Multi-configuration linear response

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... 

Multi-configuration linear response approach cind random phase approximation... 

Quack and Stohner [63,64] used the multi-configuration linear response framework in the random phase approximation to compute relative frequency shifts for all vibrational degrees of freedom of CHBrClF. 

The parity violating potentials in alanine in gas phase and solution have been studied in [106] within the framework of the multi-configuration linear response approach. Several low-energy conformers of neutral alanine as well as the zwitterionic form have been studied therein and solvent effects on structures and, for the first time, also on parity violating potentials have been accounted for within a multi-configuration self-consistent reaction field approach on the RPA and the CASSCF level of theory. The main result of these higher level calculations was, that they provided no... 

AIMD = ab initio molecular dynamics B-LYP = Becke-Lee-Yang-Parr CVC = core-valence correlation DF = density functional LDA = local density approximation MCLR = multi-configurational linear response MP2 = Mpller-Plesset second order (MRD)CI = multi-reference double-excitation configuration interaction RPA = random phase approximation TD-MCSCF = time-dependent multi-configurational self-consistent field TD-SCF = time-depen-dent self-consistent field. 

The linear response methods offer a viable alternative to the Cl procedure. A time-dependent (TD) perturbation theory (e.g., involving an oscillating electric field) combined with the SCF or MCSCF method is referred to as the TD-SCF (or random phase approximation, RPA) or the TD-MCSCF (or multi-configurational linear response, MCLR), respectively (see Time-dependent Multiconfigurational Hartree Method). 

Carravetta V, Luo Y, Agren H. Accurate photoionization cross sections of diatomic molecules by multi-configuration linear response theory. Chem Phys. 1993 174 141-153. 

Recently, the response theory formalism was applied for the calculation of singlet-triplet spectra in polyenes and aromatic hydrocarbons [83,133,134,132]. In this section we shall discuss mainly the vertical Tn <— So transitions probability in polyenes. The minimum level of accuracy includes CAS calculations of the ground state correlating all x electrons followed by linear and quadratic multi-configuration response calculations. Because the ethene molecule is the simplest representative of unsaturated hydrocarbons, different types of active spaces and AO basis sets were tested more thoroughly for this molecule in order to study the convergence of the S-T transition probability with respect to the level of accuracy. 

Both transition energies and oscillator strengths are needed for determination of optically allowed absorption spectra. In the multi-configuration version of the linear response theory (MCLR) one constructs an approximation to the exact linear response function by exposing the optimized (MC) SCF wavefunction 0> to a time-dependent perturbation. In this case the time-dependent wave function assumes the form... 

Another category of approaches that avoids the symmetry breaking problem of the orbitals for the target state is based on using a related, well-behaved HF reference instead. Examples of such techniques include quasi-restricted Hartree-Fock coupled-cluster (QRHF CC) (11,19), symmetry adapted cluster configuration interaction (SAC-CI) (22,23), coupled-cluster linear response theory (CCLRT) (24-26) or equivalently equation-of-motion coupled-cluster (EOM-CC) (27-32), Fock space multi-reference coupled-cluster (FSMRCC) (33-37), and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) (38-40). In the case of NO3 and N03, the restricted Hartree-Fock (RHF) orbitals of the closed-shell N03 anion system can be used as the reference. The anion orbitals are stable with respect to symmetry perturbations, and the system does not suffer from the artifactual symmetry breaking of the neutral and cation. 

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