Linear response theory molecular properties

The next section (Sect. 2) is devoted to a lengthy discussion of the molecular hypothesis from the point of view of quantum field theory, and this provides the basis for the subsequent discussion of optical activity. Having used linear response theory to establish the equations for optical activity (Sect. 3), we pause to discuss the properties of the wavefunctions of optically active isomers in relation to the space inversion operator (Sect. 4), before indicating how the general optical activity equations can be related to the usual Rosenfeld equation for the optical rotation in a chiral molecule. Finally (Sect. 5), there are critical remarks about what can currently be said in the microscopic quantum-mechanical theory of optical activity based on some approximate models of the field theory. 

Several transport properties can be evaluated from equilibrium simulations with use of linear response theory, which relates correlation fimctions of spontaneously fluctuating molecular properties to phenomenological transport coefficients. These relations can be used to evaluate diffusion coefficients, thermal conductivities, viscosities, IR spectra, and so on. However, most of these properties are evaluated more directly using appropriately devised techniques of nonequilibrium molecular dynamics. Particularly challenging for polymers is the direct... 

The effects of including the triple excitations in coupled cluster linear response theory for evaluating the dynamic polarizabilities have been assessed for a set of closed-shell (Ne, HF, N2, CO) and open-shell (CN, CO, O2) systems, in view of exploring a new accuracy regime for molecular properties. The main conclusions include that i) for systems with little or no static correlation, CC3 is nearly identical to CCSDT, ii) CC3 and PS(T) [pole shifted technique where the CCSD-LR poles are corrected by adding a noniterative correction due to the triples] methods perform better than CCSD but their relative accuracy is not determined yet, iii) differences between CCSD and CC3 results as well as the errors with respect to CCSDT drop when the basis set is increased, and iv) ROHF-based CC-LR approaches should be favored over their UHF counterparts while the dilfer-ences between the ROHF and UHF appear as an appropriate criterion for determining whether higher-order UHF-based CC calculations can be used. 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

When Jens Oddershede was elected a Fellow of the American Physical Society in 1993, the citation read For contribution to the theory, computation, and understanding of molecular response properties, especially through the elucidation implementation of the Polarization Propagator formalism. Although written more than a decade ago, it is still true today. The common thread that has run through Jens work for the past score of years is development of theoretical methods for studying the response properties of molecules. His primary interest has been in the development and applications of polarization propagator methods for direct calculation of electronic spectra, radiative lifetime and linear and non-linear response properties such as dynamical dipole polarizabilities and... 

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

Our present focus is on density functional theory and coupled cluster methods for describing molecular systems interacting with a structured environment, and we focus on the derivation of linear response properties and compare the expressions that we obtain for the two different electronic structure methods. Based on linear response... 

The present contribution concerns an outline of the response tlieory for the multiconfigurational self-consistent field electronic structure method coupled to molecular mechanics force fields and it gives an overview of the theoretical developments presented in the work by Poulsen et al. [7, 8, 9], The multiconfigurational self-consistent field molecular mechanics (MCSCF/MM) response method has been developed to include third order molecular properties [7, 8, 9], This contribution contains a section that describes the establisment of the energy functional for the situation where a multiconfigurational self-consistent field electronic structure method is coupled to a classical molecular mechanics field. The second section provides the necessary background for forming the fundamental equations within response theory. The third and fourth sections present the linear and quadratic, respectively, response equations for the MCSCF/MM response method. The fifth 283... 

At the moment of writing very few implementations of the theory of molecular properties at the 4-component relativistic molecular level, beyond expectation values at the closed-shell Hartree-Fock level, have been reported. The first implementation of the linear response function at the RPA level in a molecular code appears to be to MO-based module reported by Visscher et al. [97]. Quiney and co-workers [98] have reported the calculation of second-order properties at the uncoupled Hartree-Fock level (see section 5.3 for terminology). Saue and Jensen [99] have reported an AO-driven implementation of the linear response function at the RPA level and this work has been extended to quadratic response functions by Norman and Jensen [100]. Linear response functions at the DFT/LDA-level have been reported by Saue and Helgaker [101]. In this section we will review the calculation of linear and quadratic response functions at the closed-shell 4-component relativistic Hartree-Fock level. We will follow the approach of Saue and Jensen [99] where the reader is referred for further details. 

Because first-order sensitivity coefficients are easier to calculate than higher order sensitivity coefficients, it is likely that the former may be used more frequently in guiding molecular design. However, first-order sensitivity theory can provide reliable predictions only when the sensitivities of the properties of interest are approximately linear with respect to the model parameters. This linear response limit is satisfied when the perturbations of model parameters are small. For certain applications, such as in protein engineering where one amino acid is mutated into another, the linear response approximation may fail to reliably predict the change in the properties of a protein resulting from a point mutation. It is therefore useful to examine in more detail how well first-order sensitivity theory performs in guiding such predictions. 

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