Efficient “Middle” Thermostat Scheme …
279
12. Zhang Z, Liu X, Yan K, Tuckerman ME, Liu J (2019) Unified efficient thermostat scheme for
the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics. J
Phys Chem A 123(28):6056–6079
13. Liu J, Li D, Liu X (2016) Further study of path integral liouville dynamics
14. Liu J, Zhang Z (2016) Path integral liouville dynamics: Applications to infrared spectra of oh,
water, ammonia, and methane. J Chem Phys 144(3):034307
15. Li D, Han X, Chai Y, Wang C, Zhang Z, Chen Z, Liu J, Shao J (2017) Stationary state distribution
and efficiency analysis of the langevin equation via real or virtual dynamics. J Chem Phys
147(18):184104
16. Li D-z, Chen Z-f, Zhang Z-j, Liu J (2017) Understanding molecular dynamics with stochastic
processes via real or virtual dynamics. Chin J Chem Phys 30(6):735–760
17. Case DA, Ben-Shalom IY, Brozell SR, Cerutti DS, Cheatham TE III, Cruzeiro VWD, Darden
TA, Duke RE, Ghoreishi D, Gilson MK, Gohlke H, Goetz AW, Greene D, Harris R, Homeyer
N, Izadi S, Kovalenko A, Kurtzman T, Lee TS, LeGrand S, Li P, Lin C, Liu J, Luchko T, Luo R,
Mermelstein DJ, Merz KM, Miao Y, Monard G, Nguyen C, Nguyen H, Omelyan I, Onufriev
A, Pan F, Qi R, Roe DR, Roitberg A, Sagui C, Schott-Verdugo S, Shen J, Simmerling CL,
Smith J, Salomon-Ferrer R, Swails J, Walker RC, Wang J, Wei H, Wolf RM, Wu X, Xiao L,
York DM (2018) Kollman PA Amber 2018. University of California, San Francisco
18. Andersen HC (1980) Molecular dynamics simulations at constant pressure and/or temperature.
Journal of Chemical Physics 72(4):2384–2393
19. Nosé S (1984) A molecular dynamics method for simulations in the canonical ensemble. Mol
Phys 52(2):255–268
20. Hoover WG (1985) Canonical dynamics: equilibrium phase-space distributions. Phys Rev A
31(3):1695–1697
21. Martyna GJ, Klein ML, Tuckerman M (1992) Nosé–hoover chains: The canonical ensemble
via continuous dynamics. J Chem Phys 97(4):2635–2643
22. Martyna GJ, Tuckerman ME, Tobias DJ, Klein ML (1996) Explicit reversible integrators for
extended systems dynamics. Mol Phys 87(5):1117–1157
23. Tuckerman M, Berne BJ, Martyna GJ (1992) Reversible multiple time scale molecular
dynamics. J Chem Phys 97(3):1990–2001
24. Andrea TA, Swope WC, Andersen HC (1983) The role of long ranged forces in determining
the structure and properties of liquid water. J Chem Phys 79(9):4576–4584
25. Brünger A, Brooks Iii CL, Karplus M (1984) Stochastic boundary conditions for molecular
dynamics simulations of st2 water. Chem Phys Lett 105(5):495–500
26. Goga N, Rzepiela AJ, de Vries AH, Marrink SJ, Berendsen HJC (2012) Efficient algorithms
for langevin and dpd dynamics. J Chem Theory Comput 8(10):3637–3649
27. Bussi G, Parrinello M (2007) Accurate sampling using langevin dynamics. Phys Rev E
75(5):056707
28. Grønbech-Jensen N, Farago O (2013) A simple and effective verlet-type algorithm for
simulating langevin dynamics. Mol Phys 111(8):983–991
29. Leimkuhler B, Matthews C (2012) Rational construction of stochastic numerical methods for
molecular sampling. Appl Math Res Express 2013(1):34–56
30. Leimkuhler B, Matthews C (2013) Robust and efficient configurational molecular sampling
via langevin dynamics. J Chem Phys 138(17):174102
31. Leimkuhler B, Matthews C (2016) Efficient molecular dynamics using geodesic integration
and solvent–solute splitting. Proc R Soc A: Math, Phys Eng Sci 472(2189)
