Parameterized bases for calculating vibrational spectra directly from ab initio data using rectangular collocation

Journal of Chemical Theory and Computation

Volumn 8, Issue 6, 2012, Pages 2053-2061

  Chan, Matthew ^a   Manzhos, Sergei ^b   Carrington, Tucker ^c   Yamashita, Koichi ^d  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF TOKYO   (Japan)

^c QUEEN S UNIVERSITY   (Canada)

^d UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84862225096     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct300248n     Document Type: Article

References (110)

1. Carrington, J. T. Methods for calculating vibrational energy levels. In Encyclopedia of Computational Chemistry; Schleyer, v. R., Ed.; John Wiley & Sons: New York, 2003.
2. Chabal, Y. J. Surface infrared spectroscopy Surf. Sci. Rep. 1988, 8, 211-357
3. Hirschmugl, C. J. Frontiers in infrared spectroscopy at surfaces and interfaces Surf. Sci. 2002, 500, 577-604
4. Barone, V. Calculation of vibrational spectrum of water with VPT2 and the aug-cc-pVTZ basis set J. Chem. Phys. 2005, 122, 014108
5. Sibert, E. L. Theoretical studies of vibrationally excited polyatomic molecules using canonical Van Vleck perturbation theory J. Chem. Phys. 1988, 88, 4378-4390
6. Yang, W.; Peet, A. C. The collocation method for bound solutions of the Schroedinger equation Chem. Phys. Lett. 1988, 153, 98-104
7. Peet, A. C.; Yang, W. The collocation method for calculating vibrational bound states of molecular systems with application to Ar-HCl J. Chem. Phys. 1989, 90, 1746-1751
8. Bowman, J. M. The self-consistent-field approach to polyatomic vibrations Acc. Chem. Res. 1986, 19, 202-208
9. Njegic, B.; Gordon, M. S. Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties J. Chem. Phys. 2006, 125, 224102
10. Bowman, J. M.; Carrington, T.; Meyer, H. D. Variational quantum approaches for computing vibrational energies of polyatomic molecules Mol. Phys. 2008, 106, 2145-2182
11. Ritz, W. On a new method to solve certain variation problems of mathematical physics J. Reine Angew. Math. 1909, 135, 1-5
12. 2 dissociation on the 1/2 ML c(2 - 2) -Ti/Al(100) surface Phys. Chem. Chem. Phys. 2012, 14, 3234-3247
13. Frankcombe, T. J.; Collins, M. A. Potential energy surfaces for gas-surface reactions Phys. Chem. Chem. Phys. 2011, 13, 8379-8391
14. 2O on Cu(100) using a continuous potential energy surface Surf. Sci. 2010, 604, 555-561
15. 2 dissociative adsorption on the Pt(211) stepped surface J. Chem. Phys. 2008, 128, 194715
16. 2 from Ru(0001). a computational study Chem. Phys. Lett. 2007, 434, 231-236
17. Tiwari, A. K.; Nave, S.; Jackson, B. The temperature dependence of methane dissociation on Ni(111) and Pt(111) mixed quantum-classical studies of the lattice response J. Chem. Phys. 2010, 132, 134702
18. Valentini, P.; Schwartzentruber, T. E.; Cozmuta, I. ReaxFF Grand Canonical Monte Carlo simulation of adsorption and dissociation of oxygen on platinum (111) Surf. Sci. 2011, 605, 1941-1950
19. Ahmed, F.; Nagumo, R.; Miura, R.; Suzuki, A.; Tsuboi, H.; Hatakeyama, N.; Takaba, H.; Miyamoto, A. CO oxidation and NO reduction on a MgO(100) supported Pd cluster: a quantum chemical molecular dynamics study J. Phys. Chem. C 2011, 115, 24123-24132
