Jian Liu Group @PKU

Theoretical Chemistry / Chemical Dynamics

Recent Publications

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  1. Xin He, Baihua Wu, Jian Liu, Journal of Chemical Theory and Computation, [Invited Review]

  2. Haifeng Zheng, Kangyu Yan, Weihao Liang, Jian Liu, Journal of Physical Chemistry C, [Invited Feature Article]

  3. Xin He, Baihua Wu, Xiangsong Cheng, Youhao Shang, Jian Liu, "Perspective: Phase Space Mapping Nonadiabatic Dynamics", Journal of Physical Chemistry Letters, [Invited contribution]

  4. Baihua Wu, Xin He, Xiangsong Cheng, Youhao Shang, Jian Liu, Fundamental Research, [Invited contribution]

  5. Cong Wang, Lihan Zhang, Jian Liu, Jiushu Shao, "An efficient algorithm for the fourth order decomposition for path integral molecular dynamics", (in preparation)

  6. Xin He, Baihua Wu, Tom Rivlin, Jian Liu*, Eli Pollak*, "Transition Path Flight Times and Nonadiabatic Electronic Transitions", Journal of Physical Chemistry Letters, 13, 30, 6966-6974 (2022) [https://pubs.acs.org/doi/10.1021/acs.jpclett.2c01425][pdf version]

  7. Cong Wang, Lihan Zhang, Jian Liu*, Jiushu Shao*, "Generalized Fourth-order Decompositions of Imaginary Time Path Integral: Implication of the Harmonic Oscillator", Chinese Journal of Chemical Physics, 35(3), 516-536 (2022) [https://cps.scitation.org/doi/pdf/10.1063/1674-0068/cjcp2205089][Invited Contribution to the Special Topic "Quantum and Classical Dynamics in Chemistry"]

  8. Eli Pollak, Sameernandan Upadhyayula, Jian Liu,“Coherent state representation of thermal correlation functions with applications to rate theory", Journal of Chemical Physics, 156, 244101 (2022) [https://aip.scitation.org/doi/10.1063/5.0088163][pdf version]

  9. Xiaoliang Pan, Richard Van, Evgeny Epifanovsky, Jian Liu, Jingzhi Pu, Kwangho Nam, Yihan Shao, "Accelerating ab initio QM/MM Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semi-empirical QM/MM Hamiltonian", Journal of Physical Chemistry B, 126(23), 4226–4235 (2022) [https://pubs.acs.org/doi/10.1021/acs.jpcb.2c02262][pdf version]

  10. Xin He, Baihua Wu, Youhao Shang, Binqi Li, Xiangsong Cheng, Jian Liu*, "New Phase Space Formulations and Quantum Dynamics Approaches", Wiley Interdisciplinary Reviews-Computational Molecular Science, e1619 (2022) [https://doi.org/10.1002/wcms.1619] Supporting Information [Invited contribution. Front cover of this issue][pdf version][pdf link][https://arxiv.org/abs/2205.03870]

  11. Zhaoxi Sun, Payam Kalhor, Yang Xu, Jian Liu*,"Extensive Numerical Tests of the Leapfrog Integrator in the Middle Thermostat Scheme in Molecular Simulations", Chinese Journal of Chemical Physics, 34, 6, 932-948 (2021) [https://doi.org/10.1063/1674-0068/cjcp2111242] [Invited contribution to the John Zhang Festschrift][pdf version]

  12. Baihua Wu, Xin He, Jian Liu*, "Phase Space Mapping Theory for Nonadiabatic Quantum Molecular Dynamics", Volume on Time-Dependent Density Functional Theory: Nonadiabatic Molecular Dynamics, Jenny Stanford Publishing [Invited contribution] link

  13. Jian Liu*, Xin He, Baihua Wu, "Unified formulation for phase space mapping models for nonadiabatic quantum dynamics", Accounts of Chemical Research, 54, 23, 4215–4228 (2021) [https://doi.org/10.1021/acs.accounts.1c00511] [Invited contribution] [pdf version]

