Torsional path integral Monte Carlo method for calculating the absolute quantum free energy of large molecules

Nuclear quantum effects in gas-phase ethylene glycol

Path integral molecular simulations are used to explore the nuclear quantum effects (NQEs) on the structure, dihedral landscape and infrared spectrum of ethylene glycol. The simulations are carried out on a new reaction surface Hamiltonian-based model potential energy surface, with special focus on the role of the OCCO and HOCC dihedrals. In contrast with classical simulations, we analyse how the intramolecular interactions between the OH groups change due to zero-point effects as well as temperature. These are found to be weak. The NQEs on the free energy profile along the OCCO dihedral are analysed, where notable effects are seen at low temperatures and found to be correlated with the radii of gyration of the atoms. Finally, the power spectrum of the molecule from path integral simulations is compared with the experimental infrared spectrum, yielding a good agreement of band positions.

Nuclear quantum effects in gas-phase 2-fluoroethanol

Torsional motions along the FCCO and HOCC dihedrals lead to the five unique conformations of 2-fluoroethanol, of which the conformer that is gauche along both dihedrals has the lowest energy. In this work, we explore how nuclear quantum effects (NQEs) manifest in the structural parameters of the lowest energy conformer, in the intramolecular free energy landscape along the FCCO and HOCC dihedrals, and also in the infrared spectrum of the title molecule, through the use of path integral simulations. We have first developed a full dimensional potential energy surface using the reaction surface Hamiltonian framework. On this potential, we have carried out path integral molecular dynamics simulations at several temperatures starting from the minimum energy well to explore structural influences of NQEs including geometrical markers of the interaction between the OH and F groups. From the computed free energy landscapes, significant reduction of the torsional barrier is found at low temperature near the cis region of the dihedrals, which can be understood through the trends in the radii of gyration of the atomic ring polymers. We find that the inclusion of NQEs in the computation of infrared spectrum is important to obtain good agreement with the experimental band positions.

Direct Computation of the Quantum Partition Function by Path-Integral Nested Sampling

In the present work we introduce a computational approach to the absolute rovibrational quantum partition function using the path-integral formalism of quantum mechanics in combination with the nested sampling technique. The numerical applicability of path-integral nested sampling is demonstrated for small molecules of spectroscopic interest. The computational cost of the method is determined by the evaluation time of a point on the potential energy surface (PES). For efficient PES implementations, the path-integral nested sampling method can be a viable alternative to the direct-Boltzmann-summation technique of variationally computed rovibrational energies, especially for medium-sized molecules and at elevated temperatures.

Accounting for conformational flexibility and torsional anharmonicity in the H + CH3CH2OH hydrogen abstraction reactions: a multi-path variational transition state theory study

This work reports a detailed theoretical study of the hydrogen abstraction reactions from ethanol by atomic hydrogen. The calculated thermal rate constants take into account torsional anharmonicity and conformational flexibility, in addition to the variational and tunneling effects. Specifically, the kinetics calculations were performed by using multi-path canonical variational transition state theory with least-action path tunneling corrections, to which we have added the two-dimensional non-separable method to take into account torsional anharmonicity. The multi-path thermal rate constant is expressed as a sum over conformational reaction channels. Each of these channels includes all the transition states that can be reached by internal rotations. The results show that, in the interval of temperatures between 250 and 2500 K, the account for multiple paths leads to higher thermal rate constants with respect to the single path approach, mainly at low and at high temperatures. In addition, torsional anharmonicity enhances the slope of the Arrhenius plot in this range of temperatures. Finally, we show that the incorporation of tunneling into the hydrogen abstraction reactions substantially changes the contribution of each of the transition states to the conformational reaction channel.

High-precision quantum thermochemistry on nonquasiharmonic potentials: converged path-integral free energies and a systematically convergent family of generalized Pitzer-Gwinn approximations

Accurate quantum mechanical (QM) vibrational-rotational partition functions for HOOD, D(2)O(2), H(18)OOH, H(2)(18)O(2), D(18)OOH, and H(18)OOD are determined using a realistic potential energy surface for temperatures ranging from 300 to 2400 K by using the TT-FPI-ESPE path-integral Monte Carlo method. These data, together with our prior results for H(2)O(2), provide benchmarks for testing approximate methods of estimating isotope effects for systems with torsional motions. Harmonic approximations yield poor accuracy for these systems, and although the well-known Pitzer-Gwinn (PG) approximation provides better results for absolute partition functions, it yields the same results as the harmonic approximation for isotope effects because these are intrinsically quantal phenomena. We present QM generalizations of the PG approximation that can provide high accuracy for both isotope effects and absolute partition functions. These approximations can be systematically improved until they approach the accurate result and converge rapidly. These methods can also be used to obtain affordable estimates of zero-point energies from accurate partition functions-even those at relatively high temperatures.

