Atomic orbital-based cubic response theory for one-, two-, and four-component relativistic self-consistent field models (original) (raw)
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Analytic Calculations of Vibrational Hyperpolarizabilities in the Atomic Orbital Basis
The Journal of Physical Chemistry A, 2008
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. In the case of static electric fields, we therefore only need to calculate 19 response equations, independent of the size of the molecule. If we can determine the molecular energy and force field, the calculation of pure vibrational contributions to the nonlinear optical properties of the molecule is therefore a rather straightforward task. We illustrate the implementation by calculating pure vibrational contributions to the first and second hyperpolarizabilities of molecules containing up to 66 atoms using basis sets of good quality.
2006
A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen ͓Phys. Rev. 78, 29 ͑1950͔͒ transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant ␣. The resulting ␣-dependent Hamiltonian is then used to set up a perturbation theory in orders of ␣ 2 , using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in ␣ 2 for the Hartree-Fock model. However, since all relativistic considerations are contained in the ␣-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the ␣-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.
2005
We report the implementation and application of linear response density-functional theory (DFT) based on the 4-component relativistic Dirac-Coulomb Hamiltonian. The theory is cast in the language of second quantization and is based on the quasienergy formalism (Floquet theory), replacing the initial state dependence of the Runge-Gross theorem by periodic boundary conditions. Contradictions in causality and symmetry of the time arguments are thereby avoided and the exchange-correlation potential and kernel can be expressed as functional derivatives of the quasienergy. We critically review the derivation of the quasienergy analogues of the Hohenberg-Kohn theorem and the Kohn-Sham formalism and discuss the nature of the quasienergy exchange-correlation functional. Structure is imposed on the response equations in terms of Hermiticity and time-reversal symmetry. It is observed that functionals of spin and current densities, corresponding to time-antisymmetric operators, contribute to frequency-dependent and not static electric properties. Physically, this follows from the fact that only a time-dependent electric field creates a magnetic field. It is furthermore observed that hybrid functionals enhance spin polarization since only exact exchange contributes to anti-Hermitian trial vectors.
First-order relativistic corrections to response properties: the hyperpolarizability of the Ne atom
Journal of Physics B: Atomic, Molecular and Optical Physics, 2004
The computation of first-order relativistic corrections to electrical response properties has been implemented into the Dalton program at the level of closedshell coupled-cluster theory, within the framework of the direct perturbation theory (DPT) of relativistic effects. Calculations of the first-order relativistic DPT corrections to the static and frequency-dependent dipole polarizability (α) and second dipole hyperpolarizability (γ) of the Ne atom illustrate possible applications of the new code.
2014
The longitudinal polarizability (α) and second hyperpolarizability (γ ) of the H 2 molecule as a function of the internuclear distance are calculated using the PNOF5 level of theory. It is shown that PNOF5 gives accurate results for the longitudinal α and γ over the whole curve range, even for those structures exhibiting a high degree of diradical character. The good agreement between these results and reference full-CI data highlights the adequacy of PNOF5 to treat electronic systems exhibiting large static electron correlation and shows a promising accuracy in calculating nonlinear optical properties for systems covering a large range of diradical character. The results further support the paradigm of using molecules with intermediate diradical character to enhance the second hyperpolarizabilities.
Relativistic self-consistent-field atomic calculationsusing a generalization of Brillouin's theorem
Canadian Journal of Physics, 1998
When the one-body part of the relativistic Hamiltonian M is a sum of one-electron Dirac Hamiltonians, relativistic configuration interaction (CI) calculations are carried out on an ad hoc basis of positive-energy orbitals, t n ( =c 2cc6, and more recently, with the full bases of positive-energy and negative-energy orbitals, t n c Q ( =c 2cc6. . &nÄ E26QÄ E6 establishing a new variational principle for relativistic calculations of electronic structures. In this paper, on the basis of Brillouin's theorem and a relativistic multiconfiguration Hartree-Fock (RMCHF) expansion in the t n c Q ( =c 2cc6 basis, we develop equations to annihilate the coefficients of all single excitations to obtain very accurate RMCHF solutions. Moreover, after nullifying the coefficients of single excitations, the above inequality among energies becomes an equality, leading to a particular instance of an exact decoupling of positive-energy and negative-energy orbitals, irrespective of any ad hoc choice of potentials, hence rigorously justifying, for the first time, the absence of explicit projection operators in all current relativistic work where one-electron Dirac Hamiltonians are involved. We present, also for the first time, relativistic Hartree-Fock approximations for the ground states of He through Ar, which are accurate to six decimals in a.u., and which converge to the nonrelativistic results when the speed of light S <" . This accuracy was obtained by means of compact Slater-type orbital expansions through a direct translation of nonrelativistic Hartree-Fock without need to reoptimize nonlinear parameters. Our SCF equations are also valid for any open shells and for any excited states within a given symmetry, as exemplified with applications to odd-parity, a '*2, r 2 2r 2 2R 2 ?R states of neutral nitrogen.
Resolution of molecular electric hyperpolarizabilities into atomic terms
Chemical Physics Letters, 1999
Using the dipole acceleration formalism, a general theory for the resolution of molecular electric hyperpolarizabilities, at an arbitrary frequency, into atomic terms is presented. Test calculations for the molecules NH , H O and HF, at the random 3 2 phase approximation level of accuracy, are reported.
Journal of Molecular Structure, 2001
Analytical computations of the ®rst-order relativistic correction in the framework of direct perturbation theory (DPT) have recently become available at the level of coupled cluster theory with singles and doubles excitations (CCSD). At this level, large-scale calculations were performed on the hydrogen halides HX (X F; Cl, Br, I) including core-and core-valence correlation effects and a perturbative correction for connected triples excitations [CCSD(T)]. Potential energy curves were computed and spectroscopic constants (r e , v e , v e x e , B e) were derived.