20. Bahel, A.; Bacic, Z. Six-dimensional quantum treatment of the vibrations of diatomic adsorbates on solid surfaces: CO on Cu(100) J. Chem. Phys. 1999, 111, 11164-11176
21. Parl, S. C.; Bowman, J. M.; Jelski, D. A. Quantum mechanical calculation of the CO vibrations in CO/Cu(100) J. Chem. Phys. 1996, 104, 2457-2460
22. Carter, S.; Culik, S. J.; Bowman, J. M. Vibrational self-consistent field method for many-mode systems a new approach and application to the vibrations of CO adsorbed on Cu(100) J. Chem. Phys. 1997, 107, 10458-10469
23. Tremblay, J. C.; Beyvers, S.; Saalfrank, P. Selective excitation of coupled CO vibrations on a dissipative Cu(100) surface by shaped infrared laser pulses J. Chem. Phys. 2008, 128, 194709
24. Shemesh, D.; Mullin, J.; Gordon, M. S.; Gerber, R. B. Vibrational spectroscopy for glycine adsorbed on silicon clusters: Harmonic and anharmonic calculations for models of the Si(1 0 0)-2 - 1 surface Chem. Phys. 2008, 347, 218-228
25. Carnimeo, I.; Biczysko, M.; Bloino, J.; Barone, V. Reliable structural, thermodynamic, and spectroscopic properties of organic molecules adsorbed on silicon surfaces from computational modeling the case of glycine@Si(100) Phys. Chem. Chem. Phys. 2011, 13, 16713-16727
26. 2O on Pt(111) Surf. Sci. 2011, 605, 616-622
27. 3 adsorbed on the Ni(111) surface J. Phys. Chem. B 2005, 109, 8954-8960
28. Wang, Y.; Wöll, C. Chemical reactions on metal oxide surfaces investigated by vibrational spectroscopy Surf. Sci. 2009, 603, 1589-1599
29. Kossmann, J.; Rossmueller, G.; Haettig, C. Prediction of vibrational frequencies of possible intermediates and side products of the methanol synthesis on ZnO(0001) by ab initio calculations J. Chem. Phys. 2012, 136, 034706
30. Valero, R.; B., J. R.; Truhlar, D. G.; Illas, F. Density functional study of CO and NO adsorption on Ni-doped MgO(100) J. Chem. Phys. 2010, 132, 104701
31. Vayssilov, G. N.; Mihaylov, M.; Petkov, P.; Hadjiivanov, K. I.; Neyman, K. M. Reassignment of the vibrational spectra of carbonates, formates, and related surface species on ceria. a combined density functional and infrared spectroscopy investigation J. Phys. Chem. C 2011, 115, 23435-23454
32. Bowman, J. M.; Gazdy, B. A truncation/recoupling method for basis set calculations of eigenvalues and eigenvectors J. Chem. Phys. 1991, 94, 454-460
33. Zou, S.; Bowman, J. M.; Brown, A. Full-dimensionality quantum calculations of acetylene-vinylidene isomerization J. Chem. Phys. 2003, 118, 10012-10023
34. Tremblay, J. C.; Carrington, T. Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled two-term Lanczos eigensolver J. Chem. Phys. 2006, 125, 094311
35. Bacic, Z.; Light, J. C. Theoretical methods for rovibrational states of floppy molecules Annu. Rev. Phys. Chem. 1989, 40, 469-498
36. Carter, S.; Handy, N. C. A variational method for the determination of the vibrational (J = 0) energy levels of acetylene, using a Hamiltonian in internal coordinates Comput. Phys. Commun. 1988, 51, 49-58
37. 3 Chem. Phys. Lett. 1990, 173, 133-138
38. Bramley, M. J.; Carrington, T. J. Calculation of triatomic vibrational eigenstates: Product or contracted basis sets, Lanczos or conventional eigensolvers? What is the most efficient combination? J. Chem. Phys. 1994, 101, 8494-8507