Stereographic projection diffusion monte carlo (SPDMC) algorithms for molecular condensed matter

We develop and test three algorithms for diffusion Monte Carlo simulations in non-Euclidean manifolds. The methods are based on the construction of the "velocity" distribution by rejection techniques and are capable of functioning in a broad class of non-Euclidean spaces generated by holonomic constraints. The formulation of the propagator for non-Euclidean manifolds avoids the use of Lagrange multipliers; it is derived instead from the Feynman quantization in manifolds proposed by DeWitt. The manifolds are mapped onto Rd by using stereographic projection coordinates. Numerical tests are conducted for the particle in a ring of unit radius subjected to a sinusoidal potential, for the electron in the field of an infinitely massive proton, and for a water molecule modeled as an asymmetric top subjected to an external field.

Rigid quantum Monte Carlo simulations of condensed molecular matter: Water clusters in the n=2→8 range

The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.

Torsional anharmonicity in transition state theory calculations

We present a new application for the Torsional Path Integral Monte Carlo (TPIMC) method in which the TPI partition functions are introduced into the calculation of Transition State Theory (TST) rate constants. In this way, an explicit treatment of torsional anharmonicity is included in the TST calculations and the magnitude of these effects can be assessed. The new method is tested on the C(2)H(6) + H hydrogen abstraction reaction and concerted hydrogen transfer in the carbonic acid dimer, for which we have developed torsional potential energy surfaces. For the C(2)H(6) + H reaction the rate constants are halved at room temperature on including a treatment of torsional anharmonicity, while the effects are found to be much smaller for the hydrogen transfer reaction in the carbonic acid dimer.

Torsional anharmonicity in the conformational analysis of tryptamine

In this paper we calculate the relative conformer populations of the tryptamine molecule. Our approach combines high level electronic structure conformer energies with harmonic frequencies and an anharmonic treatment of the torsional motions using the torsional path integral Monte Carlo method. We have developed a 3-D potential energy surface as a function of the torsional coordinates at the B3LYP/6-31+G(d) level using 2535 grid points. Eight conformers of tryptamine were found to be significantly populated at 430 K as opposed to the experimental observation of seven. This, along with further comparisons with various experimental data, leads us to suppose that conformer interconversion occurs during the cooling phases of many of the experiments. The ordering of the calculated populations fits well with available experimental data. Torsional anharmonicity is found to affect conformer populations more significantly at 430 K than at 100 K (although overall the effects are small), while quantum mechanical effects are not important at either temperature.

Quantum mechanical single molecule partition function from path integral Monte Carlo simulations

An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.

Stereographic projection path-integral simulations of (HF)n clusters

We perform several quantum canonical ensemble simulations of (HF)(n) clusters. The HF stretches are rigid, and the stereographic projection path-integral method is employed for the simulation in the resulting curved configuration space. We make use of the reweighted random series techniques to accelerate the convergence of the path-integral simulation with respect to the number of path coefficients. We develop and test estimators for the total energy and heat capacity based on a finite difference approach for non-Euclidean spaces. The quantum effects at temperatures below 400 K are substantial for all sizes. We observe interesting thermodynamic behaviors in the quantum simulations of the octamer and the heptamer.

Quantum Simulation of a Hydrated Noradrenaline Analog with the Torsional Path Integral Method

An extended version of the torsional path integral Monte Carlo (TPIMC) method is presented and shown to be useful for studying the conformation of flexible molecules in solvated clusters. The new technique is applied to the hydrated clusters of the 2-amino-1-phenyl-ethanol (APE) molecule. APE + nH2O clusters with n = 0-4 are studied at 100 and 300 K using both classical and quantum simulations. Only at the lower temperature is the hydration number n found to impact the conformational distribution of the APE molecule. This is shown to be a result of the temperature-dependent balance between the internal energy and entropy contributions to the relative conformer free energies. Furthermore, at 100 K, large quantum effects are observed in the calculated conformer populations. A particularly large quantum shift of 30% of the total population is calculated for the APE + 2H2O cluster, which is explained in terms of the relative zero point energy of the lowest-energy hydrated structures for this cluster. Finally, qualitative agreement is found between the reported calculations and recent spectroscopy experiments on the hydrated clusters of APE, including an entropically driven preference for the formation of AG-type hydrated structures and the formation of a water "droplet" in the APE + 4H2O cluster.