  14. Xin He, Baihua Wu, Zhihao Gong, Jian Liu*, "Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics", Journal of Physical Chemistry A, 125, 31, 6845–6863 (2021) [https://doi.org/10.1021/acs.jpca.1c04429] [Invited contribution to the Tanimura Festschrift][pdf version]

  15. Xinzijian Liu, Linfeng Zhang, Jian Liu*, "Machine Learning phase space quantum dynamics approaches", Journal of Chemical Physics, 154, 184104 (2021). [https://doi.org/10.1063/5.0046689] [Invited contribution to the Special Topic 'Quantum Dynamics with ab Initio Potentials'] [pdf version]

  16. Xin He, Zhihao Gong, Baihua Wu, Jian Liu*, "Negative Zero-Point-Energy Parameter in the Meyer–Miller Mapping Model for Nonadiabatic Dynamics", Journal of Physical Chemistry Letters, 12, 2496–2501 (2021) [https://pubs.acs.org/doi/full/10.1021/acs.jpclett.1c00232] [pdf version]

  17. Zhijun Zhang, Zifei Chen, Jian Liu*, "Path Integral Liouville Dynamics Simulations of Vibrational Spectra of Formaldehyde and Hydrogen Peroxide", Chinese Journal of Chemical Physics, 33, 613 (2020) [https://doi.org/10.1063/1674-0068/cjcp2006099] [Invited contribution] [pdf version]

  18. Xinzijian Liu, Kangyu Yan, Jian Liu*, "Efficient Middle Thermostat Scheme for the Quantum/Classical Canonical Ensemble via Molecular Dynamics", Progress in Theoretical Chemistry and Physics, Springer Nature Switzerland AG (2020) [https://doi.org/10.1007/978-3-030-34941-7] [Invited contribution] [pdf version]

  19. Chaoyue Gu, Xin Nie, Jiezhang Jiang, Zifei Chen, Yifan Dong, Xin Zhang, Junjie Liu, Zhengyou Yu, Zhiwei Zhu, Jian Liu, Xiaoyun Liu, and Yuanhua Shao, "Mechanistic Study of Oxygen Reduction at Liquid/Liquid Interfaces by Hybrid Ultramicroelectrodes and Mass Spectrometry", Journal of the American Chemical Society 141, 13212−13221 (2019) [https://pubs.acs.org/doi/10.1021/jacs.9b06299] [pdf version]

  20. Xin He, Jian Liu*, "A new perspective for nonadiabatic dynamics with phase space mapping models", Journal of Chemical Physics, 151, 024105 (2019). (Invited contribution to Special Topic Issue on "Dynamics of Open Quantum Systems") [https://doi.org/10.1063/1.5108736 ][pdf version]

  21. Zhijun Zhang, Xinzijian Liu, Kangyu Yan, Mark Tuckerman, Jian Liu*, "A unified efficient thermostat scheme for the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics", Journal of Physical Chemistry A, 123, 28, 6056-6079 (2019). (Invited contribution to "Young Scientist Virtual Special Issue") [https://doi.org/10.1021/acs.jpca.9b02771][pdf version] (Highlighted in JPC Virtual Issue on New Tools and Methods )

  22. Yun-an Yan*, Jian Liu, Jiushu Shao, "A semiclassical initial-value representation for quantum propagator and Boltzmann propagator", Journal of Computational Chemistry, 40, 1161–1171 (2019) [https://doi.org/10.1002/jcc.25751][pdf version]

  23. Zhijun Zhang, Kangyu Yan, Xinzijian Liu, Jian Liu*, "A leap-frog algorithm-based efficient unified thermostat scheme via molecular dynamics", Chinese Science Bulletin，63(33), 3467-3483(2018)[Invited Contribution] [http://engine.scichina.com/doi/10.1360/N972018-00908 ] [pdf version]

