278
X. Liu et al.
5 Conclusions
In many remarks, the “middle” thermostat scheme [7, 9, 11, 12, 15, 16] (either
“VV-Middle” or “LF-Middle”) provides a promising approach to design efficient
MD/PIMD algorithms for sampling the configuration space of the canonical ensemble with or without constraints. Combination of the “middle” scheme with resonancefree MTS techniques leads to more efficient and robust algorithms for sampling the
configuration space for multi-time-scale systems [12].
It is straightforward to employ the “middle” thermostat scheme with various
advanced enhanced sampling techniques [55, 58–68] to accelerate configurational
sampling for molecular systems where rare events become important [12]. Since
the “middle” thermostat scheme is useful for any types of potential energy surfaces
or force fields (for realistic molecular systems), it will be helpful to implement
the “middle” scheme for ab initio MD or ab initio PIMD[21, 69] to reduce the
computation cost. It will be interesting to develop more efficient MD and PIMD
algorithms in the unified theoretical framework for these purposes.
Acknowledgements This work was supported by the Ministry of Science and Technology of China
(MOST) Grants No. 2016YFC0202803 and No. 2017YFA0204901, by the National Natural Science
Foundation of China (NSFC) Grants No. 21373018 and No. 21573007, by the Recruitment Program
of Global Experts, by Specialized Research Fund for the Doctoral Program of Higher Education
No. 20130001110009, and by Special Program for Applied Research on Super Computation of the
NSFC-Guangdong Joint Fund (the second phase) under Grant No. U1501501.
References
1. Allen MP, Tildesley DJ (1989) Computer simulation of liquids. Clarendon Press
2. Frenkel D, Smit B (2002) Understanding molecular simulation, 2nd edn. Academic Press, San
Diego
3. Chandler D, Wolynes PG (1981) Exploiting the isomorphism between quantum theory and the
classical statistical mechanics of polyatomic fluids. J. Chem. Phys. 74(7):4078–4095
4. Parrinello M, Rahman A (1984) Study of an f center in molten kcl. J. Chem. Phys. 80(2):860–
867
5. Berne BJ, Thirumalai D (1986) On the simulation of quantum systems: path integral methods.
Annu Rev Phys Chem 37:401–424
6. Tuckerman ME (2010) Statistical mechanics: theory and molecular simulation. Oxford
University Press, New York
7. Liu J, Li D, Liu X (2016) A simple and accurate algorithm for path integral molecular dynamics
with the langevin thermostat. J Chem Phys 145(2):024103
8. Markland TE, Ceriotti M (2018) Nuclear quantum effects enter the mainstream. Nat Rev Chem
2(3):14
9. Zhang Z, Liu X, Chen Z, Zheng H, Yan K, Liu J (2017) A unified thermostat scheme for
efficient configurational sampling for classical/quantum canonical ensembles via molecular
dynamics. J Chem Phys 147(3):034109
10. Liu X, Liu J (2018) Critical role of quantum dynamical effects in the raman spectroscopy of
liquid water. Mol Phys 116(7–8):755–779
11. Zhang Z, Yan K, Liu X, Liu J (2018) A leap-frog algorithm-based efficient unified thermostat
scheme for molecular dynamics. Chin Sci Bull 63(0023–074X):3467
X. Liu et al.
5 Conclusions
In many remarks, the “middle” thermostat scheme [7, 9, 11, 12, 15, 16] (either
“VV-Middle” or “LF-Middle”) provides a promising approach to design efficient
MD/PIMD algorithms for sampling the configuration space of the canonical ensemble with or without constraints. Combination of the “middle” scheme with resonancefree MTS techniques leads to more efficient and robust algorithms for sampling the
configuration space for multi-time-scale systems [12].
It is straightforward to employ the “middle” thermostat scheme with various
advanced enhanced sampling techniques [55, 58–68] to accelerate configurational
sampling for molecular systems where rare events become important [12]. Since
the “middle” thermostat scheme is useful for any types of potential energy surfaces
or force fields (for realistic molecular systems), it will be helpful to implement
the “middle” scheme for ab initio MD or ab initio PIMD[21, 69] to reduce the
computation cost. It will be interesting to develop more efficient MD and PIMD
algorithms in the unified theoretical framework for these purposes.
Acknowledgements This work was supported by the Ministry of Science and Technology of China
(MOST) Grants No. 2016YFC0202803 and No. 2017YFA0204901, by the National Natural Science
Foundation of China (NSFC) Grants No. 21373018 and No. 21573007, by the Recruitment Program
of Global Experts, by Specialized Research Fund for the Doctoral Program of Higher Education
No. 20130001110009, and by Special Program for Applied Research on Super Computation of the
NSFC-Guangdong Joint Fund (the second phase) under Grant No. U1501501.
References
1. Allen MP, Tildesley DJ (1989) Computer simulation of liquids. Clarendon Press
2. Frenkel D, Smit B (2002) Understanding molecular simulation, 2nd edn. Academic Press, San
Diego
3. Chandler D, Wolynes PG (1981) Exploiting the isomorphism between quantum theory and the
classical statistical mechanics of polyatomic fluids. J. Chem. Phys. 74(7):4078–4095
4. Parrinello M, Rahman A (1984) Study of an f center in molten kcl. J. Chem. Phys. 80(2):860–
867
5. Berne BJ, Thirumalai D (1986) On the simulation of quantum systems: path integral methods.
Annu Rev Phys Chem 37:401–424
6. Tuckerman ME (2010) Statistical mechanics: theory and molecular simulation. Oxford
University Press, New York
7. Liu J, Li D, Liu X (2016) A simple and accurate algorithm for path integral molecular dynamics
with the langevin thermostat. J Chem Phys 145(2):024103
8. Markland TE, Ceriotti M (2018) Nuclear quantum effects enter the mainstream. Nat Rev Chem
2(3):14
9. Zhang Z, Liu X, Chen Z, Zheng H, Yan K, Liu J (2017) A unified thermostat scheme for
efficient configurational sampling for classical/quantum canonical ensembles via molecular
dynamics. J Chem Phys 147(3):034109
10. Liu X, Liu J (2018) Critical role of quantum dynamical effects in the raman spectroscopy of
liquid water. Mol Phys 116(7–8):755–779
11. Zhang Z, Yan K, Liu X, Liu J (2018) A leap-frog algorithm-based efficient unified thermostat
scheme for molecular dynamics. Chin Sci Bull 63(0023–074X):3467