Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.     

Transfer of electronic energy to vibrational degrees of freedom in complex molecules. Part II

A study is made of the mean of the energy operator for the n-th oscillator with respect to the wave functions of part I. This mean is found to be a highly oscillatory function of time, which implies that it is best described via a distribution function giving the time spent by the function between specified limits. The probability of dissociation at a particular bond is deduced, and the results are compared with the mass spectra produced from long-chain paraffins irradiated with fast electrons. Theory is in qualitative agreement with the observed spectra. Results obtained with C¹³ labels [9] are explained.     

Water models based on a single potential energy surface and different molecular degrees of freedom

Up to now it has not been possible to neatly assess whether a deficient performance of a model is due to poor parametrization of the force field or the lack of inclusion of enough molecular properties. This work compares several molecular models in the framework of the same force field, which was designed to include many-body nonadditive effects: (a) a polarizable and flexible molecule with constraints that account for the quantal nature of the vibration [B. Hess, H. Saint-Martin, and H. J. C. Berendsen, J. Chem. Phys. 116, 9602 (2002), H. Saint-Martin, B. Hess, and H. J. C. Berendsen, J. Chem. Phys. 120, 11133 (2004)], (b) a polarizable and classically flexible molecule [H. Saint-Martin, J. Hernandez-Cobos, M. I. Bernal-Uruchurtu, I. Ortega-Blake, and H. J. C. Berendsen, J. Chem. Phys. 113, 10899 (2000)], (c) a polarizable and rigid molecule, and finally (d) a nonpolarizable and rigid molecule. The goal is to determine how significant the different molecular properties are. The results indicate that all factors--nonadditivity, polarizability, and intramolecular flexibility--are important. Still, approximations can be made in order to diminish the computational cost of the simulations with a small decrease in the accuracy of the predictions, provided that those approximations are counterbalanced by the proper inclusion of an effective molecular property, that is, an average molecular geometry or an average dipole. Hence instead of building an effective force field by parametrizing it in order to reproduce the properties of a specific phase, a building approach is proposed that is based on adequately restricting the molecular flexibility and/or polarizability of a model potential fitted to unimolecular properties, pair interactions, and many-body nonadditive contributions. In this manner, the same parental model can be used to simulate the same substance under a wide range of thermodynamic conditions. An additional advantage of this approach is that, as the force field improves by the quality of the molecular calculations, all levels of modeling can be improved.     

Transfer of electron excitation energy to vibrational degrees of freedom in complex molecules. Part I

Energy transfer is discussed for paraffin molecules excited by electrons of energy about 100 ev; the nonadiabatic transient wave function for the positive ion of a long molecule is derived and is used to examine the distribution of vibrational energy along the chain.     

Multistate multimode vibronic dynamics: entanglement of electronic and vibrational degrees of freedom in the benzene radical cation

An earlier theoretical treatment of multimode and multistate vibronic coupling in the benzene radical cation [Koppel et al., J. Chem. Phys. 117, 2657 (2002)] is extended to investigate also the behavior of the nuclear degrees of freedom and to include additional electronic states. The five lowest doublet electronic states are considered which have been shown earlier to be all interconnected through a series of conical intersections of their potential-energy surfaces. In the most extensive calculations, they are all included simultaneously in the quantum dynamical calculations performed, which represent a system of unprecedented complexity treated in this way. The results are compared with various reduced-dimensionality treatments (i.e., employing reduced vibrational and electronic function spaces). The different temporal behavior of the various electronic populations is emphasized and traced to the different locations of the various seams of conical intersections: due to the coherent oscillations of the time-dependent wave packet this leads to an oscillatory behavior in some cases and to monotonous behavior in others. A seemingly irreversible behavior of the system dynamics in this strictly microscopic treatment is confirmed. The importance of this benchmark system to highlight complex, entangled multimode, and multistate vibronic dynamics is pointed out.     

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.     

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.     

Classical description of activated conformational processes in molecular systems coupled to solvent degrees of freedom

Extended Fokker-Planck (FP) equations are generalized stochastic equations which describe the evolution of a set of coordinates, loosely referred to as solute, coupled with a relevant set of solvent variables. They are useful for the analysis of molecular dynamics in liquids, when a time-scale separation between probe motions and relaxation times of interactions with surroundings particles cannot be performed, because of persistence of slowly fluctuating components. In this article, we focus attention on a model system, made up of an angular coordinate and its conjugate momentum, submitted to a bistable potential, and coupled to a dissipative harmonic mode, to investigate the influence of polar solvents on reactive dynamics. The results are appropriate to describe dielectric effects, solvent-controlled conformational changes involving charge transfer which occur in photophysical processes, and the dynamic Stokes shifts observed in time-resolved fluorescence experiments. © 1996 John Wiley & Sons, Inc.     

Simulation of a complex spectrum: interplay of five electronic states and 21 vibrational degrees of freedom in C5H4 +

Using a five-state, all-mode vibronic coupling model Hamiltonian derived in a previous publication [A. Markmann et al., J. Chem. Phys. 122, 144320 (2005)], we have calculated the photoelectron spectrum of the pentatetraene cation in the neighborhood of the B (2)E state, which can be represented with charge-localized components. To this end, quantum nuclear dynamics calculations were performed using the multiconfiguration time-dependent Hartree method, taking all 21 vibrational normal modes into account. Compared to experiment, the main features are reproduced but higher accuracy experiments are necessary to gauge the accuracy of the predictions for the vibronic progressions at the rising flank of the spectrum.     