  24. Haobin Wang*, Xinzijian Liu, Jian Liu*, "Accurate calculation of equilibrium reduced density matrix for the system-bath model: a multilayer multiconfiguration time-dependent Hartree approach and its comparison to a multi-electronic-state path integral molecular dynamics approach", Chinese Journal of Chemical Physics, 31, 446 (2018) (Invited Contribution) [https://doi.org/10.1063/1674-0068/31/cjcp1805122 ] [pdf version]

  25. Xinzijian Liu, Jian Liu*, "Critical role of quantum dynamical effects in the Raman spectroscopy of liquid water", Molecular Physics, 116(7-8), 755-779 (2018) [https://doi.org/10.1080/00268976.2018.1434907 Invited contribution. Front cover of this issue.] Free eprints [arXiv preprint] [pdf version]

  26. Dezhang Li, Zifei Chen, Zhijun Zhang, Jian Liu*, "Understanding molecular dynamics with stochastic processes via real or virtual dynamics", Chinese Journal of Chemical Physics, 30, 735 (2017) [http://dx.doi.org/10.1063/1674-0068/30/cjcp1711223 Invited article for the CJCP special topic issue on "Chemical Dynamics"] pdf version from the CJCP website [arXiv preprint] [pdf version]

  27. Xinzijian Liu, Jian Liu*, "Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems", Journal of Chemical Physics, 148, 102319 (2018) [https://doi.org/10.1063/1.5005059 Invited article for the JCP special topic issue on "Nuclear Quantum Effects"] [arXiv preprint] [pdf version]

  28. Dezhang Li, Xu Han, Yichen Chai, Cong Wang, Zhijun Zhang, Zifei Chen, Jian Liu*, Jiushu Shao*, "Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics", Journal of Chemical Physics, 147, 184104 (2017) [https://doi.org/10.1063/1.4996204] Supplementary material [arXiv preprint] [pdf version]

  29. Zhijun Zhang, Xinzijian Liu, Zifei Chen, Haifeng Zheng, Kangyu Yan, Jian Liu*, "A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics", Journal of Chemical Physics, 147, 034109 (2017) [http://dx.doi.org/10.1063/1.4991621] Supplementary material [arXiv preprint] [pdf version]

  30. Jian Liu*,"Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactions", Journal of Chemical Physics, 146, 024110 (2017) [http://dx.doi.org/10.1063/1.4973708] [arXiv preprint] [pdf version]

  31. Jian Liu*,"A unified theoretical framework for mapping models for the multi-state Hamiltonian", Journal of Chemical Physics, 145, 204105 (2016) [http://dx.doi.org/10.1063/1.4967815] [arXiv preprint][pdf version]

  32. Jian Liu*, Dezhang Li, Xinzijian Liu, "A simple and accurate algorithm for path integral molecular dynamics", Journal of Chemical Physics, 145, 024103 (2016) [http://dx.doi.org/10.1063/1.4954990] Supplementary material [arXiv preprint (Paper + Supplemental materical)][pdf version]

  33. Jian Liu*, Zhijun Zhang, "Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane", Journal of Chemical Physics, 144, 034307 (2016) [http://dx.doi.org/10.1063/1.4939953] [pdf version]

  34. Lihong Liu, Jian Liu, Todd Martinez*, "Dynamical Correlation Effects on Photoisomerization: Ab Initio Multiple Spawning Dynamics with MS-CASPT2 for a Model trans-Protonated Schiff Base", Journal of Physical Chemistry B, 120, 1940 (2016) [http://dx.doi.org/10.1021/acs.jpcb.5b09838] Supporting Information[pdf version]

  35. Jian Liu*, Dezhang Li, Xinzijian Liu, "Further study of path integral Liouville dynamics", Scientia Sinica Chimica, 46, 27 (2016) [http://dx.doi.org/10.1360/N032015-00143 Invited article for the special issue for the Festschrift for Professor Lemin Li's 80th birthday][pdf version]

  36. Jian Liu*,"Recent advances in the linearized semiclassical initial value representation/classical Wigner model for the thermal correlation function", International Journal of Quantum Chemistry, 115(11), 657-670 (2015) [http://onlinelibrary.wiley.com/doi/10.1002/qua.24872/full Front cover of this issue. Invited contribution.][pdf version]

  37. Jian Liu*, "Path integral Liouville dynamics for thermal equilibrium systems", Journal of Chemical Physics, 140, 224107 (2014) [https://doi.org/10.1063/1.4881518 ][pdf version]

* Corresponding Author(s)

Note: The unified "middle" thermostat scheme has been implemented in AMBER (2018 version).

