Multiple-time step Ab initio molecular dynamics based on two-electron integral screening

Journal of Chemical Theory and Computation

Volumn 11, Issue 3, 2015, Pages 884-898

  Fatehi, Shervin ^a   Steele, Ryan P ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84924359451     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct500904x     Document Type: Article

References (78)

1. Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids, 1 st ed.; Clarendon Press: Oxford, 1989; pp 6-23, 71-109.
2. Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications, 2 nd ed.; Academic Press: San Diego, CA, 2002; pp 63-105.
3. Marx, D.; Hutter, J. Modern Methods and Algorithms of Quantum Chemistry; NIC Series; John von Neumann Institute of Computing: Jülich, Germany, 2000; Vol. 1; pp 301-449.
4. Tuckerman, M. E. Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms; NIC Series; John von Neumann Institute of Computing: Jülich, Germany, 2002; Vol. 10, pp 299-324.
5. Sagui, C.; Darden, T. A. Molecular dynamics simulations of biomolecules: Long-range electrostatic effects Annu. Rev. Bioph. Biom. 1999, 28, 155-179
6. Zhou, R.; Berne, B. J. A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems J. Chem. Phys. 1995, 103, 9444-9459
7. Procacci, P.; Marchi, M. Taming the Ewald sum in molecular dynamics simulations of solvated proteins via a multiple timestep algorithm J. Chem. Phys. 1996, 104, 3003-3012
8. Zhou, R.; Harder, E.; Xu, H.; Berne, B. J. Efficient multiple timestep method for use with Ewald and particle mesh Ewald for large biomolecular systems J. Chem. Phys. 2001, 115, 2348-2358
9. Tuckerman, M.; Berne, B. J.; Martyna, G. J. Reversible multiple time scale molecular dynamics J. Chem. Phys. 1992, 97, 1990-2000
10. Streett, W. B.; Tildesley, D. J.; Saville, G. Multiple time-step methods in molecular dynamics Mol. Phys. 1978, 35, 639-648
11. Swindoll, R. D.; Haile, J. M. A multiple time-step method for molecular dynamics simulations of fluids of chain molecules J. Comput. Phys. 1984, 53, 289-298
12. Grubmüller, H.; Heller, H.; Windemuth, A.; Schulten, K. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions Mol. Simul. 1991, 6, 121-142
13. Tuckerman, M. E.; Martyna, G. J.; Berne, B. J. Molecular dynamics algorithm for condensed systems with multiple time scales J. Chem. Phys. 1990, 93, 1287-1291
14. Tuckerman, M. E.; Berne, B. J.; Rossi, A. Molecular dynamics algorithm for multiple time scales: Systems with disparate masses J. Chem. Phys. 1991, 94, 1465-1469
15. Tuckerman, M. E.; Berne, B. J.; Martyna, G. J. Molecular dynamics algorithm for multiple time scales: Systems with long range forces J. Chem. Phys. 1991, 94, 6811-6815
16. Anglada, E.; Junquera, J.; Soler, J. M. Efficient mixed-force first-principles molecular dynamics Phys. Rev. E 2003, 68, 055701(R)
17. Guidon, M.; Schiffmann, F.; Hutter, J.; VandeVondele, J. Ab initio molecular dynamics using hybrid density functionals J. Chem. Phys. 2008, 128, 214104
18. Gibson, D. A.; Carter, E. A. Time-reversible multiple time scale ab initio molecular dynamics J. Phys. Chem. 1993, 97, 13429-13434
19. Tuckerman, M. E.; Parrinello, M. Integrating the Car-Parrinello equations. II. Multiple time scale techniques J. Chem. Phys. 1994, 101, 1316-1329
20. Steele, R. P. Communication: Multiple-timestep ab initio molecular dynamics with electron correlation J. Chem. Phys. 2013, 139, 011102
21. Møller, C.; Plesset, M. S. Notes on an approximation treatment for many-electron systems Phys. Rev. 1934, 46, 618-622
22. Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry; Dover Publishing: Mineola, NY, 1996; pp 140-142.
