Laser cooling of vibrational degrees of freedom of a molecular system

We consider the cooling of vibrational degrees of freedom in a photoinduced excited electronic state of a model molecular system. For the various parameters of the potential surfaces of the ground and excited electronic states and depending on the excitation frequency of a single-mode laser light, the average energy or average vibrational temperature of the excited state passes through a minimum. The amount of cooling is quantified in terms of the overlap integral between the ground and excited electronic states of the molecule. We have given an approach to calculate the Franck-Condon factor for a multimode displaced-distorted-rotated oscillator surface of the molecular system. This is subsequently used to study the effect of displacement, distortion, and Duschinsky rotation on the vibrational cooling in the excited state. The absorption spectra and also the average energy or the effective temperature of the excited electronic state are studied for the above model molecular system. Considering the non-Condon effect for the symmetry-forbidden transitions, we have discussed the absorption spectra and average temperature in the excited-state vibrational manifold.     

Enhanced sampling of particular degrees of freedom in molecular systems based on adiabatic decoupling and temperature or force scaling

A method to enhance sampling of a small subset of N(h) particular degrees of freedom of a system of N(h) + N(l) degrees of freedom is presented. It makes use of adiabatically decoupling these degrees of freedom by increasing their mass followed by either increasing their temperature or reducing their interaction or the force acting on them. The appropriate statistical-mechanical expressions for use of these methods in simulation studies are derived. As long as the subset of mass-increased degrees of freedom is small compared to the total number of degrees of freedom of the system, sampling of this subset of degrees of freedom can be much enhanced at the cost of a slight perturbation of the configurational distribution. This is illustrated for a test system of 1000 SPC, simple point charge, water molecules at 300 K and a density of 997 kg m(-3). Various fractions N(h)/(N(h) + N(l)) of water molecules were adiabatically decoupled to different degrees. The size of the diffusion coefficient of these decoupled water molecules was used as a measure for how much the sampling was enhanced and the average potential energy per water molecule was used as a measure of how much the configurational distribution of the system gets distorted. A variety of parameter values was investigated and it was found that for N(h)/(N(h) + N(l)) ≤ 0.1 the diffusion of the N(h) molecules could be enhanced by factors up to 35 depending on the method, the ratio N(h)/(N(h) + N(l)), the extent of adiabatic decoupling, and the temperature or force scaling factors, at the cost of a slight perturbation of the configurational distribution.     

Dependence of collision‐induced dissociation energy on molecular degrees of freedom as a means to assess relative binding affinity in multivalent complexes

In collision‐induced dissociation mass spectrometry experiments, the collision energy required for dissociation linearly depends on the degrees of freedom in the precursor ion. The magnitude of the slope of this relationship previously has been shown to qualitatively correlate to the relative binding strength of a noncovalently bound, monovalent complex. The goal of the work presented here is to determine if a similar methodology can be applied for assessing relative binding strengths in multivalent species. We have tested the method on complexes formed from 18‐crown‐6 and a variety of protonated, primary alkylamines, [C_nH_2n+1NH₃]⁺ (n = 9, 12, 14, 16 and 18) and alkyldiamines, [H₃NC_nH_2nNH₃]²⁺ (n = 3, 5, 6, 9 and 12), and compared our results with dissociation energies calculated using density functional theory at the B3LYP/6‐31G* level. We found that the method correctly assessed the stronger crown ether/headgroup interaction in the two divalent species (1:1 and 2:1 complexes formed from the diaminoalkanes) compared with the weaker interaction in the monovalent species (1:1 complexes formed from mono‐aminoalkanes). However, the experimental method could not distinguish between the binding strengths of the two divalent complexes, perhaps because their calculated dissociation energies were quite similar. Our preliminary results suggest that this method could potentially be used for a quick and simple analysis of binding strengths in multivalent species if the binding strengths of the species are significantly different from one another. Copyright © 2011 John Wiley & Sons, Ltd.     

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.     

Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: a general algorithm and its extension for free energy calculation on rugged energy surface

An approach is developed in the replica exchange framework to enhance conformational sampling for the quantum mechanical (QM) potential based molecular dynamics simulations. Importantly, with our enhanced sampling treatment, a decent convergence for electronic structure self-consistent-field calculation is robustly guaranteed, which is made possible in our replica exchange design by avoiding direct structure exchanges between the QM-related replicas and the activated (scaled by low scaling parameters or treated with high "effective temperatures") molecular mechanical (MM) replicas. Although the present approach represents one of the early efforts in the enhanced sampling developments specifically for quantum mechanical potentials, the QM-based simulations treated with the present technique can possess the similar sampling efficiency to the MM based simulations treated with the Hamiltonian replica exchange method (HREM). In the present paper, by combining this sampling method with one of our recent developments (the dual-topology alchemical HREM approach), we also introduce a method for the sampling enhanced QM-based free energy calculations.     

