of molecules , 1986 .

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

[35]  S. Chu.  Recent Developments in Semiclassical Floquet Theories for Intense-Field Multiphoton Processes , 1985 .

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

[37]  Henry F. Schaefer,et al.  On the evaluation of analytic energy derivatives for correlated wave functions , 1984 .

[38]  P. Jørgensen,et al.  Polarization propagator methods in atomic and molecular calculations , 1984 .

[39]  H. Monkhorst,et al.  Some aspects of the time-dependent coupled-cluster approach to dynamic response functions , 1983 .

[40]  Laurence D. Barron,et al.  Molecular Light Scattering and Optical Activity: Second Edition, revised and enlarged , 1983 .

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

[42]  P. Joergensen,et al.  Second Quantization-based Methods in Quantum Chemistry , 1981 .

[43]  Poul Jo,et al.  Transition moments and dynamic polarizabilities in a second order polarization propagator approach , 1980 .

[44]  E. Dalgaard.  Time‐dependent multiconfigurational Hartree–Fock theory , 1980 .

[45]  P. Jørgensen,et al.  A multiconfigurational time-dependent hartree-fock approach , 1979 .

[46]  Debashis Mukherjee,et al.  A response-function approach to the direct calculation of the transition-energy in a multiple-cluster expansion formalism , 1979 .

[47]  D. Santry,et al.  Calculations of second-order TDHF equations for ammonia , 1979 .

[48]  J. Linderberg,et al.  Characteristics of the consistent ground state of the random phase approximation , 1979 .

[49]  A. Stelbovics,et al.  The third-order dynamic electric susceptibility of the hydrogen molecule , 1979 .

[50]  A. Schawlow,et al.  Laser spectroscopy of atoms and molecules. , 1978, Science.

[51]  P. Jørgensen,et al.  Self-consistent time-dependent Hartree--Fock scheme , 1974 .

[52]  R. Moccia.  Time‐dependent variational principle , 1973 .

[53]  H. Sambe.  Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field , 1973 .

[54]  V. McKoy,et al.  Equations‐of‐motion method including renormalization and double‐excitation mixing , 1973 .

[55]  P. W. Langhoff,et al.  Aspects of Time-Dependent Perturbation Theory , 1972 .

[56]  P. Löwdin,et al.  SOME COMMENTS ON THE TIME-DEPENDENT VARIATION PRINCIPLE. , 1972 .

[57]  V. G. Kaveeshwar,et al.  Hartree-Fock Theory of Third-Harmonic and Intensity-Dependent Refractive-Index Coefficients , 1971 .

[58]  John F. Stanton,et al.  Coupled-cluster calculations of nuclear magnetic resonance chemical shifts , 1967 .

[59]  E. F. Hayes,et al.  Time‐Dependent Hellmann‐Feynman Theorems , 1965 .

[60]  A. D. McLACHLAN,et al.  Time-Dependent Hartree—Fock Theory for Molecules , 1964 .

[61]  A. D. McLachlan,et al.  A variational solution of the time-dependent Schrodinger equation , 1964 .

[62]  A. Dalgarno,et al.  A perturbation calculation of properties of the helium iso-electronic sequence , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[63]  J. Frenkel,et al.  Wave mechanics: Advanced general theory , 1934 .

[64]  I︠A︡kov Ilʹich Frenkelʹ.  Advanced general theory , 1934 .

[65]  P. Dirac.  Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.