23. Head-Gordon, M.; Pople, J. A. MP2 energy evaluation by direct methods Chem. Phys. Lett. 1988, 153, 503-506
24. Ochsenfeld, C.; Kussmann, J.; Lambrecht, D. S. Linear-scaling methods in quantum chemistry Rev. Comput. Chem. 2007, 23, 1-82
25. Luehr, N.; Markland, T. E.; Marti′nez, T. J. Multiple timestep integrators in ab initio molecular dynamics J. Chem. Phys. 2014, 140, 084116
26. Adamson, R. D.; Dombroski, J. P.; Gill, P. M. W. Chemistry without Coulomb tails Chem. Phys. Lett. 1996, 254, 329-336
27. Adamson, R. D.; Dombroski, J. P.; Gill, P. M. W. Efficient calculation of short-range Coulomb energies J. Comput. Chem. 1999, 20, 921-927
28. Almlöf, J.; Faegri, K., Jr.; Korsell, K. Principles for a direct scf approach to lcao-mo ab-initio calculations J. Comput. Chem. 1982, 3, 385-399
29. Häser, M.; Ahlrichs, R. Improvements on the direct SCF method J. Comput. Chem. 1989, 10, 104-111
30. Panas, I.; Almlöf, J.; Feyereisen, M. W. Ab initio methods for large systems Int. J. Quantum Chem. 1991, 40, 797-807
31. Adamson, R. D. Shell-pair economization. B.Sc. honors thesis, Massey University, Palmerston North, New Zealand, 1995.
32. Gill, P. M. W.; Johnson, B. G.; Pople, J. A. A simple yet powerful upper bound for Coulomb integrals Chem. Phys. Lett. 1994, 217, 65-68
33. Horn, H.; Weiß, H.; Häser, M.; Ehrig, M.; Ahlrichs, R. Prescreening of two-electron integral derivatives in SCF gradient and Hessian calculations J. Comput. Chem. 1991, 12, 1058-1064
34. Shao, Y.; Gan, Z.; Epifanovsky, E.; Gilbert, A. T. B.; Wormit, M.; Kussmann, J.; Lange, A. W.; Behn, A.; Deng, J.; Feng, X.; Ghosh, D.; Goldey, M.; Horn, P. R.; Jacobson, L. D.; Kaliman, I.; Khaliullin, R. Z.; Kus′, T.; Landau, A.; Liu, J.; Proynov, E. I.; Rhee, Y. M.; Richard, R. M.; Rohrdanz, M. A.; Steele, R. P.; Sundstrom, E. J.; Woodcock, H. L., III; Zimmerman, P. M.; Zuev, D.; Albrecht, B.; Alguire, E.; Austin, B.; Beran, G. J. O.; Bernard, Y. A.; Berquist, E.; Brandhorst, K.; Bravaya, K. B.; Brown, S. T.; Casanova, D.; Chang, C.; Chen, Y.; Chien, S. H.; Closser, K. D.; Crittenden, D. L.; Diedenhofen, M.; DiStasio, R. A., Jr.; Do, H.; Dutoi, A. D.; Edgar, R. G.; Fatehi, S.; Fusti- Molnar, L.; Ghysels, A.; Golubeva-Zadorozhnaya, A.; Gomes, J.; Hanson-Heine, M. W. D.; Harbach, P. H. P.; Hauser, A. W.; Hohenstein, E. G.; Holden, Z. C.; Jagau, T.; Ji, H.; Kaduk, B.; Khistyaev, K.; Kim, J.; Kim, J.; King, R. A.; Klunzinger, P.; Kosenkov, D.; Kowalczyk, T.; Krauter, C. M.; Lao, K. U.; Laurent, A.; Lawler, K. V.; Levchenko, S. V.; Lin, C. Y.; Liu, F.; Livshits, E.; Lochan, R. C.; Luenser, A.; Manohar, P.; Manzer, S. F.; Mao, S.; Mardirossian, N.; Marenich, A. V.; Maurer, S. A.; Mayhall, N. J.; Neuscamman, E.; Oana, C. M.; Olivares-Amaya, R.; O'Neill, D. P.; Parkhill, J. A.; Perrine, T. M.; Peverati, R.; Prociuk, A.; Rehn, D. R.; Rosta, E.; Russ, N. J.; Sharada, S. M.; Sharma, S.; Small, D. W.; Sodt, A.; Stein, T.; Stück, D.; Su, Y.; Thom, A. J. W.; Tsuchimochi, T.; Vanovschi, V.; Vogt, L.; Vydrov, O.; Wang, T.; Watson, M. A.; Wenzel, J.; White, A.; Williams, C. F.; Yang, J.; Yeganeh, S.; Yost, S. R.; You, Z.; Zhang, I. Y.; Zhang, X.; Zhao, Y.; Brooks, B. R.; Chan, G. K. L.; Chipman, D. M.; Cramer, C. J.; Goddard, W. A., III; Gordon, M. S.; Hehre, W. J.; Klamt, A.; Schaefer, H. F., III; Schmidt, M. W.; Sherrill, C. D.; Truhlar, D. G.; Warshel, A.; Xu, X.; Aspuru-Guzik, A.; Baer, R.; Bell, A. T.; Besley, N. A.; Chai, J.; Dreuw, A.; Dunietz, B. D.; Furlani, T. R.; Gwaltney, S. R.; Hsu, C.; Jung, Y.; Kong, J.; Lambrecht, D. S.; Liang, W.; Ochsenfeld, C.; Rassolov, V. A.; Slipchenko, L. V.; Subotnik, J. E.; Van Voorhis, T.; Herbert, J. M.; Krylov, A. I.; Gill, P. M. W.; Head-Gordon, M. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package Mol. Phys. 2015, 113, 184-215
