83. Wanko, M., Hoffmann, M., Fra ¨hmcke, J., Frauenheim, T., Elstner, M.: Effect of polarization
on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins. J. Phys. Chem.
B 112(11), 11468–11478 (2008)
84. Wanko, M., Hoffmann, M., Frauenheim, T., Elstner, M.: Effect of polarization on the opsin
shift in rhodopsins. I. A combined QM/QM/MM model for bacteriorhodopsin and pharaonis
sensory rhodopsin II. J. Phys. Chem. B 112, 11462–11467 (2008)
85. Luzhkov, V., Warshel, A.: Microscopic calculations of solvent effects on absorption spectra
of conjugated molecules. J. Am. Chem. Soc. 113, 4491–4499 (1991)
86. Thompson, M.A., Schenter, G.K.: Excited states of the bacteriochlorophyll b dimer of
rhodopseudomonas viridis: a QM/MM study of the photosynthetic reaction center that
includes MM polarization. J. Phys. Chem. 99, 6374–6386 (1995)
87. Gao, J., Alhambra, C.: Solvent effects on the bond length alternation and absorption energy of
conjugated compounds. J. Am. Chem. Soc. 119, 2962–2963 (1997)
88. Cui, Q., Guo, H., Karplus, M.: Combining ab initio and density functional theories with
semiempirical methods. J. Chem. Phys. 117, 5617–5631 (2002)
89. Hratchian, H.P., Parandekar, P.V., Raghavachari, K., Frisch, M.J., Vreven, T.: Qm:qm
electronic embedding using mulliken atomic charges: energies and analytic gradients in an
oniom framework. J. Chem. Phys. 128, 034,107 (2008)
90. Xie, W., Gao, J.: Design of a next generation force field: the X-POL potential. J. Chem.
Theory Comput. 3(6), 1890–1900 (2007)
91. Zhao, D.X., Liu, C., Wang, F.F., Yu, C.Y., Gong, L.D., Liu, S.B., Yang, Z.Z.: Development
of a polarizable force field using multiple fluctuating charges per atom. J. Chem. Theory
Comput. 6(3), 795–804 (2010)
92. Chelli, R., Procacci, P.: A transferable polarizable electrostatic force field for molecular
mechanics based on the chemical potential equalization principle. J. Chem. Phys. 117(20),
9175–9189 (2002)
93. Thole, B.: Molecular polarizabilities calculated with a modified dipole interaction. Chem.
Phys. 59, 341–350 (1981)
94. Anisimov, V.M., Lamoureux, G., Vorobyov, I.V., Huang, N., Roux, B., MacKerell, A.D.:
Determination of electrostatic parameters for a polarizable force field based on the classical
Drude oscillator. J. Chem. Theory Comput. 1(1), 153–168 (2005)
95. Drude, P.: The Theory of Optics. Dover, New York (1959)
96. Applequist, J., Carl, J.R., Fung, K.K.: An atom dipole interaction model for molecular
polarizability. Application to polyatomic molecules and determination of atom
polarizabilities. J. Am. Chem. Soc. 94(9), 2952–2960 (1972)
97. Cieplak, P., Caldwell, J., Kollman, P.: Molecular mechanical models for organic and
biological systems going beyond the atom centered two body additive approximation:
aqueous solution free energies of methanol and n-methyl acetamide, nucleic acid base, and
amide hydrogen bonding and chloroform/water partition coefficients of the nucleic acid
bases. J. Comput. Chem. 22(10), 1048–1057 (2001)
98. Ponder, J.W., Case, D.A.: Force fields for protein simulations. Adv. Protein Chem. 66, 27–85
(2003)
99. Ren, P., Ponder, J.W.: Polarizable atomic multipole water model for molecular mechanics
simulation. J. Phys. Chem. B 107, 5933–5947 (2003)
100. Ren, P.Y., Ponder, J.W.: Consistent treatment of inter- and intramolecular polarization in
molecular mechanics calculations. J. Comput. Chem. 23(16), 1497–1506 (2002)
101. Swart, M., van Duijnen, P.T.: Drf90: a polarizable force field. Mol. Simul. 32(6), 471–484
(2006)
102. Swart, M., Snijders, J.G., van Duinen, P.T.: Polarizabilities of amino acid residues.
J. Comput. Methods Sci. Eng. 4(1–2), 419–425 (2004)
103. Swart, M., Van Duijnen, P.T., Snijders, J.G.: A charge analysis derived from an atomic
multipole expansion. J. Comput. Chem. 22(1), 79–88 (2001)
4 Theoretical Methods
63
on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins. J. Phys. Chem.