39. 2. I. Using parallel supercomputers to calculate rotation-vibration energy levels J. Chem. Phys. 1999, 110, 2354-2364
40. 2 J. Chem. Phys. 1998, 108, 4804-4816
41. 2CO Spectrochim. Acta., Part A 2002, 58, 809-824
42. Luckhaus, D. 6D vibrational quantum dynamics: Generalized coordinate discrete variable representation and (a)diabatic contraction J. Chem. Phys. 2000, 113, 1329-1347
43. Wang, X. G.; Carrington, T. J. New ideas for using contracted basis functions with a Lanczos eigensolver for computing vibrational spectra of molecules with four or more atoms J. Chem. Phys. 2002, 117, 6923-6934
44. Bramley, M. J.; Handy, N. C. Efficient calculation of rovibrational eigenstates of sequentially bonded four-atom molecules J. Chem. Phys. 1993, 98, 1378-1397
45. Carter, S.; Handy, N. C. The geometry and forcefield of acetylene Mol. Phys. 2002, 100, 681-698
46. Carter, S.; Handy, N. C. The variational method for the calculation of ro-vibrational energy levels Comput. Phys. Rep. 1986, 5, 117-171
47. 13CH J. Chem. Phys. 1983, 78, 2803-2804
48. Yu, H. G. An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach J. Chem. Phys. 2002, 117, 2030-2037
49. CH = 2 regions J. Chem. Phys. 1997, 106, 9483-9496
50. 6 J. Chem. Phys. 1993, 98, 6722-6734
51. Wang, X. G.; Carrington, T. J. The utility of constraining basis function indices when using the lanczos algorithm to calculate vibrational energy levels J. Phys. Chem. A 2001, 105, 2575-2581
52. Lee, H. S.; Light, J. C. Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules J. Chem. Phys. 2004, 120, 4626-4637
53. Poirier, B. Using wavelets to extend quantum dynamics calculations to ten or more degrees of freedom J. Theor. Comput. Chem. 2003, 2, 65-72
54. Dawes, R.; Carrington, T. How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: Energy levels of coupled systems with as many as 16 coordinates J. Chem. Phys. 2005, 122, 134101
55. Gustavo, A.; Carrington, T. J. Nonproduct quadrature grids for solving the vibrational Schrödinger equation J. Chem. Phys. 2009, 131, 174103
56. Gustavo, A.; Carrington, T. J. Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C2H4 J. Chem. Phys. 2011, 135, 064101
57. Gustavo, A.; Carrington, T. J. Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12D J. Chem. Phys. 2011, 134, 054126
58. Carter, S.; Bowman, J. M.; Handy, N. C. Extensions and tests of multimodes: a code to obtain accurate vibration/rotation energies of many-mode molecules. THEOCHEM 1998, 100, 191-198
59. Manzhos, S.; Carrington, T.; Yamashita, K. Non-spectral methods for solving the Schroedinger equation for electronic and vibrational problems J. Phys. Chem. Lett. 2011, 2, 2193-2199
60. Manzhos, S.; Carrington, T. An improved neural network method for solving the Schrödinger equation Can. J. Chem. 2009, 87, 864-871
61. Manzhos, S.; Yamashita, K.; Carrington, T. On the advantages of a rectangular matrix collocation equation for computing vibrational spectra from small basis sets Chem. Phys. Lett. 2011, 511, 434-439
62. Manzhos, S.; Yamashita, K.; Carrington, T. Using a neural network based method to solve the vibrational Schrödinger equation for H2O Chem. Phys. Lett. 2009, 474, 217-221
63. Jensen, P. The potential energy surface for the electronic ground state of the water molecule determined from experimental data using a variational approach J. Mol. Spectrosc. 1989, 133, 438-460