35. Gill, P. M. W.; Johnson, B. G.; Pople, J. A. Two-electron repulsion integrals over Gaussian s functions Int. J. Quantum Chem. 1991, 40, 745-752
36. Pulay, P. Convergence acceleration of iterative sequences. The case of SCF iteration Chem. Phys. Lett. 1980, 73, 393-398
37. Pulay, P. Improved SCF convergence acceleration J. Comput. Chem. 1982, 3, 556-560
38. Lau, K. F.; Alper, H. E.; Thacher, T. S.; Stouch, T. R. Effects of switching functions on the behavior of liquid water in molecular dynamics simulations J. Phys. Chem. 1994, 98, 8785-8792
39. Morrone, J. A.; Zhou, R.; Berne, B. J. Molecular dynamics with multiple time scales: Avoid pitfalls J. Chem. Theory Comput. 2010, 6, 1798-1804
40. Gerratt, J.; Mills, I. M. Force constants and dipole-moment derivatives of molecules from perturbed Hartree-Fock calculations I. J. Chem. Phys. 1968, 49, 1719-1729
41. Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Derivative studies in Hartree-Fock and Møller-Plesset theories Int. J. Quantum Chem. 1979, 16 S13, 225-241
42. Fournier, R. Second and third derivatives of the linear combination of Gaussian type orbitals-local spin density energy J. Chem. Phys. 1990, 92, 5422-5429
43. Komornicki, A.; Fitzgerald, G. Molecular gradients and Hessians implemented in density functional theory J. Chem. Phys. 1993, 98, 1398-1421
44. Maurice, D. Single electron theories of excited states. Ph.D. thesis, University of California, Berkeley, 1998; pp 66-100.
45. Wales, D. J.; Doye, J. P. K.; Dullweber, A.; Hodges, M. P.; Naumkin, F. Y.; Calvo, F.; Hernández-Rojas, J.; Middleton, T. F. The Cambridge Cluster Database. http://www-wales.ch.cam.ac.uk/CCD.html (accessed Jan. 6, 2015).
46. n, n = 8-20: An ab initio investigation J. Phys. Chem. A 2001, 105, 10525-10537
47. Scuro, S. R.; Chin, S. A. Forward symplectic integrators and the long-time phase error in periodic motions Phys. Rev. E 2005, 71, 056703
48. Schlegel, H. B. Ab initio molecular dynamics with Born-Oppenheimer and extended Lagrangian methods using atom centered basis functions Bull. Korean Chem. Soc. 2003, 24, 837-842
49. Marquardt, D. W. An algorithm for least-squares estimation of nonlinear parameters J. Soc. Ind. Appl. Math. 1963, 11, 431-441
50. Williams, T.; Kelley, C. GNUPLOT. http://www.gnuplot.info (accessed Jan. 6, 2015).
51. Stuart, S. J.; Zhou, R.; Berne, B. J. Molecular dynamics with multiple time scales: The selection of efficient reference system propagators J. Chem. Phys. 1996, 105, 1426-1436
52. Littell, T. R.; Skeel, R. D.; Zhang, M. Error analysis of symplectic multiple timestepping SIAM J. Numer. Anal. 1997, 34, 1792-1807
53. Bishop, T. C.; Skeel, R. D.; Schulten, K. Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics J. Comput. Chem. 1997, 18, 1785-1791
54. Barash, D.; Yang, L.; Qian, X.; Schlick, T. Inherent speedup limitations in multiple timestep/particle mesh Ewald algorithms J. Comput. Chem. 2003, 24, 77-88
55. Ma, Q.; Izaguirre, J. A.; Skeel, R. D. Verlet-I/R-RESPA/Impulse is limited by nonlinear instabilities SIAM J. Sci. Comput. 2003, 24, 1951-1973
56. Koch, W.; Holthausen, M. C. A Chemist's Guide to Density Functional Theory; WILEYVCH Verlag: Weinheim, Germany, 2001; pp 105-109.
