Karplus

Karplus M and Porter R N 1970 Atoms and Molecules an Introduction for Students of Physical Chemistry (Reading, MA Addison-Wesley)... 

J is almost always positive and its magnitude often exceeds that of T. It always depends in a predictable way on the dihedral angle ( ) between the outer two of the tluee bonds in die coupling patliway. Karplus first showed theoretically that T varies to a good approximation as A cos ( ) + B cos ( ), where A and B are constants, and also that A S>B [17]. Flis equation has received wide-ranging... 

Karplus M 1959 Contact electron spin coupling of nuclear magnetic moments J. Chem. Phys. 30 11-15... 

Elber R and Karplus M 1987 A method for determining reaction paths in large molecules application to myoglobin Chem. Phys. Lett. 139 375... 

One drawback is that, as a result of the time-dependent potential due to the LHA, the energy is not conserved. Approaches to correct for this approximation, which is valid when the Gaussian wavepacket is narrow with respect to the width of the potential, include that of Coalson and Karplus [149], who use a variational principle to derive the equations of motion. This results in replacing the function values and derivatives at the central point, V, V, and V" in Eq. (41), by values averaged over the wavepacket. 

C. Brooks III, M. Karplus, and B. Pettier, Proteins. A theoretical perspective of dynamics, structure, and thermodynamics, John Wiley Sons, Inc., New York, 1988, also Adv. Chem. Phys. LXXI,... 

Bash, P.A., Field, M.J.,Karplus, M. Free energy perturbation method for chemical reactions in the condensed phase A dynamical approach baaed on a combined quantum and molecular dynamics potential. J. Am. Chem. Soc. 109 (1987) 8092-8094. 

Field, M.J., Bash, P.A., Karplus, M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J. Comput. Chem. 11 (1990) 700-733. 

Brooks III, C.L., Karplus, M. Deformable stochastic boubdaries in molecular dynamics. J. Chem. Phys. 79 (1983) 6312-6325. 

Walter Nadler, Axel T. Briinger, Klaus Schulten, and Martin Karplus. Molecular and stochastic dynamics of proteins. Proc. Natl. Acad. Sci. USA, 84 7933-7937, Nov. 1987. 

Bernhard R. Brooks, Robert E. Bruccoleri, Barry D. Olafson, David J. States, S. Swaminathan, and Martin Karplus. CHARMM A program for macro-molecular energy, minimization, and dynamics calculations. J. Comp. Chem., 4(2) 187-217, 1983. 

Charles L. Brooks III, B. Montgomery Pettitt, and Martin Karplus. Structural and energetic effects of truncating long ranged interactions in ionic and polar fluids. J. Chem. Phys., 83(ll) 5897-5908, December 1985. 

Boresch, S., Archontis, G., Karplus, M. Free energy simulations The meaning of the individual contributions from component analysis. Proteins Str. Funct. Genet., 20 (1994) 25-33... 

J. Gao, K. Kuczera, B. Tldor, and M. Karplus. Hidden thermodynamics of mutant proteins A molecular dynamics analysis. Science, 244 1069-1072, 1989. 

Brunger, A. T., Karplus, M. Polar hydrogen positions in proteins Empirical energy placement and neutron diffraction comparison. Proteins Struct. Func. Genet. 4 (1988) 148-156. 

Bashford, D., Karplus, M. Multiple-site titration curves of proteins an analysis of exact and approximate methods for their calculation. J. Phys. Chem. 95 (1991) 9556-9561. 

For future reference, the Verlet algorithm [18] can be generalized to iticlude the friction and stochastic terms above, and is typically used in the following form described by Brooks, Briinger and Karplus, known as BBK [23, 37] ... 

M. Watanabe and M. Karplus. Dynamics of molecules with internal degrees of freedom by multiple time-step methods. J. Chem. Phys., 99 8063-8074, 1993. 

Brooks, B. R., Janezic, D., Karplus, M. Harmonic Analysis of Large Systems I. Methodology. J. Comput. Chem. 16 (1995) 1522-1542 Janezic, D., Brooks, B. R. Harmonic Analysis of Large Systems II. Comparison of Different Protein Models. J. Comput. Chem. 16 (1995) 1543-1553 Janezic, D., Venable, R. M., Brooks, B. R. Harmonic Analysis of Large Systems. HI. Comparison with Molecular Dynamics. J. Comput. Chem. 16 (1995) 1554-1566... 

Watanabe, M., Karplus, M. Dynamics of Molecules with Internal Degrees of Freedom by Multiple Time-Step Methods. J. Chem. Phys. 99 (1995) 8063-8074 Figueirido, F., Levy, R. M., Zhou, R., Berne, B. J. Large Scale Simulation of Macromolecules in Solution Combining the Periodic Fast Multiple Method with Multiple Time Step Integrators. J. Chem. Phys. 106 (1997) 9835-9849 Derreumaux, P., Zhang, G., Schlick, T, Brooks, B.R. A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications. J. Comp. Chem. 15 (1994) 532-555... 

Brooks III, C. L., Karplus, M., Pettitt, B. M. Proteins A Theoretical Perspective of Dynamics, Structure and Thermodynamics. Advances in Chemical Physics, vol. LXXI. John Wiley Sons, New York, 1988. 

Figure 5,30 reprinted from Chemical Physical Letters, 194, Fischer S and M Karplus. Conjugate Peak Refinement An Algorithm for Finding Reaction Paths and Accurate Transition States in Systems with Many Degrees of Freedom. 252-261, 1992, with permission from Elsevier Science. 

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