Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations

A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two-dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic-simulation sample of the atomic configurations of the molecule. The torsional-angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal-rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis-stilbene are found to be much more strongly correlated than those in trans-stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine.     

Quantum dynamics of dissociative chemisorption of CH(4) on Ni(111): Influence of the bending vibration

Two-dimensional, three-dimensional, and four-dimensional quantum dynamic calculations are performed on the dissociative chemisorption of CH(4) on Ni(111) using the multiconfiguration time-dependent Hartree (MCTDH) method. The potential energy surface used for these calculations is 15-dimensional (15D) and was obtained with density functional theory for points which are concentrated in the region that is dynamically relevant to reaction. Many reduced dimensionality calculations were already performed on this system, but the molecule was generally treated as pseudodiatomic. The main improvement of our model is that we try to describe CH(4) as a polyatomic molecule by including a degree of freedom describing a bending vibration in our three-dimensional and four-dimensional models. Using a polyspherical coordinate system, a general expression for the 15D kinetic energy operator is derived, which discards all the singularities in the operator and includes rotational and Coriolis coupling. We use seven rigid constraints to fix the CH(3) umbrella of the molecule to its gas phase equilibrium geometry and to derive two-dimensional, three-dimensional, and four-dimensional Hamiltonians, which were used in the MCTDH method. Only four degrees of freedom evolve strongly along the 15D minimum energy path: the distance of the center of mass of the molecule to the surface, the dissociative C[Single Bond]H bond distance, the polar orientation of the molecule, and the bending angle between the dissociative C[Single Bond]H bond and the umbrella. A selection of these coordinates is included in each of our models. The polar rotation is found to be important in determining the mode selective behavior of the reaction. Furthermore, our calculations are in good agreement with the finding of Xiang et al. [J. Chem. Phys. 117, 7698 (2002)] in their reduced dimensional calculation that the helicopter motion of the umbrella symmetry axis is less efficient than its cartwheel motion for promoting the reaction. The effect of pre-exciting the bend modes is qualitatively incorrect at higher energies, suggesting the necessity of including additional rotational and vibrational degrees of freedom in the model.     

Application of torsion angle molecular dynamics for efficient sampling of protein conformations

We investigate the application of torsion angle molecular dynamics (TAMD) to augment conformational sampling of peptides and proteins. Interesting conformational changes in proteins mainly involve torsional degrees of freedom. Carrying out molecular dynamics in torsion space does not only explicitly sample the most relevant degrees of freedom, but also allows larger integration time steps with elimination of the bond and angle degrees of freedom. However, the covalent geometry needs to be fixed during internal coordinate dynamics, which can introduce severe distortions to the underlying potential surface in the extensively parameterized modern Cartesian-based protein force fields. A "projection" approach (Katritch et al. J Comput Chem 2003, 24, 254-265) is extended to construct an accurate internal coordinate force field (ICFF) from a source Cartesian force field. Torsion crossterm corrections constructed from local molecular fragments, together with softened van der Waals and electrostatic interactions, are used to recover the potential surface and incorporate implicit bond and angle flexibility. MD simulations of dipeptide models demonstrate that full flexibility in both the backbone phi/psi and side chain chi1 angles are virtually restored. The efficacy of TAMD in enhancing conformational sampling is then further examined by folding simulations of small peptides and refinement experiments of protein NMR structures. The results show that an increase of several fold in conformational sampling efficiency can be reliably achieved. The current study also reveals some complicated intrinsic properties of internal coordinate dynamics, beyond energy conservation, that can limit the maximum size of the integration time step and thus the achievable gain in sampling efficiency.     

Quasi-Hamiltonian equations of motion for internal coordinate molecular dynamics of polymers

Conventional molecular dynamics simulations of macromolecules require long computational times because the most interesting motions are very slow compared to the fast oscillations of bond lengths and bond angles that limit the integration time step. Simulation of dynamics in the space of internal coordinates, that is, with bond lengths, bond angles, and torsions as independent variables, gives a theoretical possibility of eliminating all uninteresting fast degrees of freedom from the system. This article presents a new method for internal coordinate molecular dynamics simulations of macromolecules. Equations of motion are derived that are applicable to branched chain molecules with any number of internal degrees of freedom. Equations use the canonical variables and they are much simpler than existing analogs. In the numerical tests the internal coordinate dynamics are compared with the traditional Cartesian coordinate molecular dynamics in simulations of a 56 residue globular protein. For the first time it was possible to compare the two alternative methods on identical molecular models in conventional quality tests. It is shown that the traditional and internal coordinate dynamics require the same time step size for the same accuracy and that in the standard geometry approximation of amino acids, that is, with fixed bond lengths, bond angles, and rigid aromatic groups, the characteristic step size is 4 fs, which is 2 times higher than with fixed bond lengths only. The step size can be increased up to 11 fs when rotation of hydrogen atoms is suppressed. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1354–1364, 1997     

