Mohammadhasan Dinpajooh

Non-Gaussian Lineshapes and Dynamics of Time-Resolved Linear and Nonlinear (Correlation) Spectra

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophores electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Free energy functionals for polarization fluctuations: Pekar factor revisited

The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. Within dielectric continuum models, this separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom. The main qualitative prediction of Pekars perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. Here, we study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. However, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).

Free energy of ion hydration: Interface susceptibility and scaling with the ion size.

Free energy of solvation of a spherical ion in a force-field water is studied by numerical simulations. The focus is on the linear solvation susceptibility connecting the linear response solvation free energy to the squared ion charge. Spherical hard-sphere solutes, hard-sphere ions, and Kihara solutes (Lennard-Jones modified hard-sphere core) are studied here. The scaling of the solvation susceptibility with the solute size significantly deviates from the Born equation. Using empirical offset corrections of the solute size (or the position of the first peak of the solute-solvent distribution function) do not improve the agreement with simulations. We advance a new perspective on the problem by deriving an exact relation for the radial susceptibility function of the interface. This function yields an effective cavity radius in the Born equation calculated from the solute-solvent radial distribution function. We find that the perspective of the local response, assuming significant alteration of the solvent structure by the solute, is preferable compared to the homogeneous approximation assuming intact solvent structure around the solute. The model finds a simple explanation of the asymmetry of hydration between anions and cations in denser water shells around anions and smaller cavity radii arising from the solute-solvent density profiles.

Polarizability of the active site of cytochrome c reduces the activation barrier for electron transfer

Enzymes in biology’s energy chains operate with low energy input distributed through multiple electron transfer steps between protein active sites. The general challenge of biological design is how to lower the activation barrier without sacrificing a large negative reaction free energy. We show that this goal is achieved through a large polarizability of the active site. It is polarized by allowing a large number of excited states, which are populated quantum mechanically by electrostatic fluctuations of the protein and hydration water shells. This perspective is achieved by extensive mixed quantum mechanical/molecular dynamics simulations of the half reaction of reduction of cytochrome c. The barrier for electron transfer is consistently lowered by increasing the number of excited states included in the Hamiltonian of the active site diagonalized along the classical trajectory. We suggest that molecular polarizability, in addition to much studied electrostatics of permanent charges, is a key parameter to consider in order to understand how enzymes work.

On the Density Dependence of the Integral Equation Coarse-Graining Effective Potential

Coarse-graining (CG) procedures provide computationally efficient methods for investigating the corresponding long time- and length-scale processes. In the bottom-up approaches, the effective interactions between the CG sites are obtained using the information from the atomistic simulations, but reliable CG procedures are required to preserve the structure and thermodynamics. In this regard, the integral equation coarse-graining (IECG) method is a promising approach that uses the first-principles Ornstein-Zernike equation in liquid state theory to determine the effective potential between CG sites. In this work, we present the details of the IECG method while treating the density as an intrinsic property and active variable of the CG system. Performing extensive simulations of polymer melts, we show that the IECG theory/simulation and atomistic simulation results are consistent in structural properties such as the pair-correlation functions and form factors, and also thermodynamic properties such as pressure. The atomistic simulations of the liquids show that the structure is largely sensitive to the repulsive part of the potential. Similarly, the IECG simulations of polymeric liquids show that the structure can be determined by the relatively short-range CG repulsive interactions, but the pressure is only accurately determined once the long-range, weak CG attractive interactions are included. This is in agreement with the seminal work by Widom on the influence of the potential on the phase diagram of the liquid [Widom, B. Science 1967 , 157 , 375 - 382 ]. Other aspects of the IECG theory/simulations are also discussed.

Dielectric constant of water in the interface

We define the dielectric constant (susceptibility) that should enter the Maxwell boundary value problem when applied to microscopic dielectric interfaces polarized by external fields. The dielectric constant (susceptibility) of the interface is defined by exact linear-response equations involving correlations of statistically fluctuating interface polarization and the Coulomb interaction energy of external charges with the dielectric. The theory is applied to the interface between water and spherical solutes of altering size studied by molecular dynamics (MD) simulations. The effective dielectric constant of interfacial water is found to be significantly lower than its bulk value, and it also depends on the solute size. For TIP3P water used in MD simulations, the interface dielectric constant changes from 9 to 4 when the solute radius is increased from ∼5 to 18 Å.

Accuracy, Transferability, and Efficiency of Coarse-Grained Models of Molecular Liquids

Coarse-graining (CG) approaches are becoming essential tools in the study of complex systems because they can considerably speed up computer simulations, with the promise of determining properties in a range of length scales and time scales never before possible. While much progress in this field has been achieved in recent years, application of CG methods is still inhibited by the limited understanding of a number of conceptual points that need to be resolved to open up the field of CG to a wide range of applications in material science and biology. In this paper, we present some of the key findings that emerged from the development of the integral equation theory of coarse-graining (IECG), which addresses some of the fundamental questions in coarse-graining. Although the IECG method pertains to the CG of polymer liquids, and specifically homopolymer melts are illustrated here, many of the results that emerge from the study of the IECG approach are general and apply to the CG of any molecular liquid. Through this method, we developed a formal relation between the statistical mechanics of CG and a number of predicted physical properties. On the basis of the theory of liquids, the IECG affords the analytical solution of the intermolecular potential for macromolecules represented by a Markov chain of CG sites, thus providing a transparent tool for analysis of the properties in coarse-graining. We identify three key requirements that render a CG model useful: accuracy, transferability, and computational efficiency. When these three requirements are fulfilled, the CG model becomes widely applicable and useful for studying regions in the phase space that are not covered by atomistic simulations. In the process, the IECG answers formally a number of relevant questions on how structural, thermodynamic, and dynamical properties are modified during coarse-graining. It sheds light upon how the level of CG affects the shape of the CG potential and how, in turn, the shape of the potential affects the physical properties. It tests the validity of selecting the potential-of-mean force as the effective pairwise CG potential and the role of higher-order many-body corrections to the pairwise potential to recover structural and thermodynamic consistency of the CG model. Because the IECG theory can be analytically formalized, it does not suffer from the problem of transferability and, in the canonical ensemble, leads to consistent pair distribution functions, pressure, isothermal compressibility, and excess free energy at variable levels of CG from the atomistic to the ultra-CG model, where macromolecules are represented as interpenetrable soft spheres.

Universality and Specificity in Protein Fluctuation Dynamics

We investigate the universal scaling of protein fluctuation dynamics with a site-specific diffusive model of protein motion, which predicts an initial subdiffusive regime in the configurational relaxation. The long-time dynamics of proteins is controlled by an activated regime. We argue that the hierarchical free energy barriers set the time scales of biological processes and establish an upper limit to the size of single protein domains. We find it compelling that the scaling behavior for the protein dynamics is in close agreement with the Kardar-Parisi-Zhang scaling exponents.