Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions

Journal of Chemical Physics

Volumn 144, Issue 11, 2016, Pages

  Ziegler, Benjamin ^a   Rauhut, Guntram ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHEMICAL ANALYSIS; MOLECULAR PHYSICS; POTENTIAL ENERGY SURFACES; QUANTUM CHEMISTRY; SURFACE RECONSTRUCTION;

BENCHMARK CALCULATIONS; COMPUTATIONAL COSTS; DISTRIBUTED GAUSSIANS; KRONECKER PRODUCT; LINEAR LEAST SQUARES; MEMORY REQUIREMENTS; ORDERS OF MAGNITUDE; STANDARD PROCEDURES;

POTENTIAL ENERGY;

EID: 84962248340     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4943985     Document Type: Article

References (63)

1. J. M. Bowman, G. Czako, and B. Fu, Phys. Chem. Chem. Phys. 13, 8094 (2011). 10.1039/c0cp02722g
2. P. Barragan, R. Prosmiti, Y. Wang, and J. M. Bowman, J. Chem. Phys. 136, 224302 (2012). 10.1063/1.4726126
3. S. Carter, S. Culik, and J. Bowman, J. Chem. Phys. 107, 10458 (1997). 10.1063/1.474210
4. J. Kongsted and O. Christiansen, J. Chem. Phys. 125, 124108 (2006). 10.1063/1.2352734
5. J. Bowman, S. Carter, and X. Huang, Int. Rev. Phys. Chem. 22, 533 (2003). 10.1080/0144235031000124163
6. G. Rauhut, J. Chem. Phys. 121, 9313 (2004). 10.1063/1.1804174
7. K. Yagi, S. Hirata, and K. Hirao, Theor. Chem. Acc. 118, 681 (2007). 10.1007/s00214-007-0363-x
8. G. Rauhut and B. Hartke, J. Chem. Phys. 131, 014108 (2009). 10.1063/1.3160668
9. J. C. Light, I. P. Hamilton, and L. V. Lill, J. Chem. Phys. 82, 1400 (1984). 10.1063/1.448462
10. I. P. Hamilton and J. C. Light, J. Chem. Phys. 84, 306 (1986). 10.1063/1.450139
11. V. Szalay, J. Chem. Phys. 99, 1978 (1993). 10.1063/1.465258
12. V. Szalay, J. Chem. Phys. 105, 6940 (1996). 10.1063/1.471986
13. W. Yang and A. Peet, Chem. Phys. Lett. 153, 98 (1988). 10.1016/0009-2614(88)80139-8
14. G. Avila and T. Carrington, Jr., J. Chem. Phys. 139, 134114 (2013). 10.1063/1.4821348
15. C. Marston and G. Balint-Kurti, J. Chem. Phys. 91, 3571 (1989). 10.1063/1.456888
16. D. McLaughlin and D. Thompson, J. Chem. Phys. 59, 4393 (1973). 10.1063/1.1680637
17. M. Patricio, J. L. Santos, F. Patricio, and A. J. C. Varandas, J. Math. Chem. 51, 1729 (2013). 10.1007/s10910-013-0173-4
18. J. Bowman, J. Bittman, and L. Harding, J. Chem. Phys. 85, 911 (1986). 10.1063/1.451246
19. M. Collins, S. Petrie, A. Chalk, and L. Radom, J. Chem. Phys. 112, 6625 (2000). 10.1063/1.481235
20. M. Collins, Theor. Chem. Acc. 108, 313 (2002). 10.1007/s00214-002-0383-5
21. O. Tishchenko and D. G. Truhlar, J. Chem. Phys. 132, 084109 (2010). 10.1063/1.3310296
22. D. Pelaez and H.-D. Meyer, J. Chem. Phys. 138, 014108 (2013). 10.1063/1.4773021
23. F. Otto, J. Chem. Phys. 140, 014106 (2014). 10.1063/1.4856135
24. G. Avila and T. Carrington, Jr., J. Chem. Phys. 143, 044106 (2015). 10.1063/1.4926651
25. S. Manzhos and T. Carrington, Jr., J. Chem. Phys. 125, 194105 (2006). 10.1063/1.2387950
26. S. Manzhos and T. Carrington, Jr., J. Chem. Phys. 125, 084109 (2006). 10.1063/1.2336223
27. R. Dawes, A. Passalacqua, A. F. Wagner, T. D. Sewell, M. Minkoff, and D. L. Thompson, J. Chem. Phys. 130, 144107 (2009). 10.1063/1.3111261
28. T. Ho and H. Rabitz, J. Chem. Phys. 119, 6433 (2003). 10.1063/1.1603219
29. M. Sparta, M. B. Hansen, E. Matito, D. Toffoli, and O. Christiansen, J. Chem. Theory Comput. 6, 3162 (2010). 10.1021/ct100229f
30. S. Carter, J. Bowman, and B. Braams, Chem. Phys. Lett. 342, 636 (2001). 10.1016/S0009-2614(01)00656-X
31. S. Carter and N. C. Handy, Chem. Phys. Lett. 352, 1 (2002). 10.1016/S0009-2614(01)01381-1
32. P. Lancaster and K. Salkauskas, Curve and Surface Fitting: An Introduction (Academic Press, London, 1990).