Solvated ensemble averaging in the calculation of partial atomic charges

In the calculation of partial atomic charges, for use in molecular mechanics or dynamics simulations, it is common practice to select only a single conformation for the molecule of interest. For molecules that contain rotatable bonds, it is preferable to compute the charges from several relevant conformations. We present here results from a charge derivation protocol that determines the partial charges by averaging charges computed for conformations selected from explicitly solvated MD simulations, performed under periodic boundary conditions. This approach leads to partial charges that are weighted by a realistic population of conformations and that are suitable for condensed phase simulations. This protocol can, in principle, be applied to any class of molecule and to nonaqueous solvation. Carbohydrates contain numerous hydroxyl groups that exist in an ensemble of orientations in solution, and in this report we apply ensemble averaging to a series of methyl glycosides. We report the extent to which ensemble averaging leads to charge convergence among the various monosaccharides and among the constituent atoms within a given monosaccharide. Due to the large number of conformations (200) in our ensembles, we are able to compute statistically relevant standard deviations for the partial charges. An analysis of the standard deviations allows us to assess the extent to which equivalent atom types may, nevertheless, require unique partial charges. The configurations of the hydroxyl groups exert considerable influence on internal energies, and the limits of ensemble averaged charges are discussed in terms of these properties.     

Surface bonding and dynamical behavior of the CH3SH molecule on Au(111)

The chemisorption of the undissociated CH3SH molecule on the Au(111) surface has been studied at 5 K using scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. The molecule was found to adsorb on atop Au sites on the defect-free surface. CH3SH undergoes hindered rotation about the Au-S bond on the defect-free surface which is seen in STM as a time-averaged 6-fold pattern. The pattern suggests that the potential minima directions occur for the rotating molecule at the six hollow sites surrounding the atop adsorption site. The barrier for rotation, obtained by DFT calculations, is approximately 0.1 kcal.mol(-1). At low coverages, preferential adsorption occurs at defect sites in the surface, namely, the herringbone "elbows" and random atomic step sites. Molecules adsorbed on these sites do not exhibit rotational freedom.     

Laser-operated chiral molecular switch: quantum simulations for the controlled transformation between achiral and chiral atropisomers

We report quantum dynamical simulations for the laser controlled isomerization of 1-(2-cis-fluoroethenyl)-2-fluorobenzene based on one-dimensional electronic ground and excited state potentials obtained from (TD)DFT calculations. 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers, the latter being the most stable isomer at room temperature. Using a linearly polarized IR laser pulse the molecule is excited to an internal rotation around its chiral axis, i.e. around the C-C single bond between phenyl ring and ethenyl group, changing the molecular chirality. A second linearly polarized laser pulse stops the torsion to prepare the desired enantiomeric form of the molecule. This laser control allows the selective switching between the achiral and either the left- or right-handed form of the molecule. Once the chirality is "switched on" linearly polarized UV laser pulses allow the selective change of the chirality using the electronic excited state as intermediate state.     

Computer simulation of chiral liquid crystal phases. IV. Intermolecular chirality transfer to rotamers in a cholesteric phase

Intermolecular chirality transfer was studied by investigating the conformational distribution of rotamers in a cholesteric guest-host phase using Monte Carlo (MC) simulations in the NVT ensemble. The guest-host system under investigation was given by N_c = 238 rigid, chiral Gay-Berne atropisomers as host molecules and N_a = 18 flexible Gay-Berne rotamers as guest molecules. The rigid, chiral Gay-Berne atropisomers of point symmetry group D₂ were defined by joining two Gay-Berne particles through a bond with a suitable fixed dihedral angle. The possibility of internal rotation about the bond axis without a rotational barrier was introduced as an internal degree of freedom for the guest molecules, for convenience denoted as Gay-Berne rotamers. Starting from an isotropic configuration, cholesteric phases were obtained on equilibrating the guest-host systems, whereby left-handed and right-handed cholesterics were formed depending on the M- and P-helicity of the atropisomers, respectively. Analysing the conformational distribution of the guest molecules in the cholesteric phase, we found an enantiomeric excess of rotamers of the guest molecules with the same helicity as the host molecules which is favoured on account of the intermolecular interactions in the cholesteric phase.     