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.     

Altered inertial response of generic degrees of freedom

A method to alter the inertial response of generic degrees of freedom is presented. A Hamiltonian acts on the inertial response of a set of independent configurational observables by the introduction of a kinetic bias. The method finds its natural application in reducing the spreading of arbitrary modes in a complex system. The resulting compressed spectrum allows a more efficient sampling of configurational space.     

Time-resolved vibrational spectroscopy of a molecular shuttle

Time-resolved vibrational spectroscopy is used to investigate the inter-component motion of an ultraviolet-triggered two-station molecular shuttle. The operation cycle of this molecular shuttle involves several intermediate species, which are observable in the amide I and amide II regions of the mid-IR spectrum. Using ab initio calculations on specific parts of the rotaxane, and by comparing the transient spectra of the normal rotaxane with that of the N-deuterated version, we can assign the observed vibrational modes of each species occurring during the shuttling cycle in an unambiguous way. The complete time- and frequency-dependent data set is analyzed using singular value decomposition (SVD). Using a kinetic model to describe the time-dependent concentrations of the transient species, we derive the absorption spectra associated with each stage in the operation cycle of the molecular shuttle, including the recombination of the charged species.     

Multiple time scale molecular dynamics for fluids with orientational degrees of freedom. I. Microcanonical ensemble

We propose a new approach to eliminate the resonance instabilities inherent in multiple time step molecular dynamics simulations. The approach is developed within the microcanonical ensemble on the basis of an energy-constrained technique in the presence of orientational degrees of freedom. While the single and standard multiscale methods are restricted to small time steps of 5 and 8 fs, respectively, it is shown in simulations of water that the algorithms we have derived postpone the appearance of the instabilities to larger steps of about 16 fs. Such steps are close to the upper theoretical limit of 20 fs peculiar to the microcanonical ensemble and can be used without affecting static and dynamical properties.     

Symmetry groups and representations of hamiltonians for several coupled degrees of freedom: Application to non-rigid molecular vibrations

We present a systematic method of determining finite symmetry groups for multiple coordinate hamiltonians including coupling terms. Groups are first derived separately for terms involving single coordinates. When these terms are added together, direct products of the initial groups are taken, and more symmetry operations may need to be included which involve several coordinates. When coupling terms are included, some symmetry operations must be discarded and subgroups of the product group determined. The determination of the classes, the induction and subduction of irreducible representations and characters, and assignment of molecular properties to these representations are performed along with the group derivation. We discuss the application of these methods to hamiltonians for non-rigid molecular vibrations in four membered ring molecules, molecules with two methyl groups, and the pseudorotation interconversion motion of some MX₅ molecules.     

An alternative to the effective number of degrees of freedom

 In order to calculate the expanded uncertainty when one or more of the components of the standard uncertainty is based on a small number of degrees of freedom, the ISO Guide recommends utilising the 'effective number of degrees of freedom'. Calculating and utilising the 'effective number of degrees of freedom' to obtain a confidence interval both depend upon approximations, which, however, are adequate for determining an expanded uncertainty. This paper puts forward an alternative and simpler approximation which is also adequate but which is much easier to apply than the multi-step process given in the ISO Guide. Received: 2 July 1998 · Accepted: 12 August 1998     

Transition rate prefactors for systems of many degrees of freedom

When a minimum on the potential energy surface is surrounded by multiple saddle points with similar energy barriers, the transition pathways with greater prefactors are more important than those that have similar energy barriers but smaller prefactors. In this paper, we present a theoretical formulation for the prefactors, computing the probabilities for transition paths from a minimum to its surrounding saddle points. We apply this formulation to a system of 2 degrees of freedom and a system of 14 degrees of freedom. The first is Brownian motion in a two-dimensional potential whose global anharmonicities play a dominant role in determining the transition rates. The second is a Lennard-Jones (LJ) cluster of seven particles in two dimensions. Low lying transition states of the LJ cluster, which can be reached directly from a minimum without passing through another minimum, are identified without any presumption of their characteristics nor of the product states they lead to. The probabilities are computed for paths going from an equilibrium ensemble of states near a given minimum to the surrounding transition states. These probabilities are directly related to the prefactors in the rate formula. This determination of the rate prefactors includes all anharmonicities, near or far from transition states, which are pertinent in the very sophisticated energy landscape of LJ clusters and in many other complex systems.     

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.     

Individual degrees of freedom and the solvation properties of water

Using molecular dynamics simulations in conjunction with home-developed Split Integration Symplectic Method we effectively decouple individual degrees of freedom of water molecules and connect them to corresponding thermostats. In this way, we facilitate elucidation of structural, dynamical, spectral, and hydration properties of bulk water at any given combination of rotational, translational, and vibrational temperatures. Elevated rotational temperature of the water medium is found to severely hinder hydration of polar molecules, to affect hydration of ionic species in a nonmonotonous way and to somewhat improve hydration of nonpolar species. As proteins consist of charged, polar, and nonpolar amino-acid residues, the developed methodology is also applied to critically evaluate the hypothesis that the overall decrease in protein hydration and the change in the subtle balance between hydration of various types of amino-acid residues provide a plausible physical mechanism through which microwaves enhance aberrant protein folding and aggregation.