Please visit Tutorials for more details.

Full Publications

  1. Xin He, Baihua Wu, Tom Rivlin, Jian Liu, Eli Pollak, "Transition Path Flight Times and Nonadiabatic Electronic Transitions", Journal of Physical Chemistry Letters, 13, 30, 6966-6974 (2022) [https://pubs.acs.org/doi/10.1021/acs.jpclett.2c01425][pdf version]

  2. Cong Wang, Lihan Zhang, Jian Liu, Jiushu Shao, "Generalized Fourth-order Decompositions of Imaginary Time Path Integral: Implication of the Harmonic Oscillator", Chinese Journal of Chemical Physics, 35(3), 516-536 (2022) [https://cps.scitation.org/doi/pdf/10.1063/1674-0068/cjcp2205089][Invited Contribution to the Special Topic "Quantum and Classical Dynamics in Chemistry"]

  3. Eli Pollak, Sameernandan Upadhyayula, Jian Liu,“Coherent state representation of thermal correlation functions with applications to rate theory", Journal of Chemical Physics, 156, 244101 (2022) [https://aip.scitation.org/doi/10.1063/5.0088163][pdf version]

  4. Xiaoliang Pan, Richard Van, Evgeny Epifanovsky, Jian Liu, Jingzhi Pu, Kwangho Nam, Yihan Shao, "Accelerating ab initio QM/MM Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semi-empirical QM/MM Hamiltonian", Journal of Physical Chemistry B, 126(23), 4226–4235 (2022) [https://pubs.acs.org/doi/10.1021/acs.jpcb.2c02262][pdf version]

  5. Xin He, Baihua Wu, Youhao Shang, Binqi Li, Xiangsong Cheng, Jian Liu, "New Phase Space Formulations and Quantum Dynamics Approaches", Wiley Interdisciplinary Reviews-Computational Molecular Science, e1619 (2022) [https://doi.org/10.1002/wcms.1619] Supporting Information [Invited contribution. Front cover of this issue][pdf version][pdf link][https://arxiv.org/abs/2205.03870]

  6. Zhaoxi Sun, Payam Kalhor, Yang Xu, Jian Liu,"Extensive Numerical Tests of the Leapfrog Integrator in the Middle Thermostat Scheme in Molecular Simulations", Chinese Journal of Chemical Physics, 34, 6, 932-948 (2021) [https://doi.org/10.1063/1674-0068/cjcp2111242] [Invited contribution to the John Zhang Festschrift][pdf version]

  7. Baihua Wu, Xin He, Jian Liu*, "Phase Space Mapping Theory for Nonadiabatic Quantum Molecular Dynamics", Volume on Time-Dependent Density Functional Theory: Nonadiabatic Molecular Dynamics, Jenny Stanford Publishing [Invited contribution] link

  8. Jian Liu, Xin He, Baihua Wu, "Unified formulation for phase space mapping models for nonadiabatic quantum dynamics", Accounts of Chemical Research, 54, 23, 4215–4228 (2021) [https://doi.org/10.1021/acs.accounts.1c00511] [Invited contribution] [pdf version]

  9. Xin He, Baihua Wu, Zhihao Gong, Jian Liu, "Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics", Journal of Physical Chemistry A, 125, 31, 6845–6863 (2021) [https://doi.org/10.1021/acs.jpca.1c04429] [Invited contribution to the Tanimura Festschrift][pdf version]