64. Bacic, Z.; Watt, D.; Light, J. C. A variational localized representation calculation of the vibrational levels of the water molecule up to 27000 cm-1 J. Chem. Phys. 1988, 89, 947-855
65. Bowman, J. M.; Czako, G.; Fu, B. High-dimensional potential energy surfaces for reaction dynamics calculations Phys. Chem. Chem. Phys. 2011, 13, 8094-8111
66. Behler, J. Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations Phys. Chem. Chem. Phys. 2011, 13, 17930-17955
67. Manzhos, S.; Wang, X. G.; Dawes, R.; Carrington, T. A Nested molecule-independent neural network approach for high-quality potential fits J. Phys. Chem. A 2006, 110, 5295-5304
68. Manzhos, S.; Carrington, T. Using neural networks to represent potential surfaces as sums of products J. Chem. Phys. 2006, 125, 194105
69. Seidler, P.; Kongsted, J.; Christiansen, O. Calculation of vibrational infrared intensities and Raman activities using explicit anharmonic wave functions J. Phys. Chem. A 2007, 111, 11205-11213
70. Manzhos, S.; Segawa, H.; Yamashita, K. A model for recombination in Type II dye-sensitized solar cells catechol-thiophene dyes Chem. Phys. Lett. 2011, 504, 230-235
71. Zhao, Y.; Liang, W. Z. Theoretical investigation of resonance Raman scattering of dye molecules absorbed on semiconductor surfaces J. Chem. Phys. 2011, 135, 044108
72. Ianconescu, R.; Pollak, E. Semiclassical initial value representation study of internal conversion rates J. Chem. Phys. 2011, 134, 234305
73. Niu, Y.; Peng, Q.; Deng, C.; Gao, X.; Shuai, Z. Theory of excited state decays and optical spectra application to polyatomic molecules J. Phys. Chem. A 2010, 114, 7817-7831
74. Perez-Jorda, J. M. Variational solution of the Schroedinger equation using plane waves in adaptive coordinates: the radial case J. Chem. Phys. 2010, 132, 024110
75. Perez-Jorda, J. M. Variational solution of the three-dimensional Schroedinger equation using plane waves in adaptive coordinates J. Chem. Phys. 2011, 135, 204104
76. Fattal, E.; Kosloff, R. Phase space approach for optimizing grid representations: The mapped Fourier method Phys. Rev. E 1996, 53, 1217-1227
77. Kokoouline, V.; Dulieu, O.; Kosloff, R.; Masnouseeuws, F. Mapped Fourier methods for long-range molecules: Application to perturbations in the Rb2(0u+) photoassociation spectrum J. Chem. Phys. 1999, 110, 9865-9876
78. Popelier, P. Solving the Schrödinger equation: Has everything been tried?; Imperial College Press: London, U.K., 2011.
79. Caetano, C.; Reis, J. L. J.; Amorim, J.; Lemes, M. R.; Dal Pino, A. J. Using neural networks to solve nonlinear differential equations in atomic and molecular physics Int. J. Quantum Chem. 2010, 111, 2732-2740
80. Lagaris, I. E.; Likas, A.; Fotiadis, D. I. Artificial neural network methods in quantum mechanics Comput. Phys. Commun. 1997, 104, 1-14
81. Sugawara, M. Numerical solution of the Schroedinger equation by neural network and genetic algorithm Comput. Phys. Commun. 2001, 140, 366-380
82. Manzhos, S.; Carrington, T.; Yamashita, K. Solving the vibrational Schrödinger equation without a potential energy surface using a combined neural network collocation approach. In Computer Physics; Nova Publishers: Hauppage, NY, 2011.
