Efficient computation of compliance matrices in redundant internal coordinates from Cartesian Hessians for nonstationary points

Journal of Chemical Physics

Volumn 132, Issue 18, 2010, Pages

  Brandhorst, Kai ^a   Grunenberg, Jörg ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY SETS; CARTESIANS; EFFICIENT COMPUTATION; GEOMETRY OPTIMIZATION; HESSIAN MATRICES; INTERNAL COORDINATE SYSTEMS; INTERNAL COORDINATES; NON-STATIONARY POINTS; POTENTIAL ENERGY HYPER SURFACES; STATIONARY POINTS;

MATRIX ALGEBRA;

EID: 77952711382     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3413528     Document Type: Article

References (67)

1. C. Peng, P. Y. Ayala, H. B. Schlegel, and M. J. Frisch, J. Comput. Chem. JCCHDD 0192-8651 17, 49 (1996). 10.1002/(SICI)1096-987X(19960115)17:1<49:: AID-JCC5>3.0.CO;2-0
2. G. Fogarasi, X. Zhou, P. W. Taylor, and P. Pulay, J. Am. Chem. Soc. JACSAT 0002-7863 114, 8191 (1992). 10.1021/ja00047a032
3. R. Lindh, A. Bernhardsson, and M. Schütz, Chem. Phys. Lett. CHPLBC 0009-2614 303, 567 (1999) 10.1016/S0009-2614(99)00247-X;
4. O. Farkas and B. H. Schlegel, J. Mol. Struct.: THEOCHEM THEODJ 0166-1280 666-667, 31 (2003). 10.1016/j.theochem.2003.08.010
5. B. Paizs, J. Baker, S. Suhai, and P. Pulay, J. Chem. Phys. JCPSA6 0021-9606 113, 6566 (2000) 10.1063/1.1308551; (Pubitemid 32027274)
6. K. N. Kudin, G. E. Scuseria, and H. B. Schlegel, J. Chem. Phys. JCPSA6 0021-9606 114, 2919 (2001) 10.1063/1.1340578 (Pubitemid 32253407)
7. V. Bakken and T. Helgaker, J. Chem. Phys. JCPSA6 0021-9606 117, 9160 (2002). 10.1063/1.1515483
8. P. Pulay and G. Fogarasi, J. Chem. Phys. JCPSA6 0021-9606 96, 2856 (1992). 10.1063/1.462844
9. J. Baker and W. J. Hehre, J. Comput. Chem. JCCHDD 0192-8651 12, 606 (1991) 10.1002/jcc.540120510;
10. B. Paizs, G. Fogarasi, and P. Pulay, J. Chem. Phys. JCPSA6 0021-9606 109, 6571 (1998). 10.1063/1.477309 (Pubitemid 128678285)
11. H. B. Schlegel, Theor. Chim. Acta TCHAAM 0040-5744 66, 333 (1984). 10.1007/BF00554788
12. S. J. Cyvin and N. B. Slater, Nature (London) NATUAS 0028-0836 188, 485 (1960) 10.1038/188485a0;
13. J. Grunenberg, R. Streubel, G. von Frantzius, and W. Marten, J. Chem. Phys. JCPSA6 0021-9606 119, 165 (2003) 10.1063/1.1576756;
14. J. C. Decius, J. Chem. Phys. JCPSA6 0021-9606 38, 241 (1963) 10.1063/1.1733469;
15. C. V. S. Ramachandra Rao, J. Mol. Spectrosc. JMOSA3 0022-2852 41, 105 (1972) 10.1016/0022-2852(72)90126-9;
16. P. A. Vicharelli, Spectrosc. Lett. SPLEBX 0038-7010 11, 701 (1978) 10.1080/00387017808063442;
17. E. Martínez-Torres, J. Mol. Struct. JMOSB4 0022-2860 520, 53 (2000). 10.1016/S0022-2860(99)00313-0 (Pubitemid 30151427)
18. K. Brandhorst and J. Grunenberg, ChemPhysChem CPCHFT 1439-4235 8, 1151 (2007) 10.1002/cphc.200700038;
19. K. Brandhorst and J. Grunenberg, Chem. Soc. Rev. CSRVBR 0306-0012 37, 1558 (2008). 10.1039/b717781j