32. Leimkuhler B, Matthews C (2015) Molecular dynamics with deterministic and stochastic
numerical methods. Springer
33. Hall R, Berne BJ (1984) Nonergodicity in path integral molecular dynamics. J. Chem. Phys.
81(8):3641–3643
34. Gillan MJ (1987) Quantum simulation of hydrogen in metals. Phys Rev Lett 58(6):563–566
35. Singer K, Smith W (1988) Path integral simulations of condensed phase lennard-jones systems.
Mol Phys 64(6):1215–1231
279
12. Zhang Z, Liu X, Yan K, Tuckerman ME, Liu J (2019) Unified efficient thermostat scheme for
the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics. J
Phys Chem A 123(28):6056–6079
13. Liu J, Li D, Liu X (2016) Further study of path integral liouville dynamics
14. Liu J, Zhang Z (2016) Path integral liouville dynamics: Applications to infrared spectra of oh,
water, ammonia, and methane. J Chem Phys 144(3):034307
15. Li D, Han X, Chai Y, Wang C, Zhang Z, Chen Z, Liu J, Shao J (2017) Stationary state distribution
and efficiency analysis of the langevin equation via real or virtual dynamics. J Chem Phys
147(18):184104
16. Li D-z, Chen Z-f, Zhang Z-j, Liu J (2017) Understanding molecular dynamics with stochastic
processes via real or virtual dynamics. Chin J Chem Phys 30(6):735–760
17. Case DA, Ben-Shalom IY, Brozell SR, Cerutti DS, Cheatham TE III, Cruzeiro VWD, Darden
TA, Duke RE, Ghoreishi D, Gilson MK, Gohlke H, Goetz AW, Greene D, Harris R, Homeyer
N, Izadi S, Kovalenko A, Kurtzman T, Lee TS, LeGrand S, Li P, Lin C, Liu J, Luchko T, Luo R,
Mermelstein DJ, Merz KM, Miao Y, Monard G, Nguyen C, Nguyen H, Omelyan I, Onufriev
A, Pan F, Qi R, Roe DR, Roitberg A, Sagui C, Schott-Verdugo S, Shen J, Simmerling CL,
Smith J, Salomon-Ferrer R, Swails J, Walker RC, Wang J, Wei H, Wolf RM, Wu X, Xiao L,
York DM (2018) Kollman PA Amber 2018. University of California, San Francisco
18. Andersen HC (1980) Molecular dynamics simulations at constant pressure and/or temperature.
Journal of Chemical Physics 72(4):2384–2393
19. Nosé S (1984) A molecular dynamics method for simulations in the canonical ensemble. Mol
Phys 52(2):255–268
20. Hoover WG (1985) Canonical dynamics: equilibrium phase-space distributions. Phys Rev A
31(3):1695–1697
21. Martyna GJ, Klein ML, Tuckerman M (1992) Nosé–hoover chains: The canonical ensemble
via continuous dynamics. J Chem Phys 97(4):2635–2643
22. Martyna GJ, Tuckerman ME, Tobias DJ, Klein ML (1996) Explicit reversible integrators for
extended systems dynamics. Mol Phys 87(5):1117–1157
23. Tuckerman M, Berne BJ, Martyna GJ (1992) Reversible multiple time scale molecular
dynamics. J Chem Phys 97(3):1990–2001
24. Andrea TA, Swope WC, Andersen HC (1983) The role of long ranged forces in determining
the structure and properties of liquid water. J Chem Phys 79(9):4576–4584
25. Brünger A, Brooks Iii CL, Karplus M (1984) Stochastic boundary conditions for molecular
dynamics simulations of st2 water. Chem Phys Lett 105(5):495–500
26. Goga N, Rzepiela AJ, de Vries AH, Marrink SJ, Berendsen HJC (2012) Efficient algorithms
for langevin and dpd dynamics. J Chem Theory Comput 8(10):3637–3649
27. Bussi G, Parrinello M (2007) Accurate sampling using langevin dynamics. Phys Rev E
75(5):056707
28. Grønbech-Jensen N, Farago O (2013) A simple and effective verlet-type algorithm for
simulating langevin dynamics. Mol Phys 111(8):983–991
29. Leimkuhler B, Matthews C (2012) Rational construction of stochastic numerical methods for
molecular sampling. Appl Math Res Express 2013(1):34–56
30. Leimkuhler B, Matthews C (2013) Robust and efficient configurational molecular sampling
via langevin dynamics. J Chem Phys 138(17):174102
31. Leimkuhler B, Matthews C (2016) Efficient molecular dynamics using geodesic integration
and solvent–solute splitting. Proc R Soc A: Math, Phys Eng Sci 472(2189)
32. Leimkuhler B, Matthews C (2015) Molecular dynamics with deterministic and stochastic
numerical methods. Springer
33. Hall R, Berne BJ (1984) Nonergodicity in path integral molecular dynamics. J. Chem. Phys.
81(8):3641–3643
34. Gillan MJ (1987) Quantum simulation of hydrogen in metals. Phys Rev Lett 58(6):563–566
35. Singer K, Smith W (1988) Path integral simulations of condensed phase lennard-jones systems.
Mol Phys 64(6):1215–1231