From stochastic pulse optimization to a stereoselective laser pulse sequence: simulation of a chiroptical molecular switch mounted on adamantane

Quantum dynamical simulations for the laser-controlled isomerization of 1-(2-cis-fluoroethenyl)-2-fluorobenzene mounted on adamantane are reported based on a one-dimensional electronic ground-state potential and dipole moment calculated by density functional theory. The model system 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers upon torsion around the C-C single bond connecting the phenyl ring and ethylene group. The molecule itself is bound to an adamantyl frame which serves as a model for a linker or a surface. Due to the C3 symmetry of the adamantane molecule, the molecular switch can have three equivalent orientations. An infrared picosecond pulse is used to excite the internal rotation around the chiral axis, thereby controlling the chirality of the molecule. In order to selectively switch the molecules--independent of their orientations-- from their achiral to either their left- or right-handed form, a stochastic pulse optimization algorithm is applied. A subsequent detailed analysis of the optimal pulse allows for the design of a stereoselective laser pulse sequence of analytical form. The developed control scheme of elliptically polarized laser pulses is enantioselective and orientation-selective.     

Barrier to internal rotation and π-bonding in diborane peroxide,BH2O2BH2, studied by ab inttio calculations

The barrier to internal rotation and π-bonding in diborane peroxide are studied by ab initio calculations. The calculated potential curve for rotation about the peroxide bond is similar to related potential curves calculated for butadiene, glyoxal and diimine except for predicting only a single minimum in the trans position. The lack of another minimum is probably due to steric repulsions, and the results may be considered as demonstrating a degree of conjugation in this system.     

Internal rotation and equilibrium structure of the 2-methyl-2-nitropropane molecule from joint processing of gas phase electron diffraction data,vibrational and microwave spectroscopy data,and quantum chemical calculation results

The structure and internal rotation of the 2-methyl-2-nitropropane molecule is studied by electron diffraction and quantum chemical calculations with the use of microwave and vibrational spectroscopy data. The electron diffraction data are analyzed within the general intramolecular anharmonic force field model and the quantum chemical pseudoconformer model, considering the adiabatic separation of the degree of freedom of large amplitude motion, i.e., the internal rotation of the NO₂ group. The equilibrium eclipsed configuration of the C _s symmetry molecule has the following experimental bond lengths and valence angles: r _e(N=O) = 1.226//1.226(8) Å, r _e(C–N)//r _e(C–C) = 1.520//1.515/1,521(4) Å, ∠_еC–C–N = = 109.1/106,1(8)°, ∠_еO=N=O = 124.2(6)°, ∠_eC–C–H_avg = 110(3)°. The equilibrium geometry parameters are well consistent with MP2/cc-pVTZ quantum chemical calculations and microwave spectroscopy data. The thermally average parameters previously obtained within the small vibration model show a satisfactory agreement with the new results. The electron diffraction data used in this work do not allow a reliable determination of the barrier to internal rotation. However, at a barrier of 203(2) cal/mol, which is derived from the microwave study, it follows from the electron diffraction data that the equilibrium configuration must correspond to an eclipsed arrangement of C–C and N=O bonds, which is also consistent with the results of quantum chemical calculations of various levels.     

Rotational isomerism and barriers to internal rotation in 3-halopropenes byscf-mo methods

Electronic structures of 3 halopropenes have been investigated through semiempiricalscf-mo calculations using valence basis sets of atomic orbitals (ao) constructed from Slater type orbitals (sto). The electronic structures of stable conformers have been predicted and the corresponding calculated dipole moments show good agreement with experimental data. The considerable differences between the dipole moments of various conformers confirm the hindrance to internal rotation about the C−C bond, i.e., the existence of a definite potential barrier to rotation. The barrier heights hindering the internal rotation in each system are also estimated.     

Ultrafast 2D IR anisotropy of water reveals reorientation during hydrogen-bond switching

Rearrangements of the hydrogen bond network of liquid water are believed to involve rapid and concerted hydrogen bond switching events, during which a hydrogen bond donor molecule undergoes large angle molecular reorientation as it exchanges hydrogen bonding partners. To test this picture of hydrogen bond dynamics, we have performed ultrafast 2D IR spectral anisotropy measurements on the OH stretching vibration of HOD in D(2)O to directly track the reorientation of water molecules as they change hydrogen bonding environments. Interpretation of the experimental data is assisted by modeling drawn from molecular dynamics simulations, and we quantify the degree of molecular rotation on changing local hydrogen bonding environment using restricted rotation models. From the inertial 2D anisotropy decay, we find that water molecules initiating from a strained configuration and relaxing to a stable configuration are characterized by a distribution of angles, with an average reorientation half-angle of 10°, implying an average reorientation for a full switch of ≥20°. These results provide evidence that water hydrogen bond network connectivity switches through concerted motions involving large angle molecular reorientation.     