20. L. H. Jones and R. R. Ryan, J. Chem. Phys. JCPSA6 0021-9606 52, 2003 (1970). 10.1063/1.1673251
21. L. H. Jones and B. I. Swanson, Acc. Chem. Res. ACHRE4 0001-4842 9, 128 (1976) 10.1021/ar50100a002;
22. J. K. G. Watson, J. Mol. Struct. JMOSB4 0022-2860 695-696, 71 (2004). 10.1016/j.molstruc.2003.10.033 (Pubitemid 38680528)
23. E. Martínez Torres, J. J. L. Gonzalez, and M. F. Gomez, J. Chem. Phys. JCPSA6 0021-9606 110, 3302 (1999). 10.1063/1.478195
24. J. C. Decius, J. Chem. Phys. JCPSA6 0021-9606 21, 1121 (1953). 10.1063/1.1699141
25. G. von Frantzius, R. Streubel, K. Brandhorst, and J. Grunenberg, Organometallics ORGND7 0276-7333 25, 118 (2006) 10.1021/om050489a; (Pubitemid 43061680)
26. J. Grunenberg and N. Goldberg, J. Am. Chem. Soc. JACSAT 0002-7863 122, 6045 (2000) 10.1021/ja994148y; (Pubitemid 30451109)
27. J. Grunenberg, J. Am. Chem. Soc. 126, 16310 (2004) 10.1021/ja046282a 0002-7820; (Pubitemid 40081915)
28. S. Zhu, H. Staats, K. Brandhorst, J. Grunenberg, G. Francesca, E. Dalcanale, A. Lützen, K. Rissanen, and C. A. Schalley, Angew. Chem., Int. Ed. ACIEF5 1433-7851 47, 788 (2008) 10.1002/anie.200703451;
29. C. A. Pignedoli, A. Curioni, and W. Andreoni, ChemPhysChem CPCHFT 1439-4235 6, 1795 (2005) 10.1002/cphc.200500064; (Pubitemid 41330000)
30. J. Baker and P. Pulay, J. Am. Chem. Soc. JACSAT 0002-7863 128, 11324 (2006) 10.1021/ja0618503; (Pubitemid 44338805)
31. J. Baker, J. Chem. Phys. JCPSA6 0021-9606 125, 014103 (2006). 10.1063/1.2209678 (Pubitemid 44025474)
32. It should be noted, however, that this expansion is not guaranteed to converge (Ref.).
33. E. H. Moore, Bull. Am. Math. Soc. BAMOAD 0002-9904 26, 394 (1920);
34. R. Penrose, Math. Proc. Cambridge Philos. Soc. MPCPCO 0305-0041 51, 406 (1955). 10.1017/S0305004100030401
35. I. Kolossváry and C. McMartin, J. Math. Chem. JMCHEG 0259-9791 9, 359 (1992). 10.1007/BF01166099
36. D. J. Wales, J. Chem. Phys. JCPSA6 0021-9606 113, 3926 (2000). 10.1063/1.1288003
37. P. Grochowski, Theor. Chem. Acc. TCACFW 1432-881X 121, 257 (2008). 10.1007/s00214-008-0472-1
38. P. Pulay, Applications of Electronic Structure Theory, Modern Theoretical Chemistry, Vol. 4, edited by, H. F. Schaefer III, (Plenum, New York, 1977), Chap., pp. 153-185;
39. G. Fogarasi and P. Pulay, Vibrational Spectra and Structure, edited by, J. R. Durig, (Elsevier, New York, 1985), Vol. 14, Chap., pp. 125-219.
40. A. Banerjee and N. P. Adams, Int. J. Quantum Chem. IJQCB2 0020-7608 43, 855 (1992). 10.1002/qua.560430610
41. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, 1995).
42. H. Dachsel and W. Quapp, J. Math. Chem. JMCHEG 0259-9791 6, 77 (1991). 10.1007/BF01192575
43. W. D. Allen and A. G. Császár, J. Chem. Phys. JCPSA6 0021-9606 98, 2983 (1993). 10.1063/1.464127