A reweighted random series method for stereographic projection path integrals

A set of general reweighted random series methods for metric affine spaces is developed. The extension of the theorems to metric affine spaces demands the introduction of a configuration-independent reference metric tensor; this geometric object is used to treat the path expansion coefficients beyond the core path, in both the partial averaging and the reweighted random series approach. Numerical tests are conducted by simulating a particle in a ring. The reweighted random series results show better convergence properties and better statistical quality at a fraction of the cost compared with the related partial averaging simulation.

Torsional Anharmonicity in the Conformational Analysis of β-d-Galactose

Schemes to include a treatment of torsional anharmonicity in the conformational analysis of biological molecules are introduced. The approaches combine ab initio electronic energies and harmonic frequencies with anharmonic torsional partition functions calculated using the torsional path integral Monte Carlo method on affordable potential energy surfaces. The schemes are applied to the conformational study of the monosaccharide beta-d-galactose in the gas phase. The global minimum structure is almost exclusively populated at 100 K, but a large number of conformers are present at ambient and higher temperatures. Both quantum mechanical and anharmonic effects in the torsional modes have little effect on the populations at all temperatures considered, and it is, therefore, expected that standard harmonic treatments are satisfactory for the conformational study of monosaccharides.

Collision-induced conformational changes in glycine

We present quantum dynamical calculations on the conformational changes of glycine in collisions with the He, Ne, and Ar rare-gas atoms. For two conformer interconversion processes (III-->I and IV-->I), we find that the probability of interconversion is dependent on several factors, including the energy of the collision, the angle at which the colliding atom approaches the glycine molecule, and the strength of the glycine-atom interaction. Furthermore, we show that attractive interactions between the colliding atom and the glycine molecule catalyze conformer interconversion at low collision energies. In previous infrared spectroscopy studies of glycine trapped in rare-gas matrices and helium clusters, conformer III has been consistently observed, but conformer IV has yet to be conclusively detected. Because of the calculated thermodynamic stability of conformer IV, its elusiveness has been attributed to the IV-->I conformer interconversion process. However, our calculations present little indication that IV-->I interconversion occurs more readily than III-->I interconversion. Although we cannot determine whether conformer IV interconverts during experimental Ne- and Ar-matrix depositions, our evidence suggests that the conformer should be present in helium droplets. Anharmonic vibrational frequency calculations illustrate that previous efforts to detect conformer IV may have been hindered by the overlap of its IR-absorption bands with those of other conformers. We propose that the redshifted symmetric -CH(2) stretch of conformer IV provides a means for its conclusive experimental detection.

Partial averaging and the centroid virial estimator for stereographic projection path-integral simulations in curved spaces

We develop and test three different partial averaging theories for the stereographic projection path integral in curved spaces. Additionally, we adapt and test the centroid virial estimator for the kinetic energy in curved spaces. We tested both a confining as well as a nonconfining potential for the particle in a ring. All three partial averaging theories are demonstrated to converge linearly in the asymptotic region with k(-2)max, the number of Fourier coefficients. We use an error estimator to determine the optimal parameters for an extrapolation to infinite kmax. We verify that the centroid virial estimator (derived from the primitive DeWitt path-integral formula) converges to the kinetic energy for both confining and nonconfining potentials.

The energy landscape as a unifying theme in molecular science

The potential energy surface (PES) underlies most calculations of structure, dynamics and thermodynamics in molecular science. In this contribution connections between the topology of the PES and observable properties are developed for a coarse-grained model of virus capsid self-assembly. The model predicts that a thermodynamically stable, kinetically accessible icosahedral shell exists for pentameric building blocks of the right shape: not too flat and not too spiky. The structure of the corresponding PES is probably common to other systems where directed searches avoid Levinthal's paradox, such as 'magic number' clusters, protein folding and crystallization.

Stereographic projections path integral for inertia ellipsoids: Applications to Arn–HF clusters

The DeWitt formula for inertia ellipsoids mapped by stereographic projection coordinates is developed. We discover that by remapping the quaternion parameter space with stereographic projections, considerable simplification of the differential geometry for the inertia ellipsoid with spherical symmetry takes place. The metric tensor is diagonal and contains only one independent element in that case. We find no difficulties testing and implementing the DeWitt formula for the inertia ellipsoids of asymmetric tops mapped by stereographic projections. The path integral algorithm for the treatment of Rm x S2 manifolds based on a mixture of Cartesian and stereographic projection coordinates is tested for small Arn-HF clusters in the n = 2 to n = 5 range. In particular, we determine the quantum effects of the red shift and the isomerization patterns at finite temperatures. Our findings are consistent with previously reported computations and experimental data for small Arn-HF clusters.