Linearized Semiclassical Initial Value Time Correlation FunctionsUsing the Thermal Gaussian Approximation: Applications to Condensed PhaseSystems

Liu, Jian; Miller, William H.

doi:10.1063/1.2774990

Linearized Semiclassical Initial Value Time Correlation FunctionsUsing the Thermal Gaussian Approximation: Applications to Condensed PhaseSystems

Journal Article · Tue Jul 10 04:00:00 EDT 2007 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.2774990· OSTI ID:918573

Liu, Jian; Miller, William H.

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne13 Lennard-Jones (LJ) cluster in its liquid-solid phase transition region (temperature from 4 K to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquid-like) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 K and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo (PIMC) results at 25 K. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.

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Research Organization:: Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

Sponsoring Organization:: USDOE Director. Office of Science. Basic Energy Sciences; Office of Naval Research Grant No N00014-05-1-0457

DOE Contract Number:: AC02-05CH11231

OSTI ID:: 918573

Report Number(s):: LBNL--63535; BnR: KC0301020

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Vol. 127; ISSN JCPSA6; ISSN 0021-9606

Country of Publication:: United States

Language:: English

References (76)

Classical-Limit Quantum Mechanics and the Theory of Molecular Collisions Miller, William H. Advances in Chemical Physics, Vol. 25 https://doi.org/10.1002/9780470143773.ch2	book	January 2007
The Classical S-Matrix in Molecular Collisions Miller, William H. Advances in Chemical Physics: Molecular Scattering https://doi.org/10.1002/9780470143827.ch3	book	January 1976
Physics and Chemistry of Small Clusters Jena, P.; Rao, B. K.; Khanna, S. N. https://doi.org/10.1007/978-1-4757-0357-3	book	January 1987
Physics and Chemistry of Finite Systems: From Clusters to Crystals Jena, P.; Khanna, S. N.; Rao, B. K. https://doi.org/10.1007/978-94-017-2645-0	book	January 1992
Preface Echt, O.; Recknagel, E. Zeitschrift f�r Physik D Atoms, Molecules and Clusters, Vol. 19, Issue 1-4 https://doi.org/10.1007/BF01448243	journal	March 1991
Hyper-parallel algorithms for centroid molecular dynamics: application to liquid para-hydrogen Calhoun, August; Pavese, Marc; Voth, Gregory A. Chemical Physics Letters, Vol. 262, Issue 3-4 https://doi.org/10.1016/0009-2614(96)01109-8	journal	November 1996
Quelques Propriétés Générales De L'intégrale De Configuration D'un Système De Particules Avec Interaction van Hove, L. Physica, Vol. 15, Issue 11-12 https://doi.org/10.1016/0031-8914(49)90059-2	journal	December 1949
A semiclasical justification for the use of non-spreading wavepackets in dynamics calculations Herman, Michael F.; Kluk, Edward Chemical Physics, Vol. 91, Issue 1 https://doi.org/10.1016/0301-0104(84)80039-7	journal	November 1984
Forward–backward semiclassical dynamics for systems of indistinguishable particles Nakayama, Akira; Makri, Nancy Chemical Physics, Vol. 304, Issue 1-2 https://doi.org/10.1016/j.chemphys.2004.06.029	journal	September 2004
Symmetries and detailed balance in forward–backward semiclassical dynamics Liu, Jian; Makri, Nancy Chemical Physics, Vol. 322, Issue 1-2 https://doi.org/10.1016/j.chemphys.2005.08.010	journal	March 2006
Gaussian resolutions for equilibrium density matrices Frantsuzov, Pavel; Neumaier, Arnold; Mandelshtam, Vladimir A. Chemical Physics Letters, Vol. 381, Issue 1-2 https://doi.org/10.1016/j.cplett.2003.09.104	journal	November 2003
