Transformed equation-of-motion

A change of variables, from qi, pi ) to ( Qi, Pi ), is called a canonical transformation, if the transformed equations of motion have the same form as that given in equation 4,36, but with H = H( Qi, Pi )- In particular, if there exists a canonical transformation such that % = H Pi,P2,.., F ) only, then the equations... 

M. Nooijen and R. J. Bartlett,/. Chem. Phys., 107, 6812 (1997). Similarity-Transformed Equation-of-Motion Coupled-Cluster Theory Details, Examples, And Comparisons. 

Analogous to the previous treatments /69/ the Fourier transformed equation of motion of the dilated electron propagator may now be written as... 

Nooijen M, Bartlett RJ (1997) Similarity transformed equation-of-motion coupled-cluster theory Details, examples, and comparisons. J Chem Phys 107 6812-6830. 

Equilibrium time correlation function expressions for transport properties can be derived using linear response theory [3]. Linear response theory can be carried out directly on the Wigner transformed equations of motion to obtain the transport properties as correlation functions involving Wigner transformed quantities. Alternatively, we may carry out the linear response analysis in terms of abstract operators and insert the Wigner representation of operators in the final form for the correlation function. We use the latter route here. 

A similarity-transformed equation-of-motion coupled-cluster (STEOM-CC) study of excited states <1997JCP6812> has been applied to calculate the vertical excitation spectra and various 0-0 transitions of selected... 

Fig. 1 for planar and axisymmetric (cylindrical) propagation. These were obtained by analytic (planar case) or numerical (cylindrical case) solution of the similarity-transformed equations of motion. The similarity variable f = xjUcjt. The fluid returns to rest and forms an expanding zone of motionless fluid that extends over about one-half of the distance to which the detonation has progressed at any given time. The fluid state immediately behind the detonation wave is approxi-... 

Sous J, Goel P, Nooijen M. Similarity transformed equation of motion coupled cluster theory revisited a benchmark study of valence excited states. Mol Phys. 2013 112 616-638. Trofimov AB, Krivdina IL, Weller J, Schimer J. Algebraic-diagrammatic construction propagator approach to molecular response properties. Chem Phys. 2006 329 1-10. 

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. 

The symmetry-correct anion orbitals can also be utilized in calculations of states of the N03 cation. The primary purpose of this work is to examine the NO3 ionization spectrum and the ground and low excited states of the N03 cation system by the DIP-STEOM-CCSD method (40) (double ionization potential similarity transformed equation-of-motion coupled-cluster singles and doubles). The DIP-STEOM-CCSD method is built upon the IP-EOM-CCSD method (32) (ionization potential equation-of-motion coupled-cluster singles and doubles), which in turn, has been shown to be equivalent (41,42) to singly ionized FSMRCC, such as the example of Kaldor above. The DIP-STEOM-CCSD method generates ground and excited states of the cation by deletion of... 

Of the 33 invited speakers and the seven who contributed talks, 17 accepted our invitation to contribute a chapter to this book. These chapters are complemented by three additional chapters from individuals to help develop a more cohesive book as well as an overview chapter. Approximately half of the chapters are focused on the development of ab initio electronic structure methods and consideration of specific challenging molecular systems using electronic structure theory. Some of these chapters document the dramatic developments in the range of applicability of the coupled-cluster method, including enhancements to coupled-cluster wavefunctions based on additional small multireference configuration interaction (MR-CISD) calculations, the method of moments, the similarity transformed equation of motion (STEOM) method, a state-specific multireference coupled-cluster method, and a computationally efficient approximation to variational coupled-cluster theory. The concentration on the coupled-cluster approach is balanced by an approximately equal number of chapters discussing other aspects of modem electronic stracture theory. In particular, other methods appropriate for the description of excited electronic states, such as multireference... 

---