Molecular response properties

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... 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

As the molar polarizabilities represent an easily available experimental set of data, the expressions above become important for the theoretical evaluation of molecular response properties in fact they represent the most direct quantities to compare with the computed results obtained applying a given model for the solvent effects. 

The extension of density functional theory (DFT) to the dynamical description of atomic and molecular systems offers an efficient theoretical and computational tool for chemistry and molecular spectroscopy, namely, time-dependent DFT (TDDFT) [7-11]. This tool allows us to simulate the time evolution of electronic systems, so that changes in molecular structure and bonding over time due to applied time-dependent fields can be investigated. Its response variant TDDF(R)T is used to calculate frequency-dependent molecular response properties, such as polarizabilities and hyperpolarizabilities [12-17]. Furthermore, TDDFRT overcomes the well-known difficulties in applying DFT to excited states [18], in the sense that the most important characteristics of excited states, the excitation energies and oscillator strengths, are calculated with TDDFRT [17, 19-26]. 

In the following section we shall show how all these specificities of the QM/MM and QM/continuum approaches will affect the quality of the description one can obtain applying them to the study of solvent effects on molecular response properties. 

In the previous sections we have briefly summarized the basic theory of QM/MM and QM/continuum methods showing their differences and similarities, now we can move on to describe their applications to the calculation of molecular response properties and the related spectroscopies for a generic solvated system. 

Equation (2) is an example of a sum-over-states (SOS) expression of a molecular response property. It suggests an easy way of computing / , but in practice the SOS approach is rarely taken because of its very slow convergence, i.e., because of the need to compute many excited states wavefunctions. The summation goes over all excited states and also needs to include, in principle, the continuum of unbound states. As it will be shown below, there are more economic ways of computing [1 within approximate first-principles electronic structure methods. 

Further, there are asymptotically corrected XC kernels available, and other variants (for instance kernels based on current-density functionals, or for range-separated hybrid functionals) with varying degrees of improvements over adiabatic LDA, GGA, or commonly used hybrid DFT XC kernels [45]. The approximations in the XC response kernel, in the XC potential used to determine the unperturbed MOs, and the size of the one-particle basis set, are the main factors that determine the quality of the solutions obtained from (13), and thus the accuracy of the calculated molecular response properties. Beyond these factors, the quality of the... 

Approximations made in the XC potential generally also affect the quality of the XC response kernel if it is derived from the potential. In addition, in essentially all applications of TDDFT to computations of molecular response properties, the XC kernel is adiabatic (not frequency-dependent), even though it should be a function of frequency. One of the better known consequences of the adiabatic approximation is the inability of TDDFT to describe simultaneous excitations of more than one electron. Due to the sometimes very pronounced effects from the approximations under points 1-3, along with effects from limited basis set flexibility, it is not clear how strongly the adiabatic approximation affects present-day computations of molecular chiroptical response properties in terms of its ability to predict ECD and ORD in the UV-Vis range of frequencies. 

Lazzeretti, P. (2004) Assessment of aromaticity via molecular response properties. Phys. Chem. Chem. Phys., 6, 217-223. 

With molecular response property we mean here the change in some properties of a molecule when subject to an external field of electric or magnetic type. 

Our studies on molecular response properties have been limited to the standard PCM, with the exception of the application of the lEF formalism to electric (hyper)polarizabilities. Molecular response functions are quite sensitive to the details of the calculation, by far more than energy, and can be used to test in a deeper way the various extensions of PCM we have exposed in the previous pages an example of this use of molecular response, addressed to the inclusion into HF equation of dispersion and repulsion terms, can be found in... 

An overview of the Polarizable Continuum Model (PCM) for the modelling of solvent effects on the state and the properties of quantum mechanical molecular systems is presented. The main theoretical and numerical aspects of this method are presented and discussed, together with its extension to the derivative theory. We present some selected applications concerning the evaluation of molecular response properties, and of the corresponding spectroscopic quantities, of different solvated systems. 

In particular, we shall focus on the PCM solvation methods only, showing how they have been linked to the most used QM formalisms exploited to evaluate geometries and molecular response properties both to electric and magnetic fields, or to the combination of them. The exposition will be thus divided accordingly to the following classification ... 

This series presents reviews of ciurent advances in computational methodologies and applications. The first chapter written by R. Cammi, B. Mennucci, and J. Tomasi provides an overview of their developments of the Polarizable Continuum Model (PCM). This approach has been particularly popularized after its implementation into the GAUSSIAN suite of programs. The authors reveal both the theoretical and numerical aspects of the PCM model. Also, promising extensions of the theory are discussed. Among the possible applications, examples concerning the evaluation of molecular-response properties and spectroscopic quantities are provided. 

The efficient computation of molecular response properties such as optical rotation is of paramount importance, and schemes for reducing the computational effort required for high-accuracy methods such as coupled cluster theory become even more crucial for larger, chemically relevant molecules. However, algorithmic improvements must not come at the expense of the overall accuracy of the theory, and the EOM-CCl approach of Sekino and Bartlett provides a reasonable com-... 

The bulk susceptibilities from Eq. [2] are to be related to molecular response properties denoted as a, p, and -y. These molecular properties can be defined from the Taylor series of the response of the molecular dipole moment as follows ... 

Gontrani L, Mennucci B, Tomasi J (2000) Glycine and alanine a theoretical study of solvent effects upon energetics and molecular response properties. J Mol Struct Theochem 500 113... 

The effective response theory describes the variation of the properties of the molecular solute when subjected to an external perturbing field which correspond to the Maxwell electromagnetic field in the medium. The resulting molecular response properties, represent effective response properties which can be directly related to macroscopic observables, after a proper averaging over the orientational states of the molecular solutes [31-33]. 

In PCM, reaction field effects on molecular properties and spectroscopies that arise from the cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly relate the response of the molecular solutes to the Maxwell field in the hquid, both static E and dynamic [158,194,208]. 

In the following tables all definitions of molecular response properties as derivatives of the energy or derivatives of other properties are collected. 

Molecular response properties can be described introducing the following general dehnidons ... 

Sous J, Goel P, Nooijen M. Similarity transformed equation of motion coupled cluster theory revisited a benchmark study of valence excited states. Mol Phys. 2013 112 616-638. Trofimov AB, Krivdina IL, Weller J, Schimer J. Algebraic-diagrammatic construction propagator approach to molecular response properties. Chem Phys. 2006 329 1-10. 

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