Sum rule constraints on Kubo-transformed correlation functions Braams, Bastiaan J.; Miller, Thomas F.; Manolopoulos, David E. Chemical Physics Letters, Vol. 418, Issue 1-3 https://doi.org/10.1016/j.cplett.2005.10.127	journal	January 2006
The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations Miller, William H. The Journal of Physical Chemistry A, Vol. 105, Issue 13 https://doi.org/10.1021/jp003712k	journal	April 2001
Monte Carlo Evaluation of Forward−Backward Semiclassical Correlation Functions with a Quantized Coherent State Density Makri, Nancy The Journal of Physical Chemistry B, Vol. 106, Issue 33 https://doi.org/10.1021/jp020907e	journal	August 2002
Semiclassical Theory of Vibrational Energy Relaxation in the Condensed Phase Shi, Qiang; Geva, Eitan The Journal of Physical Chemistry A, Vol. 107, Issue 43 https://doi.org/10.1021/jp030497+	journal	October 2003
Vibrational Energy Relaxation in Liquid Oxygen from a Semiclassical Molecular Dynamics Simulation Shi, Qiang; Geva, Eitan The Journal of Physical Chemistry A, Vol. 107, Issue 43 https://doi.org/10.1021/jp0304982	journal	October 2003
Phase Space Features and Statistical Aspects of Forward−Backward Semiclassical Dynamics ^† Wright, Nicholas J.; Makri, Nancy The Journal of Physical Chemistry B, Vol. 108, Issue 21 https://doi.org/10.1021/jp037600f	journal	May 2004
Quantum Diffusion in Liquid Para-hydrogen: An Application of the Feynman−Kleinert Linearized Path Integral Approximation ^† Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J. The Journal of Physical Chemistry B, Vol. 108, Issue 51 https://doi.org/10.1021/jp040425y	journal	December 2004
Vibrational Energy Relaxation Rates via the Linearized Semiclassical Approximation: Applications to Neat Diatomic Liquids and Atomic−Diatomic Liquid Mixtures Ka, Being J.; Shi, Qiang; Geva, Eitan The Journal of Physical Chemistry A, Vol. 109, Issue 25 https://doi.org/10.1021/jp051223k	journal	June 2005
Vibrational Energy Relaxation of Polyatomic Molecules in Liquid Solution via the Linearized Semiclassical Method Ka, Being J.; Geva, Eitan The Journal of Physical Chemistry A, Vol. 110, Issue 31 https://doi.org/10.1021/jp062363c	journal	August 2006
Vibrational Energy Relaxation Rates of H ₂ and D ₂ in Liquid Argon via the Linearized Semiclassical Method Navrotskaya, Irina; Geva, Eitan The Journal of Physical Chemistry A, Vol. 111, Issue 3 https://doi.org/10.1021/jp066243g	journal	January 2007
Forward−Backward Semiclassical Dynamics without Prefactors Shao, Jiushu; Makri, Nancy The Journal of Physical Chemistry A, Vol. 103, Issue 39 https://doi.org/10.1021/jp991433v	journal	September 1999
Forward−Backward Semiclassical Dynamics with Linear Scaling Shao, Jiushu; Makri, Nancy The Journal of Physical Chemistry A, Vol. 103, Issue 47 https://doi.org/10.1021/jp991837n	journal	November 1999
Spiers Memorial Lecture Quantum and semiclassical theory of chemical reaction rates Miller, William H. Faraday Discussions, Vol. 110 https://doi.org/10.1039/a805196h	journal	January 1998
Generalized forward–backward initial value representation for the calculation of correlation functions in complex systems Thoss, Michael; Wang, Haobin; Miller, William H. The Journal of Chemical Physics, Vol. 114, Issue 21 https://doi.org/10.1063/1.1359242	journal	June 2001
A self-consistent mode-coupling theory for dynamical correlations in quantum liquids: Application to liquid para -hydrogen Reichman, David R.; Rabani, Eran The Journal of Chemical Physics, Vol. 116, Issue 14 https://doi.org/10.1063/1.1458546	journal	April 2002