  10. Xinzijian Liu, Linfeng Zhang, Jian Liu, "Machine Learning phase space quantum dynamics approaches", Journal of Chemical Physics, 154, 184104 (2021). [https://doi.org/10.1063/5.0046689] [Invited contribution to the Special Topic 'Quantum Dynamics with ab Initio Potentials'] [pdf version]

  11. Xin He, Zhihao Gong, Baihua Wu, Jian Liu, "Negative Zero-Point-Energy Parameter in the Meyer–Miller Mapping Model for Nonadiabatic Dynamics", Journal of Physical Chemistry Letters, 12, 2496–2501 (2021) [https://pubs.acs.org/doi/full/10.1021/acs.jpclett.1c00232] [pdf version]

  12. Zhijun Zhang, Zifei Chen, Jian Liu, "Path Integral Liouville Dynamics Simulations of Vibrational Spectra of Formaldehyde and Hydrogen Peroxide", Chinese Journal of Chemical Physics, 33, 613 (2020) [https://doi.org/10.1063/1674-0068/cjcp2006099] [Invited contribution] [pdf version]

  13. Xinzijian Liu, Kangyu Yan, Jian Liu, "Efficient Middle Thermostat Scheme for the Quantum/Classical Canonical Ensemble via Molecular Dynamics", Progress in Theoretical Chemistry and Physics, Springer Nature Switzerland AG (2020) [https://doi.org/10.1007/978-3-030-34941-7] [Invited contribution] [pdf version]

  14. Chaoyue Gu, Xin Nie, Jiezhang Jiang, Zifei Chen, Yifan Dong, Xin Zhang, Junjie Liu, Zhengyou Yu, Zhiwei Zhu, Jian Liu, Xiaoyun Liu, and Yuanhua Shao, "Mechanistic Study of Oxygen Reduction at Liquid/Liquid Interfaces by Hybrid Ultramicroelectrodes and Mass Spectrometry", Journal of the American Chemical Society 141, 13212−13221 (2019) [https://pubs.acs.org/doi/10.1021/jacs.9b06299] [pdf version]

  15. Xin He, Jian Liu, "A new perspective for nonadiabatic dynamics with phase space mapping models", Journal of Chemical Physics, 151, 024105 (2019). (Invited contribution to Special Topic Issue on "Dynamics of Open Quantum Systems") [https://doi.org/10.1063/1.5108736 ][pdf version]

  16. Zhijun Zhang, Xinzijian Liu, Kangyu Yan, Mark Tuckerman, Jian Liu, "A unified efficient thermostat scheme for the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics", Journal of Physical Chemistry A, 123, 28, 6056-6079 (2019). (Invited contribution to "Young Scientist Virtual Special Issue") [https://doi.org/10.1021/acs.jpca.9b02771][pdf version] (Highlighted in JPC Virtual Issue on New Tools and Methods )

  17. Yun-an Yan, Jian Liu, Jiushu Shao, "A semiclassical initial-value representation for quantum propagator and Boltzmann propagator", Journal of Computational Chemistry, 40, 1161–1171 (2019) [https://doi.org/10.1002/jcc.25751] [pdf version]

  18. Zhijun Zhang, Kangyu Yan, Xinzijian Liu, Jian Liu, "A leap-frog algorithm-based efficient unified thermostat scheme via molecular dynamics", Chinese Science Bulletin，63(33), 3467-3483(2018) [Invited Contribution] [http://engine.scichina.com/doi/10.1360/N972018-00908 ] [pdf version]

  19. Haobin Wang, Xinzijian Liu, Jian Liu, "Accurate calculation of equilibrium reduced density matrix for the system-bath model: a multilayer multiconfiguration time-dependent Hartree approach and its comparison to a multi-electronic-state path integral molecular dynamics approach", Chinese Journal of Chemical Physics, 31, 446 (2018) (Invited Contribution) [https://doi.org/10.1063/1674-0068/31/cjcp1805122 ] [pdf version]