Transiting the molecular potential energy surface along low energy pathways: The TRREAT algorithm

The Transition Rapidly exploring Random Eigenvector Assisted Tree (TRREAT) algorithm is introduced to perform searches along low curvature pathways on a potential energy surface (PES). The method combines local curvature information about the PES with an iterative Rapidly exploring Random Tree algorithm (LaValle, Computer Science Department, Iowa State University, 1998, TR98–11) that quickly searches high‐dimensional spaces for feasible pathways between local minima. Herein, the method is applied to identifying conformational changes of molecular systems using Cartesian coordinates while avoiding a priori definition of collective variables. We analyze the pathway identification problem for alanine dipeptide, cyclohexane and glycine using nonreactive and reactive forcefields. We show how TRREAT‐identified pathways can be used as valuable input guesses for double‐ended methods such as the Nudged Elastic Band when ascertaining transition state energies. This method can be utilized to improve/extend the reaction databases that lie at the core of automatic chemical reaction mechanism generator software currently developed to build kinetic models of chemical reactions. © 2013 Wiley Periodicals, Inc.     

Modeling the influence of a laser pulse on the potential energy surface in optimal molecular control theory

Understanding and modeling the interaction between light and matter is essential to the theory of optical molecular control. While the effect of the electric field on a molecule's electronic structure is often not included in control theory, it can be modeled in an optimal control algorithm by a set or toolkit of potential energy surfaces indexed by discrete values of the electric field strength where the surfaces are generated by Born-Oppenheimer electronic structure calculations that directly include the electric field. Using a new optimal control algorithm with a trigonometric mapping to limit the maximum field strength explicitly, we apply the surface-toolkit method to control the hydrogen fluoride molecule. Potential energy surfaces in the presence and absence of the electric field are created with two-electron reduced-density-matrix techniques. The population dynamics show that adjusting for changes in the electronic structure of the molecule beyond the static dipole approximation can be significant for designing a field that drives a realistic quantum system to its target observable.     

Surveying a potential energy surface by eigenvector-following

We have developed a method to search potential energy surfaces which avoids some of the difficulties associated with trapping in local minima. Steps are directly taken between minima using eigenvector-following. Exploration of this space by low temperature Metropolis Monte Carlo is a useful global optimisation tool. This method successfully finds the lowest energy icosahedral minima of Lennard- Jones clusters from random starting configurations, but cannot find the global minimum in a reasonable time for difficult cases such as the 38-atom Lennard-Jones cluster where the face-centred-cubic truncated octahedron is lowest in energy. However, by performing searches at higher temperatures, we have found a pathway between the truncated octahedron and the lowest energy icosahedral minima. Such a pathway may be illustrative of some of the structural transformations that are observed for supported metal clusters by electron microscopy.     

Vapor pressure and sublimation rate of molecular crystals: role of internal degrees of freedom

It is a common practice to approximate the desorption rate of atoms from crystal surfaces with an expression of the form nueff exp(-DeltaE/kBT), where DeltaE is an activation barrier to desorb and nueff is an effective vibrational frequency approximately 10(12) s(-1). For molecular solids, however, such an approximation can lead to a many orders of magnitude underestimation of vapor pressure and sublimation rates due to neglected contributions from molecular internal degrees of freedom. Here, we develop a simple working formula that yields good estimates for a general molecular (or atomic) solid and illustrate the approach by computing equilibrium vapor pressure of three different molecular solids and an atomic solid, as well as the desorption rate of a foreign (inhibitor) molecule from the surface of a molecular solid.     

The He-LiH potential energy surface revisited. II. Rovibrational energy transfer on a three-dimensional surface

We use our rigid rotor He-LiH potential energy surface [B. K. Taylor and R. J. Hinde, J. Phys. Chem. 111, 973 (1999)] as a starting point to develop a three-dimensional potential surface that describes the interaction between He and a rotating and vibrating LiH molecule. We use a fully quantum treatment of the collision dynamics on the current potential surface to compute rovibrational state-to-state cross sections. We compute excitation and relaxation vibrational rate constants as a function of temperature by integrating these cross sections over a Maxwell-Boltzmann translational energy distribution and summing over Boltzmann-weighted initial rotational levels. The rate constants for vibrational excitation of LiH are very small for temperatures below 300 K. Rate constants for vibrational relaxation of excited LiH molecules, however, are several orders of magnitude larger and show very little temperature dependence, suggesting that the collisions that result in vibrational relaxation are governed by long-range attractive interactions.     

