Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi-Imada factorization of the Feynman path integral

The Feynman path integral approach for computing equilibrium isotope effects and isotope fractionation corrects the approximations made in standard methods, although at significantly increased computational cost. We describe an accelerated path integral approach based on three ingredients: the fourth- order Takahashi-Imada factorization of the path integral, thermodynamic integration with respect to mass, and centroid virial estimators for relevant free energy derivatives. While the frst ingredient speeds up convergence to the quantum limit, the second and third improve statistical convergence. The combined method is applied to compute the equilibrium constants for isotope exchange reactions H2+D=H+HD and H2+D2=2HD

Path integral evaluation of the kinetic isotope effects based on the quantum instanton approximation

A general method for computing kinetic isotope effects is described. The method uses the quantum-instanton approximation and is based on the thermodynamic integration with respect to the mass of the isotopes and on the path-integral Monte-Carlo evaluation of relevant thermodynamic quantities. The central ingredients of the method are the Monte-Carlo estimators for the logarithmic derivatives of the partition function and the delta-delta correlation function. Several alternative estimators for these quantities are described here and their merits are compared on the benchmark hydrogen-exchange reaction, H+H_2->H_2+H on the Truhlar-Kuppermann potential energy surface. Finally, a qualitative discussion of issues arising in many-dimensional systems is provided.Comment: 11 pages, 2 figures, proceeding

Evaluation of the nondiabaticity of quantum molecular dynamics with the dephasing representation of quantum fidelity

We propose an approximate method for evaluating the importance of non-Born-Oppenheimer effects on the quantum dynamics of nuclei. The method uses a generalization of the dephasing representation (DR) of quantum fidelity to several diabatic potential energy surfaces and its computational cost is the cost of dynamics of a classical phase space distribution. It can be implemented easily into any molecular dynamics program and also can utilize on-the-fly ab initio electronic structure information. We test the methodology on three model problems introduced by Tully and on the photodissociation of NaI. The results show that for dynamics close to the diabatic limit the decay of fidelity due to nondiabatic effects is described accurately by the DR. In this regime, unlike the mixed quantum-classical methods such as surface hopping or Ehrenfest dynamics, the DR can capture more subtle quantum effects than the population transfer between potential energy surfaces. Hence we propose using the DR to estimate the dynamical importance of diabatic, spin-orbit, or other couplings between potential energy surfaces. The acquired information can help reduce the complexity of a studied system without affecting the accuracy of the quantum simulation.Comment: 5 pages, 3 figures, section Theory extended(v2), small textual improvements(v2), added reference(v2 & v3), added acknowledgement(v3), submitted to J. Chem. Phy

Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass

Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to sampling, path integral discretization errors, and thermodynamic integration errors. While the statistical errors can be reduced with virial estimators and path integral discretization errors with high-order factorization of the Boltzmann operator, here we propose a method for accelerating isotope effect calculations by eliminating the integration error. We show that the integration error can be removed entirely by changing particle masses stochastically during the calculation and by using a piecewise linear umbrella biasing potential. Moreover, we demonstrate numerically that this approach does not increase the statistical error. The resulting acceleration of isotope effect calculations is demonstrated on a model harmonic system and on deuterated species of methane

Role of the sampling weight in evaluating classical time autocorrelation functions

We analyze how the choice of the sampling weight affects the efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phase-space density. In contrast, it is shown that the computational cost of the "standard" intuitive algorithm which samples directly from the phase-space density may scale exponentially with the number of degrees of freedom. Yet, for the stationary Gaussian distribution of harmonic systems and for the autocorrelation function of a linear function of phase-space coordinates, the computational cost of this standard algorithm is also independent of dimensionality.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

Temporal adaptations in generic and population-specific quality of life and falls efficacy in men with recent lower-limb amputations

This study examined the longitudinal changes in generic health-related quality of life (QOL), prosthesis-related QOL, falls efficacy, and walking speed in men with lower-limb amputations up to 6 months following discharge from rehabilitation. Seven male unilateral transtibial amputees completed the Medical Outcomes Study 36-Item Short Form Health Survey, the Prosthesis Evaluation Questionnaire, and the Modified Falls Efficacy Scale at 1, 3, and 6 months postdischarge from rehabilitation. Walking speed was also recorded to objectively assess participants’ mobility. Health-related QOL measures displayed increases, resulting in large effect sizes though not reaching statistical significance. Prosthesis-related QOL measures indicated that scales relating to the participants’ prostheses improved and the support of significant others was the most positively scored variable. Walking speed increased by 0.12 m/ s, although it was not significantly related to indices of QOL or falls efficacy. Falls efficacy did not improve significantly during the study period, although it was strongly related to QOL ( p < 0.05). These results provide a novel insight into how QOL and falls efficacy develop in people with lower-limb amputations, alongside changes in mobility, after discharge from rehabilitation. Further improvements in physical health following discharge may be required to elicit subsequent increases in overall QOL and concurrent improvements in falls efficacy

Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor

Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing representation. Here we improve both the accuracy of this approximation---with an amplitude correction derived from the phase-space propagator---and its efficiency---with an improved cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. We demonstrate the advantages of the new methodology by computing dispersed time-resolved stimulated emission spectra in the harmonic potential, pyrazine, and the NCO molecule. In contrast, we show that in strongly chaotic systems such as the quartic oscillator the original dephasing representation is more appropriate than either the cellular or prefactor-corrected methods.Comment: submitte

On-the-fly ab initio semiclassical dynamics: Identifying degrees of freedom essential for emission spectra of oligothiophenes

Vibrationally resolved spectra provide a stringent test of the accuracy of theoretical calculations. We combine the thawed Gaussian approximation (TGA) with an on-the-fly ab initio (OTF-AI) scheme to calculate the vibrationally resolved emission spectra of oligothiophenes with up to five rings. The efficiency of the OTF-AI-TGA permits treating all vibrational degrees of freedom on an equal footing even in pentathiophene with 105 vibrational degrees of freedom, thus obviating the need for the global harmonic approximation, popular for large systems. Besides reproducing almost perfectly the experimental emission spectra, in order to provide a deeper insight into the associated physical and chemical processes, we also develop a novel systematic approach to assess the importance and coupling between individual vibrational degrees of freedom during the dynamics. This allows us to explain how the vibrational line shapes of the oligothiophenes change with increasing number of rings. Furthermore, we observe the dynamical interplay between the quinoid and aromatic characters of individual rings in the oligothiophene chain during the dynamics and confirm that the quinoid character prevails in the center of the chain

Breaking the exponential wall in classical simulations of fidelity

We analyze the efficiency of available algorithms for the simulation of classical fidelity and show that their computational costs increase exponentially with the number of degrees of freedom for almost all initial states. Then we present an algorithm whose cost is independent of the system's dimensionality and show that, within a continuous family of algorithms, our algorithm is the only one with this property. Simultaneously we propose a general analytical approach to estimate efficiency of trajectory-based methods.Comment: 5 pages, 3 figure