  20. Xinzijian Liu, Jian Liu, "Critical role of quantum dynamical effects in the Raman spectroscopy of liquid water", Molecular Physics, 116(7-8), 755-779 (2018) [https://doi.org/10.1080/00268976.2018.1434907 Invited contribution. Front cover of this issue.] Free eprints [arXiv preprint] [pdf version]

  21. Dezhang Li, Zifei Chen, Zhijun Zhang, Jian Liu, "Understanding molecular dynamics with stochastic processes via real or virtual dynamics", Chinese Journal of Chemical Physics, 30, 735 (2017) [http://dx.doi.org/10.1063/1674-0068/30/cjcp1711223 Invited article for the CJCP special topic issue on "Chemical Dynamics"] pdf version from the CJCP website [arXiv preprint] [pdf version]

  22. Xinzijian Liu, Jian Liu, "Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems", Journal of Chemical Physics, 148, 102319 (2018) [https://doi.org/10.1063/1.5005059 Invited article for the JCP special topic issue on "Nuclear Quantum Effects"] [arXiv preprint] [pdf version]

  23. Dezhang Li, Xu Han, Yichen Chai, Cong Wang, Zhijun Zhang, Zifei Chen, Jian Liu, Jiushu Shao, "Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics", Journal of Chemical Physics, 147, 184104 (2017) [https://doi.org/10.1063/1.4996204] Supplementary material [arXiv preprint] [pdf version]

  24. Zhijun Zhang, Xinzijian Liu, Zifei Chen, Haifeng Zheng, Kangyu Yan, Jian Liu, "A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics", Journal of Chemical Physics, 147, 034109 (2017) [http://dx.doi.org/10.1063/1.4991621] Supplementary material [arXiv preprint] [pdf version]

  25. Jian Liu,"Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactions", Journal of Chemical Physics, 146, 024110 (2017) [http://dx.doi.org/10.1063/1.4973708] [arXiv preprint] [pdf version]

  26. Jian Liu,"A unified theoretical framework for mapping models for the multi-state Hamiltonian", Journal of Chemical Physics, 145, 204105 (2016) [http://dx.doi.org/10.1063/1.4967815] [arXiv preprint][pdf version]

  27. Jian Liu, Dezhang Li, Xinzijian Liu, "A simple and accurate algorithm for path integral molecular dynamics", Journal of Chemical Physics, 145, 024103 (2016) [http://dx.doi.org/10.1063/1.4954990] Supplementary material [arXiv preprint (Paper + Supplemental materical)][pdf version]

  28. Jian Liu, Zhijun Zhang, "Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane", Journal of Chemical Physics, 144, 034307 (2016) [http://dx.doi.org/10.1063/1.4939953] [pdf version]

  29. Jian Liu, Dezhang Li, Xinzijian Liu, "Further study of path integral Liouville dynamics", Scientia Sinica Chimica, 46, 27 (2016) [http://dx.doi.org/10.1360/N032015-00143 Invited article for the special issue for the Festschrift for Professor Lemin Li's 80th birthday][pdf version]

  30. Lihong Liu, Jian Liu, Todd Martinez, "Dynamical Correlation Effects on Photoisomerization: Ab Initio Multiple Spawning Dynamics with MS-CASPT2 for a Model trans-Protonated Schiff Base", Journal of Physical Chemistry B, 120, 1940 (2016) [http://dx.doi.org/10.1021/acs.jpcb.5b09838] Supporting Information[pdf version]

  31. Jian Liu, "Recent advances in the linearized semiclassical initial value representation/classical Wigner model for the thermal correlation function", International Journal of Quantum Chemistry, 115(11), 657-670 (2015) [http://onlinelibrary.wiley.com/doi/10.1002/qua.24872/full Front cover of this issue. Invited contribution.][pdf version]

  32. Jian Liu, "Path integral Liouville dynamics for thermal equilibrium systems", Journal of Chemical Physics, 140, 224107 (2014) [https://doi.org/10.1063/1.4881518 ][pdf version]