44. E. B. Wilson, Jr., J. Chem. Phys. JCPSA6 0021-9606 7, 1047 (1939) 10.1063/1.1750363;
45. M. A. Eliashevich, C. R. Acad. Sci. URSS DANKAS 0002-3264 28, 605 (1940);
46. E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955);
47. S. Califano, Vibrational States (Wiley, New York, 1976).
48. P. Pulay, Mol. Phys. MOPHAM 0026-8976 17, 197 (1969). 10.1080/00268976900100941
49. P. Vansteenkiste, D. V. Neck, V. V. Speybroeck, and M. Waroquier, J. Chem. Phys. JCPSA6 0021-9606 124, 044314 (2006). 10.1063/1.2161218 (Pubitemid 43166324)
50. W. H. Miller, N. C. Handy, and J. E. Adams, J. Chem. Phys. JCPSA6 0021-9606 72, 99 (1980). 10.1063/1.438959
51. B. Crawford and J. Overend, J. Mol. Spectrosc. JMOSA3 0022-2852 12, 307 (1964) 10.1016/0022-2852(64)90017-7;
52. C. Marcott, S. D. Ferber, H. A. Havel, A. Moscowitz, and J. Overend, Spectrochim. Acta, Part A SAMCAS 0584-8539 37, 241 (1981) 10.1016/0584-8539(81) 80169-9;
53. P. Groner and H. H. Günthard, J. Mol. Spectrosc. JMOSA3 0022-2852 61, 151 (1976). 10.1016/0022-2852(76)90238-1
54. S. L. Campbell and C. D. Meyer, Jr., Generalized Inverses of Linear Transformations (Dover, New York, 1991).
55. P. Császár and P. Pulay, J. Mol. Struct. JMOSB4 0022-2860 114, 31 (1984) 10.1016/S0022-2860(84)87198-7;
56. O. Farkas and H. B. Schlegel, Phys. Chem. Chem. Phys. PPCPFQ 1463-9076 4, 11 (2002). 10.1039/b108658h
57. T. Damm and H. K. Wimmer, J. Austral. Math. Soc. JAMADS 0263-6115 86, 33 (2009). 10.1017/S144678870800044X
58. This equation has in principle been derived earlier by Cyvin (Ref.) while his "purpose was to demonstrate that n (which is H- x+ in our formulation) is unique in the sense that all its elements in principle may be determined, but it was not intended to indicate an actual method for their determination."
59. S. -H. Lee, K. Palmo, and S. Krimm, J. Mol. Struct.: THEOCHEM THEODJ 0166-1280 546, 217 (2001) 10.1016/S0166-1280(01)00451-1; (Pubitemid 32667564)
60. If the one-row matrices B and BT refer to the same coordinate Eq. gives the corresponding diagonal element of C, whereas an off-diagonal term is accessible by choosing B and BT to refer to different internal coordinates.
61. Basic Linear Algebra Subprograms, http://www.netlib.org/blas.
62. Linear Algebra Package, http://www.netlib.org/lapack.
63. M. Fourní, J. Pommier, and B. Schleimer, Gmm++, ttp://home.gna.org/getfem/gmm-intro.
64. M. J. Frisch, G. W. Trucks, H. B. Schlegel, GAUSSIAN 03, Revision E.01, Gaussian, Inc., Wallingford, CT, 2004.
65. OH distances and the H-H distance all three eigenvalues are positive (MP2/aug-cc-pvtz level of theory).
66. J. Pesonen, J. Chem. Phys. JCPSA6 0021-9606 128, 044319 (2008). 10.1063/1.2829496 (Pubitemid 351200452)
67. S. J. Cyvin, Molecular Vibrations and Mean Square Amplitudes (Elsevier, New York, 1968).