57. Becke, A. D. A multicenter numerical integration scheme for polyatomic molecules J. Chem. Phys. 1988, 88, 2547-2553
58. Cremer, D.; Gauss, J. An unconventional SCF method for calculations on large molecules J. Comput. Chem. 1986, 7, 274-282
59. Schwegler, E.; Challacombe, M.; Head-Gordon, M. Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build J. Chem. Phys. 1997, 106, 9708-9717
60. 2 predissociation spectroscopy J. Am. Soc. Mass Spectrom. 2011, 22, 1941-1952
61. 2,3 ions: Quantifying tag effects in cryogenic ion vibrational predissociation (CIVP) spectroscopy J. Chem. Phys. 2014, 140, 221101
62. Gilbert, A. T. B. IQmol molecular viewer. http://www.iqmol.org (accessed Jan. 6, 2015).
63. Halgren, T. A. MMFF VI. MMFF94s option for energy minimization studies J. Comput. Chem. 1999, 20, 720-729
64. Herbert, J. M.; Head-Gordon, M. Accelerated, energy-conserving Born-Oppenheimer molecular dynamics via Fock matrix extrapolation Phys. Chem. Chem. Phys. 2005, 7, 3269-3275
65. Niklasson, A. M. N.; Tymczak, C. J.; Challacombe, M. Time-reversible ab initio molecular dynamics J. Chem. Phys. 2007, 126, 144103
66. Niklasson, A. M. N.; Tymczak, C. J.; Challacombe, M. Time-reversible Born-Oppenheimer molecular dynamics Phys. Rev. Lett. 2006, 97, 123001
67. Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé-Hoover chains: The canonical ensemble via continuous dynamics J. Chem. Phys. 1992, 97, 2635-2643
68. Tuckerman, M. E.; Berne, B. J.; Martyna, G. J.; Klein, M. L. Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals J. Chem. Phys. 1993, 99, 2796-2808
69. Izaguirre, J. A.; Reich, S.; Skeel, R. D. Longer time steps for molecular dynamics J. Chem. Phys. 1999, 110, 9853-9864
70. Ma, Q.; Izaguirre, J. A. Targeted mollified impulse: A multiscale stochastic integrator for long molecular dynamics simulations Multiscale Model. Simul. 2003, 2, 1-21
71. Chin, S. A. Dynamical multiple-time stepping methods for overcoming resonance instabilities J. Chem. Phys. 2004, 120, 8-13
72. Minary, P.; Tuckerman, M. E.; Martyna, G. J. Long time molecular dynamics for enhanced conformational sampling in biomolecular systems Phys. Rev. Lett. 2004, 93, 150201
73. Janežič, D.; Praprotnik, M.; Merzel, F. Molecular dynamics integration and molecular vibrational theory. I. New symplectic integrators J. Chem. Phys. 2005, 122, 174101
74. Jia, Z.; Leimkuhler, B. Geometric integrators for multiple time-scale simulation J. Phys. A: Math. Gen. 2006, 39, 5379-5403
75. Kräutler, V.; Hünenberger, P. H. A multiple timestep algorithm compatible with a large number of distance classes and an arbitrary distance dependence of the timestep size for the fast evaluation of nonbonded interactions in molecular simulations J. Comput. Chem. 2006, 27, 1163-1176
76. Omelyan, I. P. Advanced multiple time scale molecular dynamics J. Chem. Phys. 2009, 131, 104101
77. Morrone, J. A.; Markland, T. E.; Ceriotti, M.; Berne, B. J. Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances J. Chem. Phys. 2011, 134, 014103
78. Leimkuhler, B.; Margul, D. T.; Tuckerman, M. E. Stochastic, resonance-free multiple timestep algorithm for molecular dynamics with very large time steps Mol. Phys. 2013, 111, 3579-3594