Force-field modeling through quantum mechanical calculations: molecular dynamics simulations of a nematogenic molecule in its condensed phases

Interaction energy of the 4-n-pentyloxy-4'-cyanobiphenyl (5OCB) dimer is computed at MP2 level, for many geometrical arrangements using the Fragmentation Reconstruction Method (FRM). DFT calculations are performed for a number of geometries of the monomer. The resulting database is used to parameterize an atomistic intra- and inter-molecular force-field suitable for classical bulk simulations. Several structural and dynamical properties in 5OCB isotropic and liquid crystalline phases are computed from molecular dynamics simulation mainly in the NPT ensemble. Lengthy runs (more than 70 ns) and large sample sizes (up to 806 molecules) were used to determine the nematic to isotropic transition temperature up to a precision of few K. Good agreement was found in most of the investigated properties, thus validating the accuracy of the proposed model potential, only derived by quantum mechanical calculations.     

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.     

On the mechanical properties of poly(ethylene terephthalate). Force-field parametrization and conformational analysis for the prediction of the crystal moduli

A force-field suitable for the calculation of the mechanical properties of poly(ethylene terephthalate) and their relation with the molecular structure of the polymer has been developed. The force-field parameters were derived from quantum mechanical AM1 calculations and tested against thermodynamic and vibrational spectroscopy data available for a set of closely related small molecules. The crystal moduli of the two solid phases known for poly(ethylene terephthalate) were estimated by means of this new force-field considering both the isolated chain and the chain within the unit cell. Results were qualitatively consistent with reported x-ray data showing that the triclinic crystal form is stiffer than the mesomorphic phase provided that sample heterogeneities were taken into account. Although overestimated moduli resulted for both cases, divergences with experimental values were found to be slighter than those obtained by other theoretical methods. © 1996 John Wiley & Sons, Inc.     

Computational photochemistry of retinal proteins

High spectral tunability and quantum yield are the striking features of rhodopsin photochemistry. They rely on a strong and complex interaction of their chromophore, the protonated Schiff base of retinal, with its protein environment. In this article, we review the progress in the computational modeling of these systems, focusing on the optical properties and the excited state dynamics. While the earlier success of atomistic theoretical models was based on the breakthrough in X-ray crystallography and combined quantum mechanical molecular mechanical (QM/MM) methodology, recent advances point out the importance of high-level QM methods and the incorporation of effects that are neglected in conventional QM/MM or ONIOM schemes, like polarization and charge transfer.     

Quantum mechanical/molecular mechanical studies on spectral tuning mechanisms of visual pigments and other photoactive proteins

The protein environments surrounding the retinal tune electronic absorption maximum from 350 to 630 nm. Hybrid quantum mechanical/molecular mechanical (QM/MM) methods can be used in calculating excitation energies of retinal in its native protein environments and in studying the molecular basis of spectral tuning. We hereby review recent QM/MM results on the phototransduction of bovine rhodopsin, bacteriorhodopsin, sensory rhodopsin II, nonretinal photoactive yellow protein and their mutants.     

Classical and quantum mechanical infrared echoes from resonantly coupled molecular vibrations

The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting variant Planck's over 2pi-->0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity.     

Critical comparison of classical and quantum mechanical treatments of the phase equilibria of water

The Gibbs ensemble Monte Carlo simulation technique was used to compare the phase equilibria of the rigid TIP4P water model [Jorgensen et al., J. Chem. Phys. 79, 926 (1983)] utilizing classical and quantum statistical mechanics. The quantum statistical mechanical treatment generally resulted in lower liquid densities and higher vapor densities, narrowing the phase envelope. As a result, the calculated critical temperatures and normal boiling points were lower from the quantum simulations than the classical by 22 and 17 K, respectively, but the critical densities were equal within the estimated uncertainties. When the phase diagram from the quantum statistical mechanical treatment was increased by 22 K, it agreed with the classical results quite well throughout the entire simulated temperature range. A semiclassical treatment, involving a low order expansion in Planck's constant, resulted in good agreement with the path integral results for second virial coefficients, but gave densities and vapor pressures that fluctuated between the values for the classical and quantum statistical mechanics values, with no definite agreement with either.     

New force field for calcium binding sites in annexin-membrane complexes

For accurate classical molecular dynamics (MD) simulations of the calcium mediated bound complexes of annexin and membrane we have developed new force-field parameters correctly describing the interaction of the Ca ion with its environment. We have used quantum chemical calculations to investigate the potential energy surface experienced by the Ca ion within the three different binding sites found in domain 1 of annexin V (ANX V/1). Based on these calculations we were able to quantify the charge polarization of atoms within the binding sites, and to determine the geometry and force constants of harmonic restraints between the Ca ion and its coordinating oxygen atoms. Harmonic restraints were introduced to compensate for the deviations between the quantum mechanical potential energy surface and that of the classical force field. Our analysis has shown that using the refined force field for the Ca binding sites enables long-time MD simulations that conserve the initial structure of ANX V/1 significantly better than MD simulations using the standard force field.     