33. A. Cohen, C. Rabut, and L. Schumaker, Curve and Surface Fitting: Saint-Malo 99, Innovations in Applied Mathematics (Vanderbilt University Press, 2000).
34. K. Jetter, M. Buhmann, W. Haussmann, R. Schaback, and J. Stoeckler, Topics in Multivariate Approximation and Interpolation, Studies in Computational Mathematics (Elsevier Science, 2005).
35. J. M. Bowman, B. J. Braams, S. Carter, C. Chen, G. Czako, B. Fu, X. Huang, E. Kamarchik, A. R. Sharma, B. C. Shepler et al., J. Phys. Chem. Lett. 1, 1866 (2010). 10.1021/jz100626h
36. Z. Xie and J. M. Bowman, J. Chem. Theory Comput. 6, 26 (2010). 10.1021/ct9004917
37. B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577 (2009). 10.1080/01442350903234923
38. X. Wang, S. Carter, and J. M. Bowman, J. Phys. Chem. A 119, 11632 (2015). 10.1021/acs.jpca.5b09816
39. R. C. Fortenberry, Q. Yu, J. S. Mancini, J. M. Bowman, T. J. Lee, T. D. Crawford, W. F. Klemperer, and J. S. Francisco, J. Chem. Phys. 143, 071102 (2015). 10.1063/1.4929345
40. H.-Y. Lin, Y.-H. Huang, X. Wang, J. M. Bowman, Y. Nishimura, H. A. Witek, and Y.-P. Lee, Nat. Commun. 6, 7012 (2015). 10.1038/ncomms8012
41. J. Li, S. Carter, J. M. Bowman, R. Dawes, D. Xie, and H. Guo, J. Phys. Chem. Lett. 5, 2364 (2014). 10.1021/jz501059m
42. Y. Wang, S. Carter, and J. M. Bowman, J. Phys. Chem. A 117, 9343 (2013). 10.1021/jp309911w
43. G. H. Golub and C. F. Van Loan, Matrix Computations, 4th ed. (Johns Hopkins University Press, Baltimore, MD, 2013).
44. G. W. Stewart, Introduction to Matrix Computations (Academic Press, New York, 1973).
45. A. Jäckle and H.-D. Meyer, J. Chem. Phys. 104, 7974 (1996). 10.1063/1.471513
46. M. Bramley and T. Carrington, Jr., J. Chem. Phys. 99, 8519 (1993). 10.1063/1.465576
47. A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics, Texts in Applied Mathematics (Springer, Berlin, Heidelberg, 2010).
48. C. Kelley, Iterative Methods for Linear and Nonlinear Equations, Frontiers in Applied Mathematics (Society for Industrial and Applied Mathematics, 1995).
49. G. Avila and T. Carrington, J. Chem. Phys. 143, 214108 (2015). 10.1063/1.4936294
50. W. Steeb and T. Shi, Matrix Calculus and Kronecker Product with Applications and C++ Programs (World Scientific, 1997).
51. D. Forsey and R. Bartels, ACM Trans. Graphics 14, 134 (1995). 10.1145/221659.221665
52. H. Pan and Y. Lei, Electron. J. Linear Algebra 23, 1001 (2012). 10.13001/1081-3810.1571
53. C. F. Van Loan, J. Comput. Appl. Math. 123, 85 (2000). 10.1016/S0377-0427(00)00393-9
54. A. Barrlund, SIAM J. Matrix Anal. A 19, 154 (1998). 10.1137/S0895479895295027
55. D. Fausett, C. Fulton, and H. Hashish, J. Comput. Appl. Math. 78, 63 (1997). 10.1016/S0377-0427(96)00109-4
56. D. Fausett and C. Fulton, SIAM J. Matrix Anal. A 15, 219 (1994). 10.1137/S0895479891222106
57. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, 2010).
58. K. Höllig and J. Hörner, Approximation and Modeling with B-Splines (SIAM, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2013).
59. K. Höllig, Finite Element Methods with B-Splines (Society for Industrial and Applied Mathematics, Philadelphia, 2003).
60. MATLAB, version 6.5.1, The MathWorks, Inc., Natick, Massachusetts, 2015b.
61. H. Antia, Numerical Methods for Scientists and Engineers, Numerical Methods for Scientists and Engineers (Springer Verlag, New York, 2002), Vol. 1.
62. M. Agoston, Computer Graphics and Geometric Modelling: Implementation & Algorithms, Computer Graphics and Geometric Modeling (Springer, London, 2005).
63. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics (Addison-Wesley, Boston, 1989).