Accelerating the Convergence and Reducing the Variance of Path Integral Calculations of Quantum Mechanical Free Energies by Using Local Reference Potentials

2012 ◽  
Vol 8 (5) ◽  
pp. 1589-1596 ◽  
Author(s):  
Steven L. Mielke ◽  
Donald G. Truhlar
Keyword(s):  
Path Integral ◽  
Quantum Mechanical ◽  
Free Energies ◽  
Local Reference

A ‘path-by-path’ monotone extrapolation sequence for Feynman path integral calculations of quantum mechanical free energies

2003 ◽  
Vol 378 (3-4) ◽  
pp. 317-322 ◽  
Author(s):  
Steven L. Mielke ◽  
Donald G. Truhlar
Keyword(s):  
Path Integral ◽  
Quantum Mechanical ◽  
Feynman Path Integral ◽  
Free Energies ◽  
Feynman Path

scholarly journals Protein-ligand free energies of binding from full-protein DFT calculations: convergence and choice of exchange-correlation functional

2021 ◽  
Author(s):  
Lennart Gundelach ◽  
Christofer S Tautermann ◽  
Thomas Fox ◽  
Chris-Kriton Skylaris
Keyword(s):  
Drug Discovery ◽  
Ligand Binding ◽  
Dft Calculations ◽  
Quantum Mechanical ◽  
Free Energies ◽  
Ligand Interaction ◽  
Exchange Correlation ◽  
Ligand Free ◽  
Protein Ligand Interaction ◽  
Binding Free Energies

The accurate prediction of protein-ligand binding free energies with tractable computational methods has the potential to revolutionize drug discovery. Modeling the protein-ligand interaction at a quantum mechanical level, instead of...

A Semiempirical Quantum Mechanical Solvation Model for Solvation Free Energies in All Alkane Solvents

1995 ◽  
Vol 99 (18) ◽  
pp. 7137-7146 ◽  
Author(s):  
David J. Giesen ◽  
Christopher J. Cramer ◽  
Donald G. Truhlar
Keyword(s):  
Quantum Mechanical ◽  
Free Energies ◽  
Solvation Model ◽  
Alkane Solvents ◽  
Solvation Free Energies

Free energies of solvation with quantum mechanical interaction energies from classical mechanical simulations

1999 ◽  
Vol 110 (3) ◽  
pp. 1329-1337 ◽  
Author(s):  
Robert H. Wood ◽  
Eric M. Yezdimer ◽  
Shinichi Sakane ◽  
Jose A. Barriocanal ◽  
Douglas J. Doren
Keyword(s):  
Quantum Mechanical ◽  
Interaction Energies ◽  
Free Energies ◽  
Mechanical Interaction

High-Precision Quantum Thermochemistry on Nonquasiharmonic Potentials:  Converged Path-Integral Free Energies and a Systematically Convergent Family of Generalized Pitzer−Gwinn Approximations

2005 ◽  
Vol 109 (44) ◽  
pp. 10092-10099 ◽  
Author(s):  
Vanessa Audette Lynch ◽  
Steven L. Mielke ◽  
Donald G. Truhlar
Keyword(s):  
High Precision ◽  
Path Integral ◽  
Free Energies

Efficient Strategy for the Calculation of Solvation Free Energies in Water and Chloroform at the Quantum Mechanical/Molecular Mechanical Level

2017 ◽  
Vol 57 (10) ◽  
pp. 2476-2489 ◽  
Author(s):  
Meiting Wang ◽  
Pengfei Li ◽  
Xiangyu Jia ◽  
Wei Liu ◽  
Yihan Shao ◽  
...  
Keyword(s):  
Quantum Mechanical ◽  
Free Energies ◽  
Efficient Strategy ◽  
Solvation Free Energies

Computational Power of Quantum Machines, Quantum Grammars and Feasible Computation

1998 ◽  
Vol 09 (02) ◽  
pp. 213-241 ◽  
Author(s):  
E. V. Krishnamurthy
Keyword(s):  
Harmonic Oscillator ◽  
Turing Machine ◽  
Path Integral ◽  
Quantum Mechanical ◽  
Polynomial Space ◽  
Computational Power ◽  
Computational Point ◽  
Quantum Dynamical ◽  
Special Cases ◽  
Quadratic Potentials

This paper studies the computational power of quantum computers to explore as to whether they can recognize properties which are in nondeterministic polynomial-time class (NP) and beyond. To study the computational power, we use the Feynman's path integral (FPI) formulation of quantum mechanics. From a computational point of view the Feynman's path integral computes a quantum dynamical analogue of the k-ary relation computed by an Alternating Turing machine (ATM) using AND-OR Parallelism. Hence, if we can find a suitable mapping function between an instance of a mathematical problem and the corresponding interference problem, using suitable potential functions for which FPI can be integrated exactly, the computational power of a quantum computer can be bounded to that of an alternating Turing machine that can solve problems in NP (e.g, factorization problem) and in polynomial space. Unfortunately, FPI is exactly integrable only for a few problems (e.g., the harmonic oscillator) involving quadratic potentials; otherwise, they may be only approximately computable or noncomputable. This means we cannot in general solve all quantum dynamical problems exactly except for those special cases of quadratic potentials, e.g., harmonic oscillator. Since there is a one to one correspondence between the quantum mechanical problems that can be analytically solved and the path integrals that can be exactly evaluated, we can say that the noncomputability of FPI implies quantum unsolvability. This is the analogue of classical unsolvability. The Feynman's path graph can be considered as a semantic parse graph for the quantum mechanical sentence. It provides a semantic valuation function of the terminal sentence based on probability amplitudes to disambiguate a given quantum description and obtain an interpretation in a linear time. In Feynman's path integral, the kernels are partially ordered over time (different alternate paths acting concurrently at the same time) and multiplied. The semantic valuation is computable only if the FPI is computable. Thus both the expressive power and complexity aspects quantum computing are mirrored by the exact and efficient integrability of FPI.

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