Response function self-consistent field

Olsen J and J0rgensen P 1995 Time-dependent response theory with applications to self-consistent field and multiconfigurational self-consistent field wave functions Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 857-990... 

J. Olsen and P. Jorgensen. Time-Dependent Response Theory with Applications to Self-Consistent Field and Multiconfigurational Self-Consistent Field Wave Functions, in Modern Electronic Structure Theory, edited by D. R. Yarkony, volume 2, chapter 13, pp. 857-990. World Scientific, Singapore, 1995. 

Interaction ofthe electrons in the framework of the self-consistent field approximation is accounted for by considering the induced density fluctuations as a response of independent particles to Oext + Poissons equation [2], This means, physically, that collective excitations of the electrons can occur, taken into account via a chain of electron-holeexcitations. These collective excitations show up in S(q, ) as a distinct energy loss feature. Figure 2 shows the shape of the real and imaginary parts of the dielectric function in RPA (er(q, ), Si(q, )) and the resulting dielectric response... 

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]. 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

Also in response theory the summation over excited states is effectively replaced by solving a system of linear equations. Spin-orbit matrix elements are obtained from linear response functions, whereas quadratic response functions can most elegantly be utilized to compute spin-forbidden radiative transition probabilities. We refrain from going into details here, because an excellent review on this subject has been published by Agren et al.118 While these authors focus on response theory and its application in the framework of Cl and multiconfiguration self-consistent field (MCSCF) procedures, an analogous scheme using coupled-cluster electronic structure methods was presented lately by Christiansen et al.124... 

Henne Hettema, Hans Jorgen Aa. Jensen, Poul Jorgensen, and Jeppe Olsen (1992). Quadratic response functions for a multi-configurational self-consistent-field wave-function. J. Chem. Phys. 97, 1174-1190. 

We start out with a section on the energy functionals and Hamiltonians that are relevant for molecular systems interacting with a structured environment. We continue with a section that briefly describes the correlated electron structure method, the multiconfigurational self-consistent field (MCSCF) electronic structure method. In the following section we cover the procedure for obtaining the correlated MCSCF response equations for the two different models describing molecules in structured environments. The final sections provide a brief overview of the results obtained using the two methods and a conclusion. 

Olsen, J., lorgcnsen, P. Time dependent response theory with appUcations in to self consistence field (SCF and multiconfigurational self consistent field (MCSCF) wave functions, l.F.A. PRINT, Aarhus Universitet, 1994... 

The present contribution concerns an outline of the response tlieory for the multiconfigurational self-consistent field electronic structure method coupled to molecular mechanics force fields and it gives an overview of the theoretical developments presented in the work by Poulsen et al. [7, 8, 9], The multiconfigurational self-consistent field molecular mechanics (MCSCF/MM) response method has been developed to include third order molecular properties [7, 8, 9], This contribution contains a section that describes the establisment of the energy functional for the situation where a multiconfigurational self-consistent field electronic structure method is coupled to a classical molecular mechanics field. The second section provides the necessary background for forming the fundamental equations within response theory. The third and fourth sections present the linear and quadratic, respectively, response equations for the MCSCF/MM response method. The fifth 283... 

At first sight these equations do not appear to be of any use since the simple response function is merely expressed in terms of a more complicated response function of the same kind involving [P, HqI However, it is possible to obtain a closed-form expression response function, as we shall see in the linear case. At the moment little is done to reformulate Eq. (51). Olsen and Jfirgensen (1985) have shown how the quadratic and the cubic response function can be evaluated using a multiconfigurational self-consistent field (MCSCF) reference state. 

J. Kongsted, A. Osted, K.V. Mikkelsen, O. Ghristiansen, The QM/MM Approach for Wavefunctions, Energies and Response Functions within Self-Consistent Field and Coupled Cluster Theories, Mol. Phys. 100 (2002) 1813 J. Kongsted, K. Aidas, K. V. Mikkelsen,... 

P. Jprgensen, H. Jensen, J. Olsen, Linear response calculations for large scale multiconfiguration self-consistent field wave functions, J. Chem. Phys. 89 (1988) 3654-3661. 

Quadratic response theory in combination with self-consistent field (SCF), MCSCF, and coupled-cluster electronic structure methods have been used for calculation of excitation energies and transition dipole moments between excited electronic states <2000PCP5357>. The excited state polarizabilities for r-tetrazine are given by the double residues of the cubic response functions <1997CPFl(224)201>. 

We start with a brief reminder of the theory of self-assembly in a selective solvent of non-ionic amphiphilic diblock copolymers. Here, the focus is on polymorphism of the emerging copolymer nanoaggregates as a function of the intramolecular hy-drophilic/hydrophobic balance. We then proceed with a discussion of the structure of micelles formed by block copolymers with strongly dissociating PE blocks in salt-free and salt-added solutions. Subsequently, we analyze the responsive behavior of nanoaggregates formed by copolymers with pH-sensitive PE blocks. The predictions of the analytical models are systematically complemented by the results of a molecularly detailed self-consistent field (SCF) theory. Finally, the theoretical predictions are compared to the experimental data that exist to date. 

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. 

---