State-Specific Multi-Reference Coupled Cluster Formulations: Two Paradigms

Mahapatra, Uttam Sinha; Datta, B. P.; Bandyopadhyay, Barun; Mukherjee, Debashis

doi:10.1016/s0065-3276(08)60507-9

Cited by 197 publications

(203 citation statements)

References 73 publications

Supporting

Mentioning

203

Contrasting

Order By: Relevance

“…8 IC, now widely used in MR theories 7,9,41,[51][52][53] aggressively truncates the many body basis and reduces the cost of the calculation from exponential to merely polynomial in the number of active space orbitals. The difficulty with IC is that the working equations become extremely cumbersome and can often only be derived using domain specific computer algebra systems.…”

Section: Parameterizing Dynamic Correlation: Problems and Solutionsmentioning

confidence: 99%

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Sharma

Knizia

Guo

et al. 2017

J. Chem. Theory Comput.

View full text Add to dashboard Cite

We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration reference wave functions-including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multi-reference linearized coupled cluster method (MRLCC) [S. Sharma, A. Alavi, J. Chem. Phys. 143, 102815 (2015)], and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first-order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr2, pentacene and oxo-Mn(Salen), we shown that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation -calculating second order instead of third order energy corrections, use of internal contraction and approximations made in the reference wavefunction due to DMRG.

show abstract

Section: Parameterizing Dynamic Correlation: Problems and Solutionsmentioning

confidence: 99%

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Sharma

Knizia

Guo

et al. 2017

J. Chem. Theory Comput.

View full text Add to dashboard Cite

show abstract

“…Recently we have developed a rigorously size-consistent state-specific multi-reference coupledcluster (SS-MRCC) theory [9,10] involving a CAS, which is designed to bypass the intruder problem. The pilot numerical applications of the formalism gave very encouraging results for electronic states possessing varying degrees of quasi-degeneracy and avoided crossings [10,11], which indicate its efficacy and viability.…”

Section: Introductionmentioning

confidence: 99%

“…It should be mentioned here that there are non-perturbative state-specific methods as well with frozen coefficients [9,32], which are explicitly size-extensive.…”

Section: Introductionmentioning

confidence: 99%

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

Ghosh

Chattopadhyay

Jana

et al. 2002

IJMS

Self Cite

View full text Add to dashboard Cite

We present in this paper two new versions of Rayleigh-Schrödinger (RS) and the Brillouin-Wigner (BW) state-specific multi-reference perturbative theories (SS-MRPT) which stem from our state-specific multi-reference coupled-cluster formalism (SS-MRCC), developed with a complete active space (CAS). They are manifestly sizeextensive and are designed to avoid intruders. The combining coefficients c µ for the model functions φ µ are completely relaxed and are obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of interest. By invoking suitable partitioning of the hamiltonian, very convenient perturbative versions of the formalism in both the RS and the BW forms are developed for the second order energy. The unperturbed hamiltonians for these theories can be chosen to be of both Mφller-Plesset (MP) and Epstein-Nesbet (EN) type. However, we choose the corresponding Fock operator f µ for each model function φ µ , whose diagonal elements are used to define the unperturbed hamiltonian in the MP partition. In the EN partition, we additionally include all the diagonal direct and exchange ladders. Our SS-MRPT thus utilizes a multi-partitioning strategy. Illustrative numerical applications are presented for potential energy surfaces (PES) of the ground ( 1 Σ + ) and the first delta ( 1 ∆) states of CH + which possess pronounced multi-reference character. Comparison of the results with the corresponding full CI values indicates the efficacy of our formalisms.

show abstract

“…In internally contracted multireference coupled cluster (ic-MRCC) theory, [1][2][3][4][5] the wave function is written as an exponential wave operator acting on a multideterminantal reference function,…”

mentioning

confidence: 99%

“…3. A similar procedure is employed in the related internally contracted multireference configurationinteraction method.…”

mentioning

confidence: 99%

Communication: Restoring full size extensivity in internally contracted multireference coupled cluster theory

Hanauer

Köhn

2012

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

State-Specific Multi-Reference Coupled Cluster Formulations: Two Paradigms

Cited by 197 publications

References 73 publications

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

Communication: Restoring full size extensivity in internally contracted multireference coupled cluster theory

Contact Info

Product

Resources

About