We present methodology (HBFF/SVD) for optimizing the form and parameters of force fields (FF) for molecular dynamics simulations through utilizing information about properties such as the geometry, Hessian, polarizability, stress (crystals), and elastic constants (crystals). This method is based on singular value decomposition (SVD) of the Jacobian describing the partial derivatives in various properties with respect to FF parameters. HBFF/SVD is effective for optimizing the parameters for accurate FFs of organic, inorganic, and transition metal compounds. In addition it provides information on the validity of the functional form of the FF for describing the properties of interest. This method is illustrated by application to organic molecules (CH2O, C2H4, C4H6, C6H8, C6H6, and naphthalene) and inorganic molecules (Cl2CrO2 and Cl2MoO2).
REFERENCES
1.
(a) J. A. McCammon and S. C. Harvey, Dynamics of Proteins and Nucleic Acids (Cambridge U.P., Cambridge, 1987);
(b) Computer Simulation of Biomolecular Systems, edited by W. F. Gunsteren and P. K. Weiner (ESCOM, Leiden, 1989).
2.
(a)
N.
Karasawa
, S.
Dasgupta
, and W. A.
Goddard
III, J. Phys. Chem.
95
, 2260
(1991
);(b)
C. B.
Musgrave
, S.
Dasgupta
, and W. A.
Goddard
III, J. Phys. Chem.
99
, 13321
(1995
)., J. Phys. Chem.
3.
4.
5.
6.
7.
K. Rasmussen, Lecture Notes in Chemistry (Springer-Verlag, Heidelberg, 1985), Vol. 37.
8.
N. L.
Allinger
, K.
Chen
, M.
Rahman
, and A.
Pathiaseril
, J. Am. Chem. Soc.
113
, 4505
(1991
), and references therein.9.
10.
(a) FFOPT (unpublished) was written by W. A. Goddard III, S. Dasgupta, and T. E. Yamasaki;
(b) It is used in conjunction with the Vibrate module of Pro-POLYGRAF from Molecular Simulations, Inc., Burlington, MA 02154.
11.
Residue components in the Hessian optimization might be approximated by assuming that the vibrational wave function is unchanged for small changes in the force constants (see Ref. 6). However we computed these residues by finite difference of each parameter without any such approximation.
12.
P.
Pulay
, G.
Fogarasi
, G.
Pongor
, J. E.
Boggs
, and A.
Vargha
, J. Am. Chem. Soc.
105
, 7037
(1983
).13.
(a) G. Strang, Linear Algebra and its Applications (Academic, New York, 1980);
(b) W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U.P., Cambridge, 1989).
14.
S. L.
Mayo
, B. D.
Olafson
, and W. A.
Goddard
III, J. Phys. Chem.
94
, 8897
(1990
).15.
16.
(a)
A. K.
Rappé
, C. J.
Casewit
, K. S.
Colwell
, W. A.
Goddard
III, and W. M.
Skiff
, J. Am. Chem. Soc.
114
, 10024
(1992
);(b)
J. H.
Lii
and N. L.
Allinger
, J. Am. Chem. Soc.
111
, 8576
(1989
)., J. Am. Chem. Soc.
17.
P.
Pulay
, G.
Fogarasi
, G.
Pongor
, J. E.
Boggs
, and A.
Vargha
, J. Am. Chem. Soc.
105
, 7037
(1983
).18.
G.
Fogarasi
, P. G.
Szalay
, P. P.
Liescheski
, J. E.
Boggs
, and P.
Pulay
, J. Mol. Struct. (Theochem)
151
, 341
(1987
).19.
F. W.
Langkilde
, R.
Wilbrandt
, and A. M.
Brouwer
, J. Phys. Chem.
94
, 4809
(1990
).20.
(a)
R. J.
Hemley
, B. R.
Brooks
, and M.
Karplus
, J. Chem. Phys.
85
, 6550
(1986
);(b)
C. W.
Bock
, Y. N.
Panchenko
, S. V.
Krasnoschiokov
, and V. I.
