Analytic cubic and quartic force fields using density-functional theory.

We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kernels.

Analytic density functional theory calculations of pure vibrational hyperpolarizabilities: the first dipole hyperpolarizability of retinal and related molecules.

We present a general approach for the analytic calculation of pure vibrational contributions to the molecular (hyper)polarizabilities at the density functional level of theory. The analytic approach allows us to study large molecules, and we apply the new code to the study of the first dipole hyperpolarizabilities of retinal and related molecules. We investigate the importance of electron correlation as described by the B3LYP exchange-correlation functional on the pure vibrational and electronic hyperpolarizabilities and compare the computed hyperpolarizabilities with available experimental data.

Efficient calculation of ROA tensors with analytical gradients and fragmentation.

We present the results of calculations of Raman optical activity spectra of sizable systems from optical tensors of the fragments, the tensors calculated by an analytic approach at the time-dependent Hartree-Fock level of theory. The analytic approach permits large basis sets which, together with the limited geometrical extent of the fragments, obviates the need for the use of London-type orbitals. The implementation of the analytical gradient approach is formulated in the atomic orbital basis by using the elements of the density matrix as variational parameters.

Gauge-origin independent calculations of Jones birefringence.

We present the first gauge-origin independent formulation of Jones birefringence at the Hartree-Fock level of theory. Gauge-origin independence is achieved through the use of London atomic orbitals. The implementation is based on a recently proposed atomic orbital-based response theory formulation that allows for the use of both time- and perturbation-dependent basis sets [Thorvaldsen, Ruud, Kristensen, Jo̸rgensen, and Coriani, J.

Comparison of standard and damped response formulations of magnetic circular dichroism.

We apply damped response theory to the phenomenon of magnetic circular dichroism (MCD), and we investigate how the numerical instability associated with the simulation of the MCD spectrum from individually calculated A and B terms for close lying states can be remedied by the use of damped response theory. We also present a method for calculating the Faraday A term, formulated as a double residue of the quadratic response function.

Damped response theory description of two-photon absorption.

Damped response theory is applied to the calculation of two-photon absorption (TPA) spectra, which are determined directly, at each frequency, from a modified damped cubic response function. The TPA spectrum may therefore be evaluated for selected frequency ranges, making the damped TPA approach attractive for calculations on large molecules with a high density of states, where the calculation of TPA using standard theory is more problematic. Damped response theory can also be applied to the case of intermediate state resonances, where the standard TPA expression is divergent.

Variational response-function formulation of vibrational circular dichroism.

The atomic axial tensor (AAT) of vibrational circular dichroism is expressed as the frequency derivative at zero frequency of a linear response function for operators referencing a nuclear displacement and a magnetic field. This is used in the density matrix-based quasienergy derivative Lagrangian approach of Thorvaldsen et al. [J.

The ab initio calculation of molecular electric, magnetic and geometric properties.

We give an account of some recent advances in the development of ab initio methods for the calculation of molecular response properties, involving electric, magnetic, and geometric perturbations. Particular attention is given to properties in which the basis functions depend explicitly both on time and on the applied perturbations such as perturbations involving nuclear displacements or external magnetic fields when London atomic orbitals are used. We summarize a general framework based on the quasienergy for the calculation of arbitrary-order molecular properties using the elements of the density matrix in the atomic-orbital basis as the basic variables.

Arbitrary-Order Density Functional Response Theory from Automatic Differentiation.

We demonstrate how the functional derivatives appearing in perturbative time-dependent density functional theory can be calculated using automatic differentiation. The approach starts from a computer implementation of the exchange-correlation energy functional, from which arbitrary-order derivatives are generated automatically. Automatic differentiation is shown to provide an accurate, general, and efficient implementation of higher-order exchange-correlation functional derivatives that is easy to maintain.

Theoretical approaches to the calculation of Raman optical activity spectra.

In this article, we will give a brief account of the different approaches that have been presented in the literature for calculating Raman optical activity (ROA) spectra by ab initio methods. We will also outline the general structure of a self-consistent-field-based approach for analytic calculations of ROA spectra, including also contributions from London orbitals. The use of London orbitals ensures that the relevant ROA parameters are gauge origin independent.

Gauge-Origin Independent Formulation and Implementation of Magneto-Optical Activity within Atomic-Orbital-Density Based Hartree-Fock and Kohn-Sham Response Theories.

A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(ω) of the Faraday effect and the ℬ term of magnetic circular dichroism. The approach is expressed in terms of an atomic-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional theory.

Analytic ab initio calculations of coherent anti-Stokes Raman scattering (CARS).

We present a theory for the analytic calculation of frequency-dependent polarizability gradients, and apply the methodology to the calculation of coherent anti-Stokes Raman scattering (CARS). The formalism used is based on an open-ended theory for the calculation of frequency-dependent molecular response properties of arbitrary order, also including contributions from perturbation-dependent basis sets. An important feature of our approach is the close connection between the formalism--which is fully matrix-based in an atomic orbital basis--and the implementation, allowing for the rapid implementation of higher-order molecular properties.

Analytic calculations of nonlinear mixed electric and magnetic frequency-dependent molecular properties using London atomic orbitals: Buckingham birefringence.

We present the results of the first gauge-origin independent calculations, carried out at Hartree-Fock level, of the molecular parameters that describe the electric-field-induced linear birefringence, also known as Buckingham birefringence. Focus is in particular on the temperature-independent contribution to the observable. We employ a recently developed analytical scheme for calculating frequency-dependent molecular properties of arbitrary order for self-consistent field methods using basis sets that depend explicitly on the frequency and on the external perturbations.

A density matrix-based quasienergy formulation of the Kohn-Sham density functional response theory using perturbation- and time-dependent basis sets.

A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used.

Efficient elimination of response parameters in molecular property calculations for variational and nonvariational energies.

A general method is presented for the efficient elimination of response parameters in molecular property calculations for variational and nonvariational energies. For variational energies, Wigner's 2n+1 rule is obtained as a special case of the more general k(2n+1) rule, which states that for a subset of k perturbations within a total set of z>or=k perturbations, response parameters may be eliminated according to the 2n+1 rule (normally applied to the full set of perturbations). Nonvariational energies may be treated by introducing Lagrange multipliers that satisfy the stronger 2n+2 rule for the k perturbations, while the wave-function parameters still satisfy the 2n+1 rule for the k perturbations.

Analytical calculations of frequency-dependent hypermagnetizabilities and Cotton-Mouton constants using London atomic orbitals.

We present the first gauge-origin-independent, frequency-dependent calculations of the hypermagnetizability anisotropy, which determines the temperature-independent contribution to magnetic-field-induced linear birefringence, the so-called Cotton-Mouton effect. A density-matrix-based scheme for analytical calculations of frequency-dependent molecular properties for self-consistent field models has recently been developed, which is also valid with frequency- and field-dependent basis sets. Applying this scheme to Hartree-Fock wave functions and using London atomic orbitals in order to obtain gauge-origin-independent results, we have calculated the hypermagnetizability anisotropy.

Analytic calculations of vibrational hyperpolarizabilities in the atomic orbital basis.

We present an analytic scheme for the calculation of pure vibrational contributions to linear and nonlinear optical properties such as the polarizability and the first and second hyperpolarizabilities. The formalism is fully expressed in terms of a perturbation- and time-dependent atomic orbital basis, using the elements of the density matrix in the atomic orbital basis as the basic variables. We calculate perturbed densities up to third order with respect to the electric field in accordance with the n + 1 rule, and the approach is therefore applicable for the calculation of pure vibrational contributions involving all vibrational coordinates in large molecular complexes.