Optimal Spectrum Estimation in Statistical Mechanics

ChemPhysChem

Volumn 4, Issue 11, 2003, Pages 1227-1230

  Wheeler, Ralph A ^a   Dong, Haitao ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Molecular dynamics; Principal component analysis; Signal processing; Statistical mechanics; Vibrational spectroscopy

Indexed keywords

INTELLIGENT SYSTEMS; MOLECULAR DYNAMICS; MONTE CARLO METHODS; QUANTUM THEORY; SIGNAL PROCESSING; SPECTRUM ANALYSIS; STATISTICAL MECHANICS; VIBRATIONAL SPECTROSCOPY; VIBRATIONS (MECHANICAL);

CONDENSED PHASE; CORRELATION FUNCTION; FOURIER; NUMERICAL TESTS; PRINCIPAL MODE ANALYSIS; QUANTUM MECHANICAL; SPECTRUM ESTIMATION;

PRINCIPAL COMPONENT ANALYSIS;

ARTICLE; CORRELATION ANALYSIS; FOURIER TRANSFORMATION; MATHEMATICAL COMPUTING; MOLECULAR MECHANICS; MONTE CARLO METHOD; PRINCIPAL COMPONENT ANALYSIS; QUANTUM MECHANICS; SPECTRUM; STATISTICS;

EID: 0344413575     PISSN: 14394235     EISSN: None     Source Type: Journal    
DOI: 10.1002/cphc.200300750     Document Type: Article

References (32)

1. D. A. McQuarrie, Statistical Mechanics, University Science Books, Sausalito, CA, 2000.
2. L. E. Reichl, A Modern Course in Statistical Physics, Wiley, New York, 1998.
3. M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1989.
4. B. J. Berne, G. D. Harp, Adv. Chem. Phys. 1970, 17, 63 - 227, and references therein.
5. R. G. Gordon, Adv. Magn. Res. 1968, 3, 1 - 42, and references therein.
6. M. B. Priestley, Spectral Analysis and Time Series, Vol. 1, Univariate Series, Academic Press, London, 1981, chapt. 7.
7. D. B. Percival, A. T. Walden, Spectral Analysis for Physical Applications, Cambridge University Press, Cambridge, 1993.
8. D. Neuhauser in Highly Excited Molecules, ACS Symp. Ser., Vol. 678 (Ed.: G. C. Schatz), American Chemical Society, Washington DC, 1997, pp. 26 - 38, and references therein.
9. X.-G. Shao, A. K.-M. Leung, F.-T. Chau, Acc. Chem. Res. 2003, 36, 276 - 283.
10. W. K. Pratt, Digital Image Processing, Wiley, New York, 1978.
11. K. Fukunaga, Introduction to Statistical Pattern Recognition, Academic Press, New York, 1972.
12. D. F. Morrison, Multivadate Statistical Methods, McGraw-Hill, New York, 1990.
13. D. A. Case, Curr. Opin. Struct. Biol. 1994, 4, 285 - 290.
14. S. Hayward, N. Go, Annu. Rev. Phys. Chem. 1995, 46, 233 - 250, and references therein.
15. A. Kitao, N. Go, Curr. Opin. Struct. Biol. 1999, 9, 164 - 169, and references therein.
16. A. Dür, SIAM J. Control Optim. 1998, 36, 1937 - 1939.
17. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran, Cambridge University Press, Cambridge, 1992. FFT calculation details: For each of the three numerical tests, 11 segments of 8192 data points were collected. Overlapping of the segments was allowed with a Bartlett window function used for each segment. For water and liquid water, much longer trajectories of 30000 steps were needed for FFT calculations (compared to 1000 steps for PCA). The segment size was set to 4092 data points and therefore 7 segments in each trajectory were collected. Overlapping of segments was allowed and the Bartlett window function was used.
18. K. Binder, Rep. Prog. Phys. 1997, 60, 487 - 559.
19. D. Thirumalai, B. J. Berne, Comput. Phys. Commun. 1991, 63, 415 - 426.
20. N. G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981.
21. E. B. Wilson, Jr., J. C. Decius, P. C. Cross, Molecular Vibrations, the theory of Infrared and Raman vibrational spectra, Dover Publications, New York, 1955.
22. R. A. Wheeler, H. Dong, S. E. Boesch, ChemPhysChem 2003, 4, 382 - 384.
23. U. Grenander, G. Szegö, Toeplitz Forms and Their Applications, Univ. of California Press, Los Angeles, 1958.
24. C. Lanczos, Linear Differential Operators, D. van Nostrand Company Ltd., London, 1961, chapt. 3.9.
25. F. Dinc, C. Teodosiu, Nonlinear and Random Vibrations, Academic Press, New York, 1973.
26. D. F. Smith, Jr., J. Overend, Spectrochim. Acta A 1972, 28, 471 - 483.
27. The Aldrich Library of FT-IR Spectra, Ed. 1, Vol. 1 (Ed.: C.J. Pouchert), Aldrich Chemical Company, Milwaukee, WI, 1985, p. 190.
28. P. J. Stephens, F. J. Devlin, C. F. Chablowski, M. J. Frisch, J. Phys. Chem. 1994, 98, 11623 - 11627.
29. R. J. Harrison, T. P. Straatsma, M. Dupuis, E. J. Bylaska, G. I. Fann, T. L. Windus, E. Apra, J. Anchell, D. Bernholdt, P. Borowski, T. Clark, D. Clerc, H. Dachsel, B. de Jong, M. Deegan, K. Dyall, D. Elwood, H. Fruchtl, E. Glendenning, M. Gutowski, A. Hess, J. Jaffe, B. Johnson, J. Ju, R. Kendall, R. Kobayashi, R, Kutteh, Z. Lin, R. Littlefield, X. Long, B. Meng, J. Nieplocha, S. Niu, M. Rosing, G. Sandrone, M. Stave, H. Taylor, G. Thomas, J. van Lenthe, K. Wolinski, A. Wong, Z. Zhang, NWChem, A Computational Chemistry Package for Parallel Computers, Version 4.0, Pacific Northwest National Laboratory, Richland, WA, 2000.
30. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, M. L. Klein, J. Chem. Phys. 1983, 79, 926 - 935.
31. A. K. Grafton, R. A. Wheeler, J. Comput. Chem. 1998, 19, 1663 - 1674.
32. M. J. Field, P. A. Bash, M. Karplus, J. Comput. Chem. 1990, 11, 700 - 733.