Coupled-Perturbed SCF Approach for Calculating Static Polarizabilities and Hyperpolarizabilities with Nonorthogonal Localized Molecular Orbitals.

Coupled-perturbed self-consistent-field (CPSCF) approach has been broadly used for polarizabilities and hyperpolarizabilities computation. To extend this application to large systems, we have reformulated the CPSCF equations with nonorthogonal localized molecular orbitals (NOLMOs). NOLMOs are the most localized representation of electronic degrees of freedom. Methods based on NOLMOs are potentially ideal for investigating large systems. In atomic orbital representation, with a static external electric field added, the wave function and SCF operator of unperturbed NOLMO-SCF wave function/orbitals are expanded to different orders of perturbations. We have derived the corresponding equations up to the third order, which are significantly different from those of a conventional CPSCF method because of the release of the orthogonal restrictions on MOs. The solution to these equations has been implemented. Several chemical systems are used to verify our method. This work represents the first step toward efficient calculations of molecular response and excitation properties with NOLMOs.

[1]  Steven K. Burger,et al.  Linear-scaling quantum calculations using non-orthogonal localized molecular orbitals , 2008, Journal of physics. Condensed matter : an Institute of Physics journal.

[2]  Kai Song,et al.  Syntheses and properties of two-dimensional charged nonlinear optical chromophores incorporating redox-switchable cis-tetraammineruthenium(II) centers. , 2005, Journal of the American Chemical Society.

[3]  Benny G. Johnson,et al.  THE CONTINUOUS FAST MULTIPOLE METHOD , 1994 .

[4]  Weitao Yang,et al.  A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules , 1995 .

[5]  Qin Wu,et al.  ALGEBRAIC EQUATION AND ITERATIVE OPTIMIZATION FOR THE OPTIMIZED EFFECTIVE POTENTIAL IN DENSITY FUNCTIONAL THEORY , 2003 .

[6]  Lemin Li,et al.  An efficient method for constructing nonorthogonal localized molecular orbitals. , 2004, The Journal of chemical physics.

[7]  Weitao Yang,et al.  Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals. , 2010, Physical chemistry chemical physics : PCCP.

[8]  B. Kirtman,et al.  Elongation method with cutoff technique for linear SCF scaling , 2005 .

[9]  Paul G. Mezey,et al.  A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions , 1989 .

[10]  B. Kirtman,et al.  Local space approximation for treatment of impurities in polymers. Solitons in polyacetylene , 1987 .

[11]  G. Golub,et al.  A Hessenberg-Schur method for the problem AX + XB= C , 1979 .

[12]  R. Bartlett,et al.  Nuclear spin–spin coupling constants evaluated using many body methods , 1986 .

[13]  J. Cioslowski.  Partitioning of electronic properties in two‐center, one‐electron coulombic systems , 1990 .

[14]  Filipp Furche,et al.  On the density matrix based approach to time-dependent density functional response theory , 2001 .

[15]  Martin Head-Gordon,et al.  Derivation and efficient implementation of the fast multipole method , 1994 .

[16]  S. F. Boys.  Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another , 1960 .

[17]  W. Niessen,et al.  Density localization of atomic and molecular orbitals , 1973 .

[18]  H. Nakai,et al.  Novel approach to excited-state calculations of large molecules based on divide-and-conquer method: application to photoactive yellow protein. , 2013, The journal of physical chemistry. B.

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

[20]  Yang,et al.  Direct calculation of electron density in density-functional theory. , 1991, Physical review letters.

[21]  Y. Aoki,et al.  An elongation method for large systems toward bio-systems. , 2012, Physical chemistry chemical physics : PCCP.

[22]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[23]  Fred G. Gustavson,et al.  Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition , 1978, TOMS.

[24]  B. Champagne,et al.  Design and characterization of molecular nonlinear optical switches. , 2013, Accounts of chemical research.

[25]  J. Franklin.  On Tikhonov’s method for ill-posed problems , 1974 .

[26]  Feizhi Ding,et al.  An efficient method for calculating dynamical hyperpolarizabilities using real-time time-dependent density functional theory. , 2013, The Journal of chemical physics.

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

[28]  Weitao Yang.  Absolute-energy-minimum principles for linear-scaling electronic-structure calculations , 1997 .

[30]  S. Karna.  A “direct” time-dependent coupled perturbed Hartree—Fock—Roothaan approach to calculate molecular (hyper)polarizabilities , 1993 .

[31]  S. Tretiak,et al.  Enhanced Two‐Photon Absorption of Organic Chromophores: Theoretical and Experimental Assessments , 2008 .

[32]  J. S. Binkley,et al.  Derivative studies in hartree-fock and møller-plesset theories , 2009 .

[33]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[34]  A. Williamson,et al.  Optimized nonorthogonal localized orbitals for linear scaling quantum Monte Carlo calculations , 2005 .

[35]  Feng Long Gu,et al.  Effective preconditioning for ab initio ground state energy minimization with non-orthogonal localized molecular orbitals. , 2013, Physical chemistry chemical physics : PCCP.

[36]  Mauro Leonardi,et al.  On the application of singular value decomposition and Tikhonov regularization to ill-posed problems in hyperbolic passive location , 2013, Math. Comput. Model..

[37]  A. Becke.  A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[38]  Yuriko Aoki,et al.  A theoretical synthesis of polymers by using uniform localization of molecular orbitals: Proposal of an elongation method , 1991 .

[39]  J. Hutter,et al.  A smooth script-l1-norm sparseness function for orbital based linear scaling total energy minimization. , 2008, The Journal of chemical physics.

[40]  Weitao Yang,et al.  Optimized effective potentials in finite basis sets. , 2007, Physical review letters.

[41]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[42]  T J Zuehlsdorff,et al.  Linear-scaling time-dependent density-functional theory in the linear response formalism. , 2013, The Journal of chemical physics.

[43]  Jörg Kussmann,et al.  A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels. , 2007, The Journal of chemical physics.

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

[45]  Guanhua Chen,et al.  Time-dependent density-functional theory/localized density matrix method for dynamic hyperpolarizability. , 2007, The Journal of chemical physics.

[46]  U. Nagashima,et al.  Geometrical structure of benzene and naphthalene: ultrahigh-resolution laser spectroscopy and ab initio calculation. , 2011, The Journal of chemical physics.

[47]  Liang Zhao,et al.  Signal restoration combining Tikhonov regularization and multilevel method with thresholding strategy. , 2013, Journal of the Optical Society of America. A, Optics, image science, and vision.

[48]  Efficient construction of nonorthogonal localized molecular orbitals in large systems. , 2010, The journal of physical chemistry. A.

[49]  B. Kirtman,et al.  Local space approximation for configuration interaction and coupled cluster wave functions , 1986 .

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

[51]  Horst Weiss,et al.  A direct algorithm for self‐consistent‐field linear response theory and application to C60: Excitation energies, oscillator strengths, and frequency‐dependent polarizabilities , 1993 .

[52]  Jörg Kussmann,et al.  Linear‐scaling self‐consistent field methods for large molecules , 2013 .

[53]  K. Ruedenberg,et al.  Electron pairs, localized orbitals and electron correlation , 2002 .

[54]  Satoshi Yokojima,et al.  Linear-scaling localized-density-matrix method for the ground and excited states of one-dimensional molecular systems , 1999 .