Ab Initio Methods for the Calculation of NMR Shielding and Indirect Spin-Spin Coupling Constants

Predicting the electronic structure of extended organic molecules constitutes an important fundamental task of modern chemistry. Studies of electronic excitations, charge-transfer, energy-transfer, and isomerization of conjugated systems form the basis for our understanding of the photophysics and photochemistry of complex molecules1-3 as well as organic nanostructures and supramolecular assemblies.4,5 Photosynthesis and other photochemical biological processes that constitute the basis of life on Earth involve assemblies of conjugated chromophores such as porphyrins, chlorophylls, and carotenoids.6-8 Apart from the fundamental interest, these studies are also closely connected to numerous important technological applications.9 Conjugated polymers are primary candidates for new organic optical materials with large nonlinear polarizabilities.10-19 Potential applications include electroluminescence, light emitting diodes, ultrafast switches, photodetectors, biosensors, and optical limiting materials.20-27 Optical spectroscopy which allows chemists and physicists to probe the dynamics of vibrations and electronic excitations of molecules and solids is a powerful tool for the study of molecular electronic structure. The theoretical techniques used for describing spectra of isolated small molecules are usually quite different from those of molecular crystals, and many intermediate size systems, such as clusters and polymers, are not readily described by the methods developed for either of these limiting cases.28

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Density Matrix Analysis and Simulation of Electronic Excitations in Conjugated and Aggregated Molecules

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

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

The advantages of the propagator formalism, as a direct method of calculating ionization energies, are stressed. The propagator equations are derived for closed-shell systems using an operator method instead of the usual diagrammatic derivations. The equations enable the development of an interpretation of the ionization energies in terms of conceptually simple quantities, such as pair correlation energies and associated relaxation effects, and retain the idea of orbital ionization. Infinite summations appearing in the self-energy terms are replaced by finite expressions involving functions satisfying uncoupled inhomogeneous differential equations. Certain high-order propagator equations are derived, and a connection with the Bethe-Goldstone formulation of pair correlation is made. Several computational procedures are advocated as forming the basis for balanced calculations of atomic and molecular ionization energies.

Direct calculation of ionization energies

A practical polarization propagator method devised for the treatment of valence electron excitations in atoms and molecules is presented. This method, referred to as (second-order) algebraic-diagrammatic construction (ADC(2)), allows for a theoretical description of single and double excitations consistently through second and first order, respectively, of perturbation theory. The computational scheme is essentially an eigenvalue problem of a Hermitian secular matrix defined with respect to the space of singly and doubly excited configurations. The configuration space is smaller (more compact) than that of comparable configuration interaction (CI) expansions and the method leads to size-consistent results. The performance of the ADC(2) method is tested in exemplary applications to Ne, Ar and CO, where detailed comparison can be made with experiment and previous theoretical results. While the accuracy of the absolute excitation energies is only moderate, a very satisfactory description is obtained for the relative energies and, in particular, for the spectral intensities. Aspects related to the Thomas-Reiche-Kuhn sum rule and the equivalence of the dipole-length and dipole-velocity forms of the transition moments are discussed. Due to the relatively small computational expense and the possibility of a direct ADC(2) formulation this method should prove particularly useful in applications to large molecules.

https://iopscience.iop.org/article/10.1088/0953-4075/28/12/003/pdf

An efficient polarization propagator approach to valence electron excitation spectra

Correlated calculations of indirect nuclear spin-spin coupling constants for XH4 (X = Si, Ge, and Sn)

A formal scheme is developed for finding the particle‐hole propagator by means of a self‐consistent decoupling procedure analogous to the Hartree‐Fock decoupling for the electron propagator. The self‐consistency comes from a contour integration of the Fourier transform of the propagator, utilizing a method introduced by Coulson. The method yields oscillator strengths and excitation energies, as well as the two‐particle density matrix, which allows any one‐ or two‐particle operator expectation value to be evaluated. The stability of the scheme is discussed, and comparisons with other, related, approximations are made.

Self-consistent polarization propagator approximation as a modified random phase method

We have derived a self‐consistent time‐dependent Hartree‐Fock scheme based on a Green's function approach. The contour integral is performed analytically, which makes the computational effort per iteration comparable with a normal time‐dependent Hartree‐Fock calculation. The excitation energies are found as poles for the polarization propagator in the energy representation. The corresponding residues determine the transition moments. Comparison is made with other similar random‐phase approximations. We have applied our scheme to the π‐electron systems of trans ‐butadiene, pyridine, and benzene. The triplet spectra of those molecules especially are considerably improved over normal time‐dependent Hartree‐Fock results.

Self-consistent time-dependent Hartree--Fock scheme

Coupled hartree-fock and second order polarization propagator calculations of indirect nuclear spin-spin coupling constants for diatomic molecules

Excitation energies and transition moments have been determined from a second order polarization propagator and the effect of including energy shifted denominators has been investigated. Results for Be and CH+ show a change of 2–5% for the transition moments and of 0–20% for the singlet excitation energies in a second order approach compared to a first order (time-dependent Hartree-Fock) approximation. Both Be and CH+ are triplet unstable in the time-dependent Hartree-Fock approximation. The triplet instability is removed for Be but not for CH+ in a second order polarization propagator approach.

Determination of excitation energies and transition moments in a second order polarization propagator approach. Application to the Be atom and the CH+ molecule

Jens Oddershede

Papers

Correlated calculations of indirect nuclear spin-spin coupling constants for XH4 (X = Si, Ge, and Sn)

Self-consistent polarization propagator approximation as a modified random phase method

Self-consistent time-dependent Hartree--Fock scheme

Coupled hartree-fock and second order polarization propagator calculations of indirect nuclear spin-spin coupling constants for diatomic molecules

Determination of excitation energies and transition moments in a second order polarization propagator approach. Application to the Be atom and the CH+ molecule