Linear response studies, molecular dynamics

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 next two chapters are devoted to ultrafast radiationless transitions. In Chapter 5, the generalized linear response theory is used to treat the non-equilibrium dynamics of molecular systems. This method, based on the density matrix method, can also be used to calculate the transient spectroscopic signals that are often monitored experimentally. As an application of the method, the authors present the study of the interfadal photo-induced electron transfer in dye-sensitized solar cell as observed by transient absorption spectroscopy. Chapter 6 uses the density matrix method to discuss important processes that occur in the bacterial photosynthetic reaction center, which has congested electronic structure within 200-1500cm 1 and weak interactions between these electronic states. Therefore, this biological system is an ideal system to examine theoretical models (memory effect, coherence effect, vibrational relaxation, etc.) and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, internal conversion theory, etc.) for treating ultrafast radiationless transition phenomena. 

An alternative approach to DS study is to examine the dynamic molecular properties of a substance directly in the time domain. In the linear response approximation, the fluctuations of polarization caused by thermal motion are the same as for the macroscopic rearrangements induced by the electric field [27,28], Thus, one can equate the relaxation function < )(t) and the macroscopic dipole correlation function (DCF) V(t) as follows ... 

Clarke and co-workers studied the effect of chain configurational properties on the stress—strain behavior of glassy linear polymers. They examined the relationship between chain structure and strain hardening by employing controlled stress molecular dynamics on a polyethylenelike chain. Variation of the sample preparation history produces chemically identical materials with vastly different responses to applied stress. 

Figure 3 presents a comparison of the non-equilibrium solvent response functions, Eq (1), for both the photoexcitation ("up") and non-adiabatic ("down") transitions (cf. Fig. 2). The two traces are markedly different the inertial component for the downwards transition is faster and accounts for a much larger total percentage of the total solvation response than that following photoexcitation. The solvent molecular motions underlying the upwards dynamics have been explored in detail in previous work, where it was also determined that the solvent response falls within the linear regime. Unfortunately, the relatively small amount of time the electron spends in the excited state prevents the calculation of the equilibrium excited state solvent response function due to poor statistics, leaving the matter of linear response for the downwards S(t) unresolved. Whether the radiationless transition obeys linear response or not, it is clear that the upward and downwards solvation response behave very differently, due in part to the very different equilibrium solvation structures of the ground and excited state species. Interestingly, the downwards S(t), with its much larger inertial component, resembles the aqueous solvation response computed in other simulation studies, and bears a striking similarity to that recently determined in experimental work based on a combination of depolarized Raman and optical Kerr effect data. ...

Studies[71-73] of the free energy curves for electron transfer at liquid/liquid interfaces have been concerned with several issues. First, to what degree is the linear response assumption which leads to parabolic free energy curves accurate Second, what qualitatively new features does the interface region introduce into the solvent free energy curves Finaly, how do continuum electrostatic models for the free energy curves compare with the molecular dynamics results Here we consider the first two points. For a recent study of continuum models see reference [73]. 

Other Work on Water-Related Systems. Sonoda et al.61 have simulated a time-resolved optical Kerr effect experiment. In this model, which uses molecular dynamics to represent the behaviour of the extended medium, the principle intermolecular effects are generated by the dipole-induced-dipole (DID) mechanism, but the effect of the second order molecular response is also include through terms involving the static molecular / tensor, calculated by an MP2 method. Weber et al.6S have applied ab initio linear scaling response theory to water clusters. Skaf and Vechi69 have used MP2/6-311 ++ G(d,p) calculation of the a and y tensors of water and dimethylsulfoxide (DMSO) to carry out a molecular dynamics simulation of DMSO/Water mixtures. Frediani et al.70 have used a new development of the polarizable continuum model to study the polarizability of halides at the water/air interface. 

One example of the use of linear response theory has been that of Hwang et al. in their studies of an reaction in solution. > o In their work, based on the empirical valence bond (EVB) method discussed earlier, they defined their reaction coordinate Q as the electrostatic contribution to the energy gap between the two valence bond states that are coupled together to create the potential energy surface on which the reaction occurs. Thus, the solvent coordinate is zero at the point where both valence states are solvated equivalently (i.e., at the transition state). Hwang et al. studied the time dependence of this coordinate through both molecular dynamics simulations and through a linear response treatment ... 

The linear-response approach has played an important role in the construction of most modern theories of transport processes (see, e.g. Ref. [3]). Moreover, it has had a profound impact on the development of classical molecular dynamics simulations - a field that was emerging at the same time. Linear-response theory showed how linear transport coefficients can be computed in a simulation, by studying the decay of fluctuations in equilibrium. More specifically, most transport coefficients can be expressed as time integrals of (au-to)correlation functions of microscopic fluxes (e.g. the... 

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... 

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