Multiple steps and multiple excitations in photoisomerization of azobenzene

Detailed understanding of femtosecond-scale photochemical processes requires dynamical simulations that are complementary to interpretations based on transitions between energy surfaces. For cis to trans photoisomerization of azobenzene following a 100 fs laser pulse, we find that the mechanism is rotation about the central NN bond, and the process is complete in less than 1 ps. The initial excitation and subsequent de-excitation are each achieved via multiple steps, with the molecule always in a superposition of electronic states, as the 3N nuclear degrees of freedom are excited by the laser pulse.     

A critical comparison of approximation methods and models for equilibrium properties of low-barrier hydrogen bonds

Recent experimental evidence has led to the conclusion that short, strong hydrogen bonds can stabilize transition states of enzyme catalyzed biochemical reactions. Evidence for such hydrogen bonds is the low value of the isotopic fractionation factor, phi, which is defined as the equilibrium constant for the generic reaction, R-H + DOH <--> R-D + HOH, where H is the hydrogen atom participating in the low-barrier hydrogen bond in a molecule R-H. In this work we assess two approximation methods for computing the isotopic fractionation factors for single and multidimensional systems containing a low-barrier hydrogen bond. These methods are WKB and an approach that corrects the classical partition function via a quantum correction factor. We find that the latter approach is universally accurate and applicable in both single and multidimensional systems containing a low-barrier hydrogen bond. We also assess two different models for the coupling of a molecule's low-barrier hydrogen bond to other degrees of freedom, both internal and external to the molecule, and show that each leads to a lowering of the fractionation factor.     

Conformation of ethylene glycol: Isometric group,ab initio study of internal H bonding and ir-matrix spectra of the species CH2OHCH2OH,CD2OHCD2OH and CH2ODCH2OD

The isometric group of a semirigid model of the ethylene glycol molecule with 3 internal degrees of freedom is derived. Results of extensiveab initio computation of the electronic potential function with a Gaussian lobe basis set are presented from which two differentr _e conformations are predicted. Both feature one single internal H bond in which one of the lone electron pairs of the acceptor O atom is involved. Symmetry sets of isometricr _e-conformations and of transition points of the potential function are discussed. Infrared matrix spectra of glycol and 2 deuterated modifications are presented and discussed on the basis of two internally bonded conformations predicted byab initio calculations. Dedicated to Prof. H. Hartmann on the occasion of his 60th birthday.     

On the internal rotations in p-cresol in its ground and first electronically excited states

The overall rotation and internal rotation of p-cresol (4-methyl-phenol) has been studied by comparison of the microwave spectrum with accurate ab initio calculations using the principal axis method in the electronic ground state. Both internal rotations, the torsions of the methyl and the hydroxyl groups relative to the aromatic ring, have been investigated. The internal rotation of the hydroxyl group can be approximately described as the motion of a symmetrical rotor on an asymmetric frame. For the methyl group it has been found that the potential barrier hindering its internal rotation is very small with the first two nonvanishing Fourier coefficients of the potential V(3) and V(6) in the same order of magnitude. Different splittings of b-type transitions for the A and E species of the methyl torsion indicate a top-top interaction between both internal rotors through the benzene ring. An effective coupling potential for the top-top interaction could be estimated. The hindering barriers of the hydroxyl and methyl rotation have been calculated using second-order Moller-Plesset perturbation theory and the approximate coupled-cluster singles-and-doubles model (CC2) in the ground state and using CC2 and the algebraic diagrammatic construction through second order in the first electronically excited state. The results are in excellent agreement with the experimental values.     

Hydrogen confined in single-wall carbon nanotubes: Anisotropy effects on ro-vibrational quantum levels

The energy levels of a hydrogen molecule embedded in the cavity of single-walled carbon nanotubes with different morphologies are studied using quantum dynamics simulations. All degrees of freedom of the confined molecule are explicitly included in our model, revealing that the vibrational motion is notably affected by the presence of a confining potential. The most relevant effects are nevertheless found in the rotational motion of the molecule and the appearance of a quantized translational motion. We further analyze the dependence of the confinement effects on the interaction potential, considering different parameters for the carbon-hydrogen interaction.     

A stereographic projection path integral study of the coupling between the orientation and the bending degrees of freedom of water

A Monte Carlo path integral method to study the coupling between the rotation and bending degrees of freedom for water is developed. It is demonstrated that soft internal degrees of freedom that are not stretching in nature can be mapped with stereographic projection coordinates. For water, the bending coordinate is orthogonal to the stereographic projection coordinates used to map its orientation. Methods are developed to compute the classical and quantum Jacobian terms so that the proper infinitely stiff spring constant limit is recovered in the classical limit, and so that the nonconstant nature of the Riemann Cartan curvature scalar is properly accounted in the quantum simulations. The theory is used to investigate the effects of the geometric coupling between the bending and the rotating degrees of freedom for the water monomer in an external field in the 250 to 500 K range. We detect no evidence of geometric coupling between the bending degree of freedom and the orientations.