  33. Jian Liu, “Two more approaches for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics”, Journal of Chemical Physics, 134, 194110 (2011) [http://dx.doi.org/10.1063/1.3589406 ] [pdf version]

  34. Jian Liu, William H. Miller, “An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics: II. Thermal correlation functions”, Journal of Chemical Physics, 134, 104102 (2011) [http://dx.doi.org/10.1063/1.3555274 ] [pdf version]

  35. Jian Liu, William H. Miller, “An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics: I. Theories”, Journal of Chemical Physics, 134, 104101 (2011) [http://dx.doi.org/10.1063/1.3555273 ] [pdf version]

  36. Jian Liu, William H. Miller, Georgios S. Fanourgakis, Sotiris S. Xantheas, Imoto Sho, and Shinji Saito “Insights in quantum dynamical effects in the Infrared spectroscopy of liquid water from a semiclassical study with an ab initio-based flexible and polarizable force field”, Journal of Chemical Physics, 135, 244503 (2011) [http://dx.doi.org/10.1063/1.3670960 ] [pdf version]

  37. Jian Liu, Berni J. Alder, William H. Miller, “A semiclassical study of the thermal conductivity of low temperature liquids” Journal of Chemical Physics, 135, 114105 (2011) [http://dx.doi.org/10.1063/1.3639107 ][pdf version]

  38. Jian Liu, William H. Miller, Francesco Paesani, Wei Zhang, and David Case, “Quantum dynamical effects in liquid water: A semiclassical study on the diffusion and the infrared absorption spectrum” Journal of Chemical Physics, 131, 164509 (2009) [http://dx.doi.org/10.1063/1.3254372 ] [pdf version]

  39. Jian Liu, William H. Miller, “A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids”, Journal of Chemical Physics, 131, 074113 (2009) [http://dx.doi.org/10.1063/1.3202438 ] [pdf version]

  40. Jian Liu, William H. Miller, “Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation”, Journal of Chemical Physics, 129, 124111 (2008) [http://dx.doi.org/10.1063/1.2981065 ] [pdf version]

  41. Jian Liu, William H. Miller, “Test of the consistency of various linearized semiclassical initial value time correlation functions in application to inelastic scattering from liquid para-hydrogen”, Journal of Chemical Physics, 128, 144511 (2008) [http://dx.doi.org/10.1063/1.2889945 ] [pdf version]

  42. Jian Liu, William H. Miller, “Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: Applications to condensed phase systems”, Journal of Chemical Physics, 127, 114506 (2007) [http://dx.doi.org/10.1063/1.2774990 ] [pdf version]

  43. Jian Liu, William H. Miller, “Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation”, Journal of Chemical Physics, 126, 234110 (2007) [http://dx.doi.org/10.1063/1.2743023 ] [pdf version]

  44. Jian Liu, William H. Miller, “Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions”, Journal of Chemical Physics, 125, 224104 (2006) [http://dx.doi.org/10.1063/1.2395941 ] [pdf version]

  45. Jian Liu, Akira Nakayama, Nancy Makri, “Long-time behavior of quantized distributions in forward-backward semiclassical dynamics”, Molecular Physics, 104, 1267 (2006) [http://dx.doi.org/10.1080/00268970500525754 ] [pdf version]

  46. Jian Liu, Nancy Makri, “Symmetries and detailed balance in forward-backward semiclassical dynamics”, Chemical Physics, 322, 23 (2006) [http://dx.doi.org/10.1016/j.chemphys.2005.08.010 ] [pdf version]

  47. Jian Liu, Nancy Makri, “Bohm’s formulation in imaginary time: Estimation of energy eigenvalues”, Molecular Physics, 103, 1083 (2005) [http://dx.doi.org/10.1080/00268970512331339387 ] [pdf version]

  48. Jian Liu, Nancy Makri, “Monte Carlo Bohmian dynamics from trajectory stability properties”, Journal of Physical Chemistry A, 108, 5408 (2004) [http://dx.doi.org/10.1021/jp040149n ] [pdf version]