Self-consistent field molecular gradients

Proton-transfer reactions of iV-tetrachlorosalicylideneaniline (140) and N-tetrachlorosalicylideneaniline-l-pyrenylamine (171) have been investigated by using a semiempirical self-consistent field molecular orbital (SCF MO) method with an energy gradient technique.94 From the calculated potential barriers (81.27 and 87.30kJmol-1) for 140 and 171, respectively, it can be seen that the... 

Figure 4.12. The interfacial profile predicted by self-consistent field theory for an interface between highly incompatible polymers of hi relative molecular masses. The bold line is the self-consistent field solution of equation (4.3.10), whereas the finer line is the function 0a(z) 0.5 1 + Erf [zv /(2wi)], which has the same gradient at 2 = 0 as tiiat of the tanh profile.

AIMD = ab initio molecular dynamics B-LYP = Becke-Lee-Yang-Parr CCSD = coupled cluster single double excitations CVC = core-valence correlation ECP = effective core potential DF = density functional GDA = gradient corrected density approximation MCLR = multiconfigurational linear response MP2 = M0ller-Plesset second-order (MRD)CI = multi-reference double-excitation configuration interaction RPA = random phase approximation TD-MCSCF = time-dependent multiconfigurational self-consistent field TD-SCF = time-dependent self-consistent field. 

In simple terms, eqn [52] are diffusion equations in the component densities, which take into account the noise in the system. Dynamics of the molecular ensemble is based on the assumption that for each type of site a the local flux is proportional to the local site concentration 4> . At equilibrium, = constant, which results in the familiar self-consistent field equations for an inhomogeneous polymer system. When the system is not in equilibrium, the negative gradient -V/i,j(r) represents an effective thermodynamic force that drives collective relaxation processes. The time integration of eqn [52] generates an ensemble of density fields with the Boltzmann distribution. 

Having seen how the evaluation of energy derivatives for fully variational wavefunctions is simplified by the 2n -i- 1 rule, let us now consider the molecular gradient for the simplest model of ab initio theory - the self-consistent field (SCF) model. We will see that, although the result for fully variational wavefunctions (equation 18) may be applied also to SCF energies, we cannot do this without first considering carefully the functional form of the energy expression. With minor modifications, the formalism presented here may be applied also to density-functional theory (DFT). 

Basis Sets Correlation Consistent Sets Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field G2 Theory Geometry Optimization 1 Gradient Theory Inter-molecular Interactions by Perturbation Theory Molecular Magnetic Properties NMR Chemical Shift Computation Ab Initio NMR Chemical Shift Computation Structural Applications Self-consistent Reaction Field Methods Spin Contamination. 

The next five chapters are each devoted to the study of one particular computational model of ab initio electronic-structure theory Chapter 10 is devoted to the Hartree-Fock model. Important topics discussed are the parametrization of the wave function, stationary conditions, the calculation of the electronic gradient, first- and second-order methods of optimization, the self-consistent field method, direct (integral-driven) techniques, canonical orbitals, Koopmans theorem, and size-extensivity. Also discussed is the direct optimization of the one-electron density, in which the construction of molecular orbitals is avoided, as required for calculations whose cost scales linearly with the size of the system. 

In 1996, Munn extended the microscopic theory of bulk second-harmonic generation from molecular crystals to encompass magnetic dipole and electric quadrupole effects [96] and included all contributions up to second order in the electric field or bilinear in the electric field and the electric field gradient or the magnetic field. This was accomplished by replacing the usual polarization of Refs. 72 and 84 by an effective polarization as well as by defining an effective quadrupole moment. Consequently, the self-consistently evaluated local electric field and electric field gradient were expressed in terms of various molecular response coefficients and lattice multipole tensor sums (up to octupole). In this... 

While this result confirmed the feasibility of the general approach, it did not precipitate wider exploration of dielectric medium effects. Recently, however, Wiberg et al. have incorporated the Onsager self-consistent reaction-field model into ab initio MO theory in an implementation which provides analytical gradients and second derivatives. The model considers just the dipole of the solute molecules and a spherical cavity whose radius is chosen for a given solute molecule from the molecular volume estimated at the 0.001 eB electron-density contour (B is the Bohr radius), plus an empirical constant 0.5 A to account for the nearest approach of solvent molecules [164]. Cieplak and Wiberg have used this model to probe solvent effects on the transition states for nucleophilic additions to substituted acetaldehydes [165]. For each... 

---