Pupyshev
, J. Mol. Struct.
148
, 131
(1986
);(c)
P. G.
Szalay
, A.
Karpfen
, and H.
Lischka
, J. Chem. Phys.
87
, 3530
(1987
).21.
22.
R. G. Parr, Quantum Theory of Molecular Electronic Structure (Benjamin, New York, 1964).
23.
24.
R. H.
Baughman
, B. E.
Kohler
, I. J.
Levy
, and C.
Spangler
, Synth. Metals
11
, 37
(1985
).25.
L.
Goodman
, A. G.
Ozkabak
, and S. N.
Thakur
, J. Phys. Chem.
95
, 9044
(1991
).26.
H.
Sellers
, P.
Pulay
, and J. E.
Boggs
, J. Am. Chem. Soc.
107
, 6487
(1985
).27.
Tables of Interatomic Distances and Configuration in Molecules and Ions, edited by L. E. Sutton (The Chemical Society, London, 1958).
28.
(c)
C. J.
Marsden
, L.
Hedberg
, and K.
Hedberg
, Inorg. Chem.
21
, 1115
(1982
);(e)
T. V.
Iorns
and F. E.
Stafford
, J. Am. Chem. Soc.
88
, 4819
(1966
);(g)
I. R.
Beattie
, K. M. S.
Livingston
, D. J.
Reynolds
, and G. A.
Ozin
, J. Chem. Soc. A
1210
(1970
); , J. Chem. Soc. A
(h)
W.
Levason
, R.
Narayanaswamy
, J. S.
Ogden
, A. J.
Rest
, and J. W.
Turff
, J. Chem. Soc. Dalton Trans.
2009
(1982
);(i)
D. L.
Neikirk
, J. C.
Fagerli
, M. L.
Smith
, D.
Mosman
, and T. C.
Devore
, J. Mol. Struct.
244
, 165
(1991
);(j) A. K. Rappé and W. A. Goddard III, in Potential Energy Surfaces and Dynamics Calculations, edited by D. G. Truhlar (Plenum, New York, 1981), pp. 661–684;
(k)
A. K.
Rappé
and W. A.
Goddard
III, J. Am. Chem. Soc.
102
, 5114
(1980
);29.
For example, see: H. Fuhrer, V. B. Kartha, K. G. Kidd, P. J. Krueger, and H. H. Mantsch, Normal Coordinate Analysis (N.R.C.C. Bulletin No. 15, 1976).
30.
We may write the least-squares equation (2a) as, and solve by diagonalization of instead of using the SVD of G. However, in this approach the condition ratio is also squared making the control of the numerical solution quite difficult.
31.
K.
Palmö
, L.-O.
Pietilä
, and S.
Krimm
, J. Comput. Chem.
12
, 385
(1991
).32.
P.
Pulay
, G.
Fogarasi
, F.
Pang
, and J. E.
Boggs
, J. Am. Chem. Soc.
101
, 2550
(1979
).33.
34.
K.
Yamada
, T.
Nakagawa
, K.
Kuchitsu
, and Y.
Morino
, J. Mol. Spectrosc.
38
, 70
(1971
).35.
GAUSSIAN 90, Revision F, M. J. Frisch, M. Head-Gordon, G. W. Trucks, J. B. Foresman, H. B. Schlegel, K. Raghavachari, M. Robb, J. S. Binkley, C. Gonzalez, D. J. Defrees, D. J. Fox, R. A. Whiteside, R. Seeger, C. F. Melius, J. Baker, R. L. Martin, L. R. Kahn, J. J. P. Stewart, S. Topiol, and J. A. Pople (Gaussian, Inc., Pittsburgh, PA, 1990).
36.
T. H. Dunning and P. J. Hay, in Modern Theoretical Chemistry, edited by H. F. Schaefer III (Plenum, New York, 1976), Vol. 3.
37.
38.
T.
Shimanouchi
, Tables of Molecular Vibrational Frequencies, Nat. Stand. Ref. Data. Ser., Nat. Bur. Stand.
39
, 1972
.
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