Linear-response methods

Where C/bOUnd represents the interaction energy between the drug and the enzyme and Uunboun i is the corresponding term in solution. The superscripts elec and vdw refer to the electrostatic and van der Waals components and the 

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Carlson, H. A., Jorgensen, W. L. An extended linear response method for determining free energies of hydration. J. Phys. Chem. 99 (1995) 10667-10673... 

Appendix 11.3 Expansion of Zwanzig Expression for the Free Energy Difference for the Linear Response Method... 

Carlson H A and W L Jorgensen 1995. An Extended Linear Response Method for Determining Free Energies of Hydration. Journal of Physical Chemistry 99 10667-10673. 

Jones-Hertzog D K and W L Jorgensen 1997. Binding Affinities for Sulphonamide Inhibitors witl Human Thrombin Using Monte Carlo Simulations with a Linear Response Method. Journal o Medicinal Chemistry 40 1539-1549. 

X Chen, A Tropsha. A generalized linear response method Application to the hydration free energy calculations. J Comput Chem 20 749-759, 1999. 

RH Smith Jr, WL Jorgensen, J Tirado-Rives, ML Lamb, PAJ Janssen, CJ Michejda, MBK Smith. Prediction of binding affinities for TIBO inhibitors of HIV-1 reverse transcriptase using Monte Carlo simulations m a linear response method. J Med Chem 41 5272-5286, 1998. 

Jones-Hertzog, D.K. Jorgensen, W.L., Binding affinities for sulfonamide inhibitors with human thrombin using Monte Carlo simulations with a linear response method, J. Med. Chem. 1997, 40, 1539-1549... 

Lamb, M.L. Tirado-Rives, J. Jorgensen, W.L., Estimation of the binding affinities of FKBP12 inhibitors using a linear response method, Bioorg. Med. Chem. 1999, 7, 851-860... 

H. A. Carlson and W. L Jorgensen, An extended linear response method for determining... 

FKBP12 inhibitors using a linear response method, Bioorg. Med. Chem 7 851 (1999). 

Calculations of Dipole and Quadrupole Polarizability Radial Functions for LiH and HF A Comparison of Different Linear Response Methods... 

The article is organized as follows. The main features of the linear response theory methods at different levels of correlation are presented in Section 2. Section 3 describes the calculation of the dipole and quadmpole polarizabilities of two small diatomic molecules LiH and HF. Different computational aspects are discussed for each of them. The LiH molecule permits very accurate MCSCF studies employing large basis sets and CASs. This gives us the opportunity to benchmark the results from the other linear response methods with respect to both the shape of the polarizability radial functions and their values in the vibrational ground states. The second molecule, HF, is undoubtedly one of the most studied molecules. We use it here in order to examine the dependence of the dipole and quadmpole polarizabilities on the size of the active space in the CAS and RASSCF approaches. The conclusions of this study will be important for our future studies of dipole and quadmpole polarizabilities of heavier diatomic molecules. 

He also investigated the dependence of the properties on the internuclear distance in the vicinity of the equilibrium internuclear separation R. However, our goal was not to look for the most accurate values or to compare with them, but to study the performance of various linear response methods. In particular we wanted to find out which level of correlation is necessary in order to reproduce the correct dependence on the internuclear distance for a wider range of R. In Fig. 6, it can be seen that the CCSD dipole polarizability curve is sufficiently close to the results of the calculations. The SOPPA... 

Fig. 6. HF dipole polarizability tensors (in atomic units) calculated by different linear response methods in comparison with MCSCF method.

SOPPA(CCSD) calculations with the CCSD or MCSCF PEC are also larger. In general the differences in the ZPVC are larger between the different PEC than between the different linear response methods. The SOPPA(CCSD) results for the equilibrium geometry as well as the vibrationally averaged polarizabilities are in both molecules in better agreement with the MCSCF results than the pure SOPPA values. 

Calculation of rotational and vibrational g factors by linear response methods using multiconfigurational self-consistent-field wave functions is described in detail elsewhere [18,27]. 

In the self-consistent field linear response method [25,46,48] also known as random phase approximation (RPA) [49] or first order polarization propagator approximation [25,46], which is equivalent to the coupled Hartree-Fock theory [50], the reference state is approximated by the Hartree-Fock self-consistent field wavefunction < scf) and the set of operators /i j consists of single excitation and de-excitation operators with respect to orbital rotation operators [51],... 

The theory of wideband complex permittivity of water described in the review drastically differs from the empirical double Debye representation [17, 54] of the complex permittivity given for water by formula (280b). Evolution of the employed potential profiles, in which a dipole moves, explored by a dynamic linear-response method can be illustrated as follows ... 

At a given computational level, the solvent relaxation contribution to the excitation energy may be approximated by using two basically different methods, the state-specific method (SS) and the linear response method (LR), depending on the QM methodology used. This directly involves the problem of extending the PCM basic model to a QM description proper for excited states. 

R. Cammi, S. Comi, B. Mennucci, J. Tomasi, Electronic excitation energies of molecules in solution State specific and linear response methods for nonequilibrium continuum solvation models. J. Chem. Phys. 122, 104513 (2005)... 

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