Semiclassical calculation of thermal rate constants in full Cartesian space: The benchmark reaction D+H2→DH+H Yamamoto, Takeshi; Miller, William H. The Journal of Chemical Physics, Vol. 118, Issue 5 https://doi.org/10.1063/1.1533081	journal	February 2003
A relationship between semiclassical and centroid correlation functions Shi, Qiang; Geva, Eitan The Journal of Chemical Physics, Vol. 118, Issue 18 https://doi.org/10.1063/1.1564814	journal	May 2003
Forward–backward semiclassical dynamics for quantum fluids using pair propagators: Application to liquid para -hydrogen Nakayama, Akira; Makri, Nancy The Journal of Chemical Physics, Vol. 119, Issue 16 https://doi.org/10.1063/1.1611473	journal	October 2003
Heat capacity estimators for random series path-integral methods by finite-difference schemes Predescu, Cristian; Sabo, Dubravko; Doll, J. D. The Journal of Chemical Physics, Vol. 119, Issue 23 https://doi.org/10.1063/1.1625366	journal	December 2003
Practical evaluation of condensed phase quantum correlation functions: A Feynman–Kleinert variational linearized path integral method Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J. The Journal of Chemical Physics, Vol. 119, Issue 23 https://doi.org/10.1063/1.1626631	journal	December 2003
Classical S Matrix: Numerical Application to Inelastic Collisions Miller, William H. The Journal of Chemical Physics, Vol. 53, Issue 9 https://doi.org/10.1063/1.1674535	journal	November 1970
Theory of Semiclassical Transition Probabilities (S Matrix) for Inelastic and Reactive Collisions Marcus, R. A. The Journal of Chemical Physics, Vol. 54, Issue 9 https://doi.org/10.1063/1.1675453	journal	May 1971
Theory of Semiclassical Transition Probabilities ( S Matrix) for Inelastic and Reactive Collisions. Uniformization with Elastic Collision Trajectories Marcus, R. A. The Journal of Chemical Physics, Vol. 56, Issue 7 https://doi.org/10.1063/1.1677730	journal	April 1972
A centroid molecular dynamics study of liquid para -hydrogen and ortho -deuterium Hone, Tyler D.; Voth, Gregory A. The Journal of Chemical Physics, Vol. 121, Issue 13 https://doi.org/10.1063/1.1780951	journal	October 2004
Quantum statistical mechanics with Gaussians: Equilibrium properties of van der Waals clusters Frantsuzov, Pavel A.; Mandelshtam, Vladimir A. The Journal of Chemical Physics, Vol. 121, Issue 19 https://doi.org/10.1063/1.1804495	journal	November 2004
Quantum diffusion in liquid para -hydrogen from ring-polymer molecular dynamics Miller, Thomas F.; Manolopoulos, David E. The Journal of Chemical Physics, Vol. 122, Issue 18 https://doi.org/10.1063/1.1893956	journal	May 2005
A comparative study of imaginary time path integral based methods for quantum dynamics Hone, Tyler D.; Rossky, Peter J.; Voth, Gregory A. The Journal of Chemical Physics, Vol. 124, Issue 15 https://doi.org/10.1063/1.2186636	journal	April 2006
Symmetrized correlation function for liquid para -hydrogen using complex-time pair-product propagators Nakayama, Akira; Makri, Nancy The Journal of Chemical Physics, Vol. 125, Issue 2 https://doi.org/10.1063/1.2209682	journal	July 2006
Including quantum effects in the dynamics of complex (i.e., large) molecular systems Miller, William H. The Journal of Chemical Physics, Vol. 125, Issue 13 https://doi.org/10.1063/1.2211608	journal	October 2006
Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions Liu, Jian; Miller, William H. The Journal of Chemical Physics, Vol. 125, Issue 22 https://doi.org/10.1063/1.2395941	journal	December 2006
Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation Liu, Jian; Miller, William H. The Journal of Chemical Physics, Vol. 126, Issue 23 https://doi.org/10.1063/1.2743023	journal	June 2007