B 112(11), 11468–11478 (2008)
84. Wanko, M., Hoffmann, M., Frauenheim, T., Elstner, M.: Effect of polarization on the opsin
shift in rhodopsins. I. A combined QM/QM/MM model for bacteriorhodopsin and pharaonis
sensory rhodopsin II. J. Phys. Chem. B 112, 11462–11467 (2008)
85. Luzhkov, V., Warshel, A.: Microscopic calculations of solvent effects on absorption spectra
of conjugated molecules. J. Am. Chem. Soc. 113, 4491–4499 (1991)
86. Thompson, M.A., Schenter, G.K.: Excited states of the bacteriochlorophyll b dimer of
rhodopseudomonas viridis: a QM/MM study of the photosynthetic reaction center that
includes MM polarization. J. Phys. Chem. 99, 6374–6386 (1995)
87. Gao, J., Alhambra, C.: Solvent effects on the bond length alternation and absorption energy of
conjugated compounds. J. Am. Chem. Soc. 119, 2962–2963 (1997)
88. Cui, Q., Guo, H., Karplus, M.: Combining ab initio and density functional theories with
semiempirical methods. J. Chem. Phys. 117, 5617–5631 (2002)
89. Hratchian, H.P., Parandekar, P.V., Raghavachari, K., Frisch, M.J., Vreven, T.: Qm:qm
electronic embedding using mulliken atomic charges: energies and analytic gradients in an
oniom framework. J. Chem. Phys. 128, 034,107 (2008)
90. Xie, W., Gao, J.: Design of a next generation force field: the X-POL potential. J. Chem.
Theory Comput. 3(6), 1890–1900 (2007)
91. Zhao, D.X., Liu, C., Wang, F.F., Yu, C.Y., Gong, L.D., Liu, S.B., Yang, Z.Z.: Development
of a polarizable force field using multiple fluctuating charges per atom. J. Chem. Theory
Comput. 6(3), 795–804 (2010)
92. Chelli, R., Procacci, P.: A transferable polarizable electrostatic force field for molecular
mechanics based on the chemical potential equalization principle. J. Chem. Phys. 117(20),
9175–9189 (2002)
93. Thole, B.: Molecular polarizabilities calculated with a modified dipole interaction. Chem.
Phys. 59, 341–350 (1981)
94. Anisimov, V.M., Lamoureux, G., Vorobyov, I.V., Huang, N., Roux, B., MacKerell, A.D.:
Determination of electrostatic parameters for a polarizable force field based on the classical
Drude oscillator. J. Chem. Theory Comput. 1(1), 153–168 (2005)
95. Drude, P.: The Theory of Optics. Dover, New York (1959)
96. Applequist, J., Carl, J.R., Fung, K.K.: An atom dipole interaction model for molecular
polarizability. Application to polyatomic molecules and determination of atom
polarizabilities. J. Am. Chem. Soc. 94(9), 2952–2960 (1972)
97. Cieplak, P., Caldwell, J., Kollman, P.: Molecular mechanical models for organic and
biological systems going beyond the atom centered two body additive approximation:
aqueous solution free energies of methanol and n-methyl acetamide, nucleic acid base, and
amide hydrogen bonding and chloroform/water partition coefficients of the nucleic acid
bases. J. Comput. Chem. 22(10), 1048–1057 (2001)
98. Ponder, J.W., Case, D.A.: Force fields for protein simulations. Adv. Protein Chem. 66, 27–85
(2003)
99. Ren, P., Ponder, J.W.: Polarizable atomic multipole water model for molecular mechanics
simulation. J. Phys. Chem. B 107, 5933–5947 (2003)
100. Ren, P.Y., Ponder, J.W.: Consistent treatment of inter- and intramolecular polarization in
molecular mechanics calculations. J. Comput. Chem. 23(16), 1497–1506 (2002)
101. Swart, M., van Duijnen, P.T.: Drf90: a polarizable force field. Mol. Simul. 32(6), 471–484
(2006)
102. Swart, M., Snijders, J.G., van Duinen, P.T.: Polarizabilities of amino acid residues.
J. Comput. Methods Sci. Eng. 4(1–2), 419–425 (2004)
103. Swart, M., Van Duijnen, P.T., Snijders, J.G.: A charge analysis derived from an atomic
multipole expansion. J. Comput. Chem. 22(1), 79–88 (2001)
4 Theoretical Methods
63