83. Davis, M. J.; Heller, E. J. Quantum dynamical tunneling in bound states J. Chem. Phys. 1981, 75, 246-254
84. Davis, M. J.; Heller, E. J. Semiclassical Gaussian basis set method for molecular vibrational wave functions J. Chem. Phys. 1979, 71, 3383-3395
85. Hamilton, I. P.; Light, J. C. On distributed Gaussian bases for simple model multidimensional vibrational problems J. Chem. Phys. 1986, 84, 306-317
86. Peet, A. C. The use of distributed Gaussian basis sets for calculating energy levels of weakly bound complexes J. Chem. Phys. 1989, 90, 4363-4369
87. Chesick, J. P. Gaussian basis sets for model anharmonic oscillator systems J. Chem. Phys. 1968, 49, 3772-3774
88. Poirier, B.; Light, J. C. Efficient distributed Gaussian basis for rovibrational spectroscopy calculations J. Chem. Phys. 2000, 113, 211-217
89. Heller, E. J. Frozen Gaussians: a very simple semiclassical approximation J. Chem. Phys. 1981, 75, 2923-2931
90. Thompson, A. L.; Punwong, C.; Martinez, T. J. Optimization of width parameters for quantum dynamics with frozen Gaussian basis sets Chem. Phys. 2010, 370, 70-77
91. Worth, G. A.; Cederbaum, L. S. Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics Int. Rev. Phys. Chem. 2008, 27, 569-606
92. Donoho, D. L. High-Dimensional Data Analysis: The curses and blessings of dimensionality. Aide-Memoire of a Lecture at AMS Conference on Mathematical Challenges of the 21st Century; AMS, Los Angeles, CA, August 6-11, 2000. http://www-stat.stanford.edu/∼donoho/Lectures/AMS2000/AMS2000.html (accesses Apr 28, 2012)
93. Yagi, K.; Karasawa, H.; Hirata, S.; Hirao, K. First-principles quantum calculations on the infrared spectrum and vibrational dynamics of the guanine-cytosine base pair Chem. Phys. Chem. 2009, 10, 1442-1444
94. Hammer, T.; Coutinho-Neto, M. D.; Viel, A.; Manthe, U. Multiconfigurational time-dependent Hartree calculations for tunneling splittings of vibrational states: Theoretical considerations and application to malonaldehyde J. Chem. Phys. 2009, 131, 224109
95. Wang, Y.; Braams, B. J.; Bowman, J. M.; Carter, S.; Tew, D. P. Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface J. Chem. Phys. 2008, 128, 224314
96. Watson, J. K. G. Simplification of the molecular vibration-rotation hamiltonian Mol. Phys. 1968, 15, 479
97. Jacobi, K.; Beduerfti, K.; Wang, Y.; Ertl, E. From monomers to ice - new vibrational characteristics of H2O adsorbed on Pt(1 1 1) Surf. Sci. 2001, 472, 9-20
98. MATLAB, version R2009b; MathWorks, Inc.: Natick, MA, 2009.
99. Boutry, G.; Elad, M.; Golub, G. H.; Milanfar, P. The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach SIAM J. Matrix Anal. Appl. 2005, 27, 582-601
100. Perdew, P. J.; Yue, W. Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation Phys. Rev. B 1986, 33, 8800-8802
101. Kohn, W.; Sham, L. J. Self-consistent equations including exchange and correlation effects Phys. Rev. 1965, 140, A1133-A1138
102. Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. The SIESTA method for ab initio order-N materials simulation J. Phys.: Condens. Matter 2002, 14, 2745
103. Garashchuk, S.; Light, J. C. Quasirandom distributed Gaussian bases for bound problems J. Chem. Phys. 2001, 114, 3929-3939
104. Sobol, I. M. On the distribution of points in a cube and the approximate evaluation of integrals USSR Comput. Math. Math. Phys. 1967, 7, 86-112
105. Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numeric recipes in Fortran 77: The art of scientific computing; W. H. Press: 1997; Vol. 1.
106. OBryant, I. EFinder (a MATLAB program); University of North Dakota: Grand Forks, ND, 2005.
107. Manzhos, S.; Carrington, T. A random-sampling high dimensional model representation neural network for building potential energy surfaces J. Chem. Phys. 2006, 125, 084109
108. Russell, D. J. I. NIST Computational Chemistry Comparison and Benchmark Database. In NIST Standard Reference Database Number 101; NIST: Gaithersburg, MD, 2005.
109. Sälli, E.; Hänninen, V.; Halonen, L. Variationally calculated vibrational energy levels of ammonia adsorbed on a Ni(111) Surface J. Phys. Chem. C 2010, 114, 4550-4556
110. Ulusoy, I. S.; Scribano, Y.; Benoit, D. M.; Tschetschetkin, A.; Maurer, N.; Koslowski, B.; Ziemann, P. Vibrations of a single adsorbed organic molecule: anharmonicity matters! Phys. Chem. Chem. Phys. 2011, 13, 612-618