Response theory

Linear response theory is an example of a microscopic approach to the foundations of non-equilibrium thennodynamics. It requires knowledge of tire Hamiltonian for the underlying microscopic description. In principle, it produces explicit fomuilae for the relaxation parameters that make up the Onsager coefficients. In reality, these expressions are extremely difficult to evaluate and approximation methods are necessary. Nevertheless, they provide a deeper insight into the physics. 

The usual context for linear response theory is that the system is prepared in the infinite past, —> -x, to be in equilibrium witii Hamiltonian H and then is turned on. This means that pit ) is given by the canonical density matrix... 

Poul Jorgensen [13] has been involved in developing such so-called response theories for perturbations that may be time dependent (e.g. as in the interaction of light s electromagnetic radiation). 

Olsen J and J0rgensen P 1995 Time-dependent response theory with applioations to self-oonsistent field and multioonfigurational self-oonsistent field wave funotions Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Soientifio) pp 857-990... 

Holian B L and Evans D J 1985 Classical response theory in the Heisenberg pictured. Chem. Phys. 83 3560-6... 

We first examine the reiationship between particie dynamics and the scattering of radiation in the case where both the energy and momentum transferred between the sampie and the incident radiation are measured. Linear response theory aiiows dynamic structure factors to be written in terms of equiiibrium flucmations of the sampie. For neutron scattering from a system of identicai particies, this is [i,5,6]... 

The first-order term in this expansion renormalizes the potential V Q) while the bilinear term is analogous to the last term in (5.38). This is the linear-response theory for the bath. In fact, it shows... 

When the MFA is used in absence of the external field (J,- = 0) the Lagrange multipliers //, are assumed to give the actual density, p, known by construction. In presence of the field the MFA gives a correction Spi to the density p,. By using the linear response theory we can establish a hnear functional relation between J, and 8pi. The fields Pi r) can be expressed in term of a new field 8pi r) defined according to Pi r) = pi + 8pi + 8pi r). Now, we may perform a functional expansion of in terms of 8pi f). If this expansion is limited to a quadratic form in 8pj r) we get the following result [32]... 

Dispersion coefficients for second hyperpolarizabilities using coupled cluster cubic response theory... 

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. 

When the linear response theory is applied to electric conductivity in an ionic melt, the total charge current J t) can be defined as... 

Saue and Jensen used linear response theory within the random phase approximation (RPA) at the Dirac level to obtain static and dynamic dipole polarizabilities for Cu2, Ag2 and Au2 [167]. The isotropic static dipole polarizability shows a similar anomaly compared with atomic gold, that is, Saue and Jensen obtained (nonrelativ-istic values in parentheses) 14.2 for Cu2 (15.1 A ), 17.3 A for Ag2 (20.5 A ), and 12.1 A for Au2 (20.2 A ). They also pointed out that relativistic and nonrelativistic dispersion curves do not resemble one another for Auz [167]. We briefly mention that Au2 is metastable at 5 eV with respect to 2 Au with a barrier to dissociation of 0.3 eV [168, 169]. 

More recently, Filatov has developed a Unear response theory for the isomer shift and used it in conjunction with ab initio methods [71-73]. In many respects, this theory is more rigorous than the cahbration approach described earlier. Hence, it will be briefly outhned here. Filatov considered a linear response treatment in which the perturbation was taken as the radial expansion of a finite sized nucleus. The resulting equation for the isomer shift is ... 

Casida, M. E., 1995, Time Dependent Density Functional Response Theory for Molecules in Recent Advances in Density Functional Methods, Part I, Chong, D. P. (ed.), World Scientific, Singapore. 

Casida, M. E., Jamorski, C., Casida, K. C., Salahub, D. R., 1998, Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory Characterization and Correction of the Time-Dependent Local Density Approximation Ionization Threshold , J. Chem. Phys., 108, 4439. 

This correlation can be quantitatively accounted for on the basis of the linear response theory and the RPA... 

It can be shown that the assumption of a weak perturbation central to linear response theory can be relaxed in this case [9]. The equations presented in this section relating the kinetic coefficients with the microscopic dynamics of the system remain valid for arbitrarily strong perturbations. 

Linear Response Theory and Free Energy Calculations... 

The dielectric response of a solvated protein to a perturbing charge, such as a redox electron or a titrating proton, is related to the equilibrium fluctuations of the unperturbed system through linear response theory [49, 50]. In the spirit of free energy... 

Linear Response Theory Application to Proton Binding and )Ka Shifts... 

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