Tamm—Dancoff approximation

The matrix Bis numerically much less important than A and accordingly y << x. This suggests a simplification of the foregoing equations by setting B = 0. This Tamm-Dancoff approximation [11] leads to a symmetric matrix eigenvalue equation... 

The corrected Linear Response approach (cLR) consists in the use the TDDFT relaxed density and the corresponding apparent charges (7-38) into Eqs. (7-36) and (7-37) to obtain the first-order approximation to the state specific free energy of the excited state. The details of the implementation are described in Ref. [17], This corrected Linear Response computational scheme can be applied to the analogous of the Time Dependent Hartree-Fock approach either in the complete (Random Phase Approximation) or approximated (Tamm-Dancoff approximation or Cl singles, CIS) version. 

As it is not possible to obtain TDDFT-SS results, the results refer to CIS method. In fact, this method can be obtained from two points of view one is to consider the method as a standard Cl, in which the wave function of the excited state is constructed by single excitations from the HF determinant and thus a SS solvent response can be obtained the other is to consider CIS as the result of the Tamm-Dancoff approximation applied to the linear response equation based on the HF wave function. The two ways of looking at the CIS method give the same equations in vacuo, but, as discussed above, they differ for molecules in solution due to the nature of the effective Hamiltonian. 

It is important to note, that for the accurate estimation of spectral intensities of the theoretical spectra it is not sufficient to consider only the lowest order processes. A sufficiently accurate yet relative simple computational scheme is the two-particle-hole Tamm-Dancoff approximation [36]. E>ue to the difficulties and complications involved in the computations there are only few such studies [32-35]. The majority of the authors use a simplified model for the estimation of the ionization energies, based on one of the following approximations ... 

J. Hutter (2003) Excited state nuclear forces from the Tamm-Dancoff approximation to time-dependent density functional theory within the plane wave basis set framework. J. Chem,. Phys. 118, p. 3928... 

FOCI - first-order configuration interaction. Outer valence Green s function. Extended two-particle-hole Tamm-Dancoff approximation. 

Obviously, those are the same considerations as we went through in order to obtain Eqs (90) and (91) and the electron propagator method and the ADC are thus equivalent methods. Using n = 2 in Eq. (93) we determine and n — 3 gives The U matrix in Eq. (93) corresponds to the transition matrix (cf. Eq. (75)). Both and only contain C and D terms (see Eqs (87), (88), (90) and (91), i.e. hj = hj alone. From Eq. (63) we see that we may classify the operators in hj as 2p-lh (two-particle, one-hole) and 2h-lp operators, and the n = 3 ADC approach, corresponding to the third-order electron propagator method, is therefore referred to as the extended 2p-lh Tamm-Dancoff approximation (TDA) (Walter and Schirmer, 1981). A fourth-order approximation to the ADC equations has also been described (Schirmer et ai, 1983) but not yet tested in actual applications. 

AGPTDA antisyrametrized geminal power Tamm-Dancoff approximation (Section VII. C),... 

Liu J, Liang W (2011) Analytical Hessian of electronic excited states in time-dependent density functional theory with Tamm-Dancoff approximation. J Chem Phys 135 014113... 

In case of LR-TDDFT, the forces on the nuclei are derived within the Tamm-DancofF approximation [36,37] from nuclear derivatives of the excited-state energies using the extended Lagrangian formalism introduced by Hutter [34], In general, LR-TDDFT MD simulations are about 70-90 times faster than P-TDDFT MD simulations. The LR-TDDFT scheme has also been combined with our QM/MM approach [38,39] in order to enable the calculation of excitation spectra [40-42] and excited-state dynamics in condensed-phase systems. 

SAOP functional, all-electron calculation, COSMO spin-flip transitions have been calculated within the Tamm-Dancoff approximation. 

This has been called the Tamm-Dancoff approximation [104] and corresponds to singly excited Cl in the reference Hartree-Fock orbitals. Adding de-excitation operators to obtain the full operator App (ft)) one obtains the random-phase... 

In the following it will be outlined, how the parity violating potentials are computed within a sum-over-states approach, namely on the uncoupled Hartree-Fock (UCHF) level, and within the configuration interaction singles approach (CIS) which is equivalent to the Tamm-Dancoff approximation (TDA), that avoids, however, the sum over intermediate states. Then a further extension is discussed, namely the random phase approximation (RPA) and an implementation along similar lines within a density functional theory (DFT) ansatz, and finally a multi-configuration linear response approach is described, which represents a systematic procedure that... 

The equivalent Tamm-Dancoff approximation, for which also 0rhf) represents the reference state, is obtained, if first all terms involving a state transfer operator are omitted, while those that include excitation operators are retained. Therefore, only the elements An and Bn of the generalised Hessian matrix (126) survive. Second, the contribution of jBh, which gives rise to terms that involve double excitations with respect to the RHF reference state, is omitted. Here again, the explicit construction of the intermediate states can be avoided. 

The RPA, together with a simpler variant, the so-called Tamm-Dancoff Approximation, is now used in all forms of many-body theories (nuclear, solid state and molecular) in a wide variety of notations and formulations. It is an interesting exercise to consult these publications and contrast the notation and techniques used in this area with the ones used in this work. In this respect the book The nuclear many-body problem by P. Ring and P. Schuck (Springer-Verlag, 1980) might prove a useful starting point. 

The FOSEP approximation has to be compared with two other well-known first order approximation schemes, the Tamm-Dancoff approximation (TDA) [11,30] and the random phase approximation (RPA) [31,32,11,30]. The TDA leads to a hermitian eigenvalue problem of half the dimension of FOSEP. In fact the upper left (ph-ph) block of the FOSEP matrix coincides with... 

---