Classical and quantum mechanical calculations of conformational probability density distributions. Two-rotor molecules

In order to study the dynamical structure of a two-rotor molecule, such as acetone, as a function of temperature, conformational probability density distributions are computed by using three different approaches: the so-called current approach, the classical approach, and the quantum mechanical oscillator approach. It is found that the three procedures yield comparable results, at least at normal temperature (25°C), although the current and, especially, the classical approaches give rise to too sharp distributions when compared with the quantum mechanical results. Owing to its simplicity, the current approach may be used advantageously, and it is easily extendible to many-rotor systems. Finally, it is verified that deuteration does not affect appreciably the conformation.     

Tuning of retinal twisting in bacteriorhodopsin controls the directionality of the early photocycle steps

Productive proton pumping by bacteriorhodopsin requires that, after the all-trans to 13-cis photoisomerization of the retinal chromophore, the photocycle proceeds with proton transfer and not with thermal back-isomerization. The question of how the protein controls these events in the active site is addressed here using quantum mechanical/molecular mechanical reaction-path calculations. The results indicate that, while retinal twisting significantly contributes to lowering the barrier for the thermal cis-trans back-isomerization, the rate-limiting barrier for this isomerization is still 5-6 kcal/mol larger than that for the first proton-transfer step. In this way, the retinal twisting is finely tuned so as to store energy to drive the subsequent photocycle while preventing wasteful back-isomerization.     

An Empirically Optimized Classical Force-Field for Molecular Simulations of 2,4,6-Trinitrotoluene (TNT) and 2,4-Dinitrotoluene (DNT)

An empirical classical all-atom specific force-field for use in molecular dynamics simulations (MD) has been developed to reproduce the experimental densities and structures of trinitrotoluene (TNT) in its crystalline and liquid phases at six different temperatures, as well as its enthalpies of sublimation and fusion. The average structural parameters and partial charges were obtained from density functional theory optimizations of single molecules at the B3LYP/6-311+G** level. The other constants for the potential were adjusted in order to obtain a classical force-field, which is able to reproduce the aforementioned properties for TNT with a high degree of accuracy. This force-field was also found to predict closely the experimental densities and structures of 2,4-dinitrotoluene (2,4-DNT) in its crystalline and liquid phases as well as its enthalpy of sublimation. It was a bit less successful for its enthalpy of fusion, but it still remained reasonable, and the model mechanical properties were of the right order of magnitude. As such, this fairly simple force-field can be used for MD simulations of both TNT and 2,4-DNT nitroaromatic compounds.     

Effect of noise on the classical and quantum mechanical nonlinear response of resonantly coupled anharmonic oscillators

Multidimensional infrared spectroscopy probes coupled molecular vibrations in complex, condensed phase systems. Recent theoretical studies have focused on the analytic structure of the nonlinear response functions required to calculate experimental observables in a perturbative treatment of the radiation-matter interaction. Classical mechanical nonlinear response functions have been shown to exhibit unbounded growth for anharmonic, integrable systems, as a consequence of the nonlinearity of classical mechanics, a feature that is absent in a quantum mechanical treatment. We explore the analytic structure of the third-order vibrational response function for an exactly solvable quantum mechanical model that includes some of the important and theoretically challenging aspects of realistic models of condensed phase systems: anharmonicity, resonant coupling, fluctuations, and a well-defined classical mechanical limit.     

Excitation spectroscopy of retinal and related polyenes

Abstract— Fluorescence excitation spectra of all-trans retinal and the related polyene hydrocarbons anhydrovitamin A and diphenyloctatetraene show that only retinal has a wavelength-dependent fluorescence quantum yield. Three possibilities for the unusual quantum yield behavior of retinal are considered. We conclude that competition between a fast radiationless process (perhaps of photochemical origin) and internal conversion between ¹ππ* states and a low-lying ¹nπ* state provides the best rationalization for the data now in hand.     

Quantum mechanical model for the dissociative adsorption of diatomic molecules on metal surfaces

A quantum mechanical nonadiabatic theory of dissociative adsorption of diatomic molecules X2 on metal surface is presented. The following reaction coordinates are used to construct crossing diabatic potential energy surfaces (PES): the distance y between the atoms of the X2 molecule, the distance x of the X2 molecular axis from the surface, the set of coordinates describing possible displacements of metal atoms under adsorption. Expression for the rate constant is derived using the model potentials describing vibrations along these coordinates. The calculated dependency of the rate constant W on the reaction heat DeltaE is compared with that in classical approximation. It is shown that quantum effects lead to a weaker dependence of W on DeltaE as compared to that for classical one.     