Time‐dependent approach to semiclassical dynamics Heller, Eric J. The Journal of Chemical Physics, Vol. 62, Issue 4 https://doi.org/10.1063/1.430620	journal	February 1975
Wigner phase space method: Analysis for semiclassical applications Heller, Eric J. The Journal of Chemical Physics, Vol. 65, Issue 4 https://doi.org/10.1063/1.433238	journal	August 1976
The isotropic intermolecular potential for H ₂ and D ₂ in the solid and gas phases Silvera, Isaac F.; Goldman, Victor V. The Journal of Chemical Physics, Vol. 69, Issue 9 https://doi.org/10.1063/1.437103	journal	November 1978
A new approach to molecular collisions: Statistical quasiclassical method Lee, Hai‐Woong; Scully, Marlan O. The Journal of Chemical Physics, Vol. 73, Issue 5 https://doi.org/10.1063/1.440419	journal	September 1980
Quantum mechanical rate constants for bimolecular reactions Miller, William H.; Schwartz, Steven D.; Tromp, John W. The Journal of Chemical Physics, Vol. 79, Issue 10 https://doi.org/10.1063/1.445581	journal	November 1983
Melting and freezing in isothermal Ar ₁ ₃ clusters Davis, Heidi L.; Jellinek, Julius; Berry, R. Stephen The Journal of Chemical Physics, Vol. 86, Issue 11 https://doi.org/10.1063/1.452436	journal	June 1987
Structure and binding of Lennard‐Jones clusters: 13≤ N ≤147 Northby, J. A. The Journal of Chemical Physics, Vol. 87, Issue 10 https://doi.org/10.1063/1.453492	journal	November 1987
Theoretical studies of the energetics and structures of atomic clusters Xie, J.; Northby, J. A.; Freeman, David L. The Journal of Chemical Physics, Vol. 91, Issue 1 https://doi.org/10.1063/1.457447	journal	July 1989
Cellular dynamics: A new semiclassical approach to time‐dependent quantum mechanics Heller, Eric J. The Journal of Chemical Physics, Vol. 94, Issue 4 https://doi.org/10.1063/1.459848	journal	February 1991
Reply to Comment on: Semiclassical time evolution without root searches: Comments and perspective Heller, E. J. The Journal of Chemical Physics, Vol. 95, Issue 12 https://doi.org/10.1063/1.461178	journal	December 1991
Numerical study of semiclassical initial value methods for dynamics Kay, Kenneth G. The Journal of Chemical Physics, Vol. 100, Issue 6 https://doi.org/10.1063/1.466273	journal	March 1994
Integral expressions for the semiclassical time‐dependent propagator Kay, Kenneth G. The Journal of Chemical Physics, Vol. 100, Issue 6 https://doi.org/10.1063/1.466320	journal	March 1994
Mixed semiclassical–classical approaches to the dynamics of complex molecular systems Sun, Xiong; Miller, William H. The Journal of Chemical Physics, Vol. 106, Issue 3 https://doi.org/10.1063/1.473171	journal	January 1997
A new quantum transition state theory Pollak, Eli; Liao, Jie-Lou The Journal of Chemical Physics, Vol. 108, Issue 7 https://doi.org/10.1063/1.475665	journal	February 1998
Semiclassical approximations for the calculation of thermal rate constants for chemical reactions in complex molecular systems Wang, Haobin; Sun, Xiong; Miller, William H. The Journal of Chemical Physics, Vol. 108, Issue 23 https://doi.org/10.1063/1.476447	journal	June 1998
Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation Sun, Xiong; Wang, Haobin; Miller, William H. The Journal of Chemical Physics, Vol. 109, Issue 17 https://doi.org/10.1063/1.477389	journal	November 1998
Forward–backward initial value representation for semiclassical time correlation functions Sun, Xiong; Miller, William H. The Journal of Chemical Physics, Vol. 110, Issue 14 https://doi.org/10.1063/1.478571	journal	April 1999