Reaction path as a gradient line on a potential energy surface

The reaction path is shown to be always a gradient line on a potential energy surface (PES ) of a molecule. The properties of gradient lines on the PES are elucidated. Correct symmetry conservation rules along the gradient line are derived. The behavior of the gradient line on a PES with different topologies are considered. © 1994 John Wiley & Sons, Inc.     

Effective van der Waals surface energy of self-assembled monolayer films having systematically varying degrees of molecular fluorination

The systematic variation of the van der Waals surface energy with fluorination for a series of self-assembled monolayers (SAMs) generated by the adsorption of partially fluorinated alkanethiols onto the surface of gold is examined experimentally and theoretically. The surface energy is elucidated on the basis of an effective Hamaker constant, which is obtained as a combination of the respective Hamaker constants of fluorocarbons and hydrocarbons; the fraction depends on the degree of fluorination. The good agreement between experiment and theory is discussed. In addition, the Hamaker constants of various liquids contacted on the well-defined hydrophobic surfaces are interpreted using modified Lifshitz theory.     

Simulation of electronic and geometric degrees of freedom using a kink-based path integral formulation: application to molecular systems

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. The results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. A comparison with density functional theory (DFT) and second-order Moller-Plesset (MP2) level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.     

Relative Gibbs energies in solution through continuum models: effect of the loss of translational degrees of freedom in bimolecular reactions on Gibbs energy barriers

We present here a cell model for evaluating Gibbs energy barriers corresponding to bimolecular reactions (or processes of larger molecularity) in which a loss of translational degrees of freedom takes place along the reaction coordinate. With this model, we have studied the Walden inversion processes: Xa- + H3CXb --> XaCH3 + Xb- (X = F, Cl, Br, and I). In these processes, our model yields an increase of about 2.3-3.4 kcal/mol in Gibbs energy in solution corresponding to the loss of the translational degrees of freedom when passing from separate reactants to the TS in good agreement with experimental data. The corresponding value in the gas phase is about 6.7-7.1 kcal/mol. When the difference between these two figures is used to correct the results obtained by the standard UAHF implementation of the continuum model, the theoretical results are brought significantly closer to the experimental ones. This seems to indicate that for these reactions the parametrization used does not adequately introduce the increase in Gibbs energy corresponding to the constriction of the translational motion of the species along the reaction coordinate when passing from the gas phase to solution. Therefore, we believe that continuum models could perform much better if we released the parametrization process from the task of taking into account the constriction in translation motion in solution, which could be more adequately evaluated using the cell model proposed here, thus allowing it to focus on better reproducing all the remaining solvation effects.     

Supercomputer docking with a large number of degrees of freedom

ABSTRACT

Docking represents one of the most popular computational approaches in drug design. It has reached popularity owing to capability of identifying correct conformations of a ligand within an active site of the target-protein and of estimating the binding affinity of a ligand that is immensely helpful in prediction of compound activity. Despite many success stories, there are challenges, in particular, handling with a large number of degrees of freedom in solving the docking problem. Here, we show that SOL-P, the docking program based on the new Tensor Train algorithm, is capable to dock successfully oligopeptides having up to 25 torsions. To make the study comparative we have performed docking of the same oligopeptides with the SOL program which uses the same force field as that utilized by SOL-P and has common features of many docking programs: the genetic algorithm of the global optimization and the grid approximation. SOL has managed to dock only one oligopeptide. Moreover, we present the results of docking with SOL-P ligands into proteins with moveable atoms. Relying on visual observations we have determined the common protein atom groups displaced after docking which seem to be crucial for successful prediction of experimental conformations of ligands.     

Ag vibrational levels of cyclobutadiene on a new potential energy surface

GVB /[5s3p1d/3s1p] energies were calculated for 31 geometries of cyclobutadiene in the D_2h point group. These geometries differed in the values of the symmetrized internal coordinates for two CC stretching and one CCH bending modes. The data points were fitted to the expansions of in powers of . Variational calculations provided the following energies of the lowest A_g vibrational levels (with respect to the vibrational ground state): 4.4; 1161.2; 1162.3; 1304.0; 1322.8; 1920.3; and 1991.0 cm^?1.     

Exploring the potential energy surface of retinal, a comparison of the performance of different methods

The ground state structure of retinal has been investigated. We found that DFT and CASSCF produce different results for the bond length alternation in a model system of retinal. Quantum mechanics/molecular mechanics calculations including the closest surrounding amino acids have been performed, using DFT and CASSCF to calculate the structure of retinal in the protein cavity. The planarity of the retinal molecule is affected by the surrounding protein. DFT and CASSCF produce different twist angles. The difference between CASSCF and DFT appears to be related to the positively charged nitrogen of the Schiff base, which leads to different pi-bond orders produced by the two methods.