Time-dependent density functional theory excited state nonadiabatic dynamics combined with quantum mechanical/molecular mechanical approach: photodynamics of indole in water

We present a combination of time-dependent density functional theory with the quantum mechanical/molecular mechanical approach which can be applied to study nonadiabatic dynamical processes in molecular systems interacting with the environment. Our method is illustrated on the example of ultrafast excited state dynamics of indole in water. We compare the mechanisms of nonradiative relaxation and the electronic state lifetimes for isolated indole, indole in a sphere of classical water, and indole + 3H(2)O embedded in a classical water sphere. In the case of isolated indole, the initial excitation to the S(2) electronic state is followed by an ultrafast internal conversion to the S(1) state with a time constant of 17 fs. The S(1) state is long living (>30 ps) and deactivates to the ground state along the N-H stretching coordinate. This deactivation mechanism remains unchanged for indole in a classical water sphere. However, the lifetimes of the S(2) and S(1) electronic states are extended. The inclusion of three explicit water molecules opens a new relaxation channel which involves the electron transfer to the solvent, leading eventually to the formation of a solvated electron. The relaxation to the ground state takes place on a time scale of 60 fs and contributes to the lowering of the fluorescence quantum yield. Our simulations demonstrate the importance of including explicit water molecules in the theoretical treatment of solvated systems.     

Force-field parametrization of retro-inverso modified residues: Development of torsional and electrostatic parameters

Summary Torsional and the electrostatic parameters for molecular mechanics studies of retro-inverso modified peptides have been developed using quantum mechanical calculations. The resulting parameters have been compared with those calculated for conventional peptides. Rotational profiles, which were obtained spanning the corresponding dihedral angle, were corrected by removing the energy contributions associated to changes in interactions different from torsion under study. For this purpose, the torsional energy associated to each point of the profiles was estimated as the corresponding quantum mechanical energy minus the bonding and nonbonding energy contributions produced by the perturbations that the variation of the spanned dihedral angle causes in the bond distances, bond angles and the other dihedral angles. These energies were calculated using force-field expressions. The corrected profiles were fitted to a three-term Fourier expansion to derive the torsional parameters. Atomic charges for retro-inverso modified residues were derived from the rigorously calculated quantum mechanical electrostatic potential. Furthermore, the reliability of electrostatic models based on geometry-dependent charges and fixed charges has been examined.     

The photoisomerization of retinal

Abstract— –Quantum efficiencies have been measured for the photoisomerization of four stereoisomers of retinal (all-trans, 13-cis, 11 cis, and 9-cis) in two solvents at different wavelengths of irradiation and at various temperatures. In heane at 25°C the quantum efficiencies for isomerization at 365 nm are: 9-cis to trans, 0.5; 13-cis to trans, 0.4; 11-cis to trans, 0.2; all-trans to monocis isomers, 0.2-0.06, depending upon assumptions made regarding the stereo-isomeric composition of the product. These values vary somewhat with the wavelength of the irradiating light. The quantum efficiency for the photoisomerization of all-trans retinal in hexane decreases by a factor of 30 when the temperature is lowered from 25° to – 65°C; the activation energy for this photoisomerization is about 5 kcal/mole. The quantum efficiencies for the isomerization of the monocis isomers to all-trans retinal in hexane are virtually independent of temperature. In ethanol the rates of photoisomerization from trans to cis or cis to trans depend only slightly on the temperature between 25° and – 65°C. The photosensitivities of the stereoisomers of retinal are of the same order of magnitude as those of the retinylidene chromophores of rhodopsin (11 -cis), metarhodopsin I (all-trans), and isorhodopsin (9-cis); but it is not yet possible to derive the photochemistry of rhodopsin uniquely and quantitatively from that of retinal.     

ForceFit: A code to fit classical force fields to quantum mechanical potential energy surfaces

The ForceFit program package has been developed for fitting classical force field parameters based upon a force matching algorithm to quantum mechanical gradients of configurations that span the potential energy surface of the system. The program, which runs under UNIX and is written in C++, is an easy‐to‐use, nonproprietary platform that enables gradient fitting of a wide variety of functional force field forms to quantum mechanical information obtained from an array of common electronic structure codes. All aspects of the fitting process are run from a graphical user interface, from the parsing of quantum mechanical data, assembling of a potential energy surface database, setting the force field, and variables to be optimized, choosing a molecular mechanics code for comparison to the reference data, and finally, the initiation of a least squares minimization algorithm. Furthermore, the code is based on a modular templated code design that enables the facile addition of new functionality to the program. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

On effective potentials in classical mechanical systems

A classical mechanical variational method for computing effective potentials due to exact, first order and adiabatic constraints is presented. The effective potential can be used to envision in configuration space the restricted motion imposed by the constraints relative to the full potential. It can locate effective equilibrium structures and transition barriers and saddles and can be used when combined with semi-classical ideas to delineate regions of quantum packet flow and stationary state localization. The latter gives information on energy flow in a system and on the nature of basis sets needed for full quantum calculations. The advantage of the method is that is does not involve the solution of any equations of motion. The ideas are illustrated by some examples coming from the area of atomic and molecular dynamics.