Phase transitions and adjacent phenomena in simple atomic systems Berry, R. S.; Smirnov, Boris M. Physics-Uspekhi, Vol. 48, Issue 4 https://doi.org/10.1070/PU2005v048n04ABEH002022	journal	April 2005
Quantum dynamics of complex molecular systems Miller, W. H. Proceedings of the National Academy of Sciences, Vol. 102, Issue 19 https://doi.org/10.1073/pnas.0408043102	journal	May 2005
Simulation of dynamical properties of normal and superfluid helium Nakayama, A.; Makri, N. Proceedings of the National Academy of Sciences, Vol. 102, Issue 12 https://doi.org/10.1073/pnas.0501127102	journal	March 2005
The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: Application to liquid para-hydrogen Rabani, E.; Reichman, D. R.; Krilov, G. Proceedings of the National Academy of Sciences, Vol. 99, Issue 3 https://doi.org/10.1073/pnas.261540698	journal	February 2002
Physical cluster mechanics: Statics and energy surfaces for monatomic systems Hoare, M. R.; Pal, P. Advances in Physics, Vol. 20, Issue 84 https://doi.org/10.1080/00018737100101231	journal	March 1971
Long-time behaviour of quantized distributions in forward–backward semiclassical dynamics Liu, J.; Nakayama, A.; Makri, N. Molecular Physics, Vol. 104, Issue 8 https://doi.org/10.1080/00268970500525754	journal	April 2006
On the Quantum Correction For Thermodynamic Equilibrium Wigner, E. Physical Review, Vol. 40, Issue 5 https://doi.org/10.1103/PhysRev.40.749	journal	June 1932
Semiclassical propagation: Phase indices and the initial-value formalism Campolieti, G.; Brumer, Paul Physical Review A, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevA.50.997	journal	August 1994
Transformation theory for phase-space representations of quantum mechanics Wilkie, Joshua; Brumer, Paul Physical Review A, Vol. 61, Issue 6 https://doi.org/10.1103/PhysRevA.61.064101	journal	May 2000
Microscopic collective dynamics in liquid p a r a − H 2 Bermejo, F. J.; Fåk, B.; Bennington, S. M. Physical Review B, Vol. 60, Issue 22 https://doi.org/10.1103/PhysRevB.60.15154	journal	December 1999
Size-temperature phase diagram for small Lennard-Jones clusters Frantsuzov, Pavel A.; Mandelshtam, Vladimir A. Physical Review E, Vol. 72, Issue 3 https://doi.org/10.1103/PhysRevE.72.037102	journal	September 2005
Quantum Effects on Liquid Dynamics as Evidenced by the Presence of Well-Defined Collective Excitations in Liquid para -Hydrogen Bermejo, F. J.; Kinugawa, K.; Cabrillo, C. Physical Review Letters, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevLett.84.5359	journal	June 2000
Structural Transformations and Melting in Neon Clusters: Quantum versus Classical Mechanics Frantsuzov, Pavel A.; Meluzzi, Dario; Mandelshtam, Vladimir A. Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.113401	journal	March 2006
COMPUTATIONAL STUDIES OF CLUSTERS:Methods and Results Freeman, David L.; Doll, J. D. Annual Review of Physical Chemistry, Vol. 47, Issue 1 https://doi.org/10.1146/annurev.physchem.47.1.43	journal	October 1996
STRUCTURE AND TRANSFORMATION: Large Molecular Clusters as Models of Condensed Matter Bartell, Lawrence S. Annual Review of Physical Chemistry, Vol. 49, Issue 1 https://doi.org/10.1146/annurev.physchem.49.1.43	journal	October 1998
Semiclassical Description of Molecular Dynamics Based on Initial-Value Representation Methods Thoss, Michael; Wang, Haobin Annual Review of Physical Chemistry, Vol. 55, Issue 1 https://doi.org/10.1146/annurev.physchem.55.091602.094429	journal	June 2004
Semiclassical Initial Value Treatments of Atoms and Molecules Kay, Kenneth G. Annual Review of Physical Chemistry, Vol. 56, Issue 1 https://doi.org/10.1146/annurev.physchem.56.092503.141257	journal	May 2005

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