Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states.

@article{Sharma2015MultireferenceLC,
  title={Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states.},
  author={Sandeep Sharma and Ali Alavi},
  journal={The Journal of chemical physics},
  year={2015},
  volume={143 10},
  pages={
          102815
        }
}
We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two… 
Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory.
We present two efficient and intruder-free methods for treating dynamic correlation on top of general multiconfiguration reference wave functions - including such as obtained by the density matrix
Externally-Contracted Multireference Configuration Interaction Method Using a DMRG Reference Wave Function.
TLDR
The DMRG-ec-MRCI method is promising for dealing with a larger active space than 30 orbitals and large basis sets because of high computation and storage costs of high-order reduced density matrices (RDMs) and the crucial dependence of the MRCI Hamiltonian dimension on the number of virtual orbitals.
Multi-state local complete active space second-order perturbation theory using pair natural orbitals (PNO-MS-CASPT2).
A multistate complete active space second-order perturbation theory (CASPT2) method is presented, which utilizes domains of pair natural orbitals and projected atomic orbitals for the virtual space
Multireference Approaches to Spin‐State Energetics of Transition Metal Complexes Utilizing the Density Matrix Renormalization Group
The accurate and reliable calculation of different electronic states in transition metal systems is a persistent challenge for theoretical chemistry. The widespread use of density functional theory
REMP: A hybrid perturbation theory providing improved electronic wavefunctions and properties.
TLDR
REMP is shown to fulfill all required fundamental boundary conditions of proper wavefunction based quantum chemical methods (unitary invariance and size consistency) and shows equal performance as the best coupled pair approaches or pCCSD methods as well as thebest double hybrid density functionals.
Matrix Product States with Large Sites.
TLDR
It is explained how a generic cluster MPS can often lead to an increase in computational cost and instead a special cluster structure is proposed, involving only the first and last orbitals/sites, with a wider scope for computational advantage.
Post-Density Matrix Renormalization Group Methods for Describing Dynamic Electron Correlation with Large Active Spaces.
TLDR
This work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods, and classification into two main categories depending on whether high-order n-electron reduced density matrices are used.
Perturbation Theories Based on the Density Matrix Renormalization Group
TLDR
This thesis presents a combination of the DMRG and the strongly-contracted variant of second order N -electron valence state perturbation theory (SC-NEVPT2) that uses an efficient algorithm to compute high order reduced density matrices from D MRG wave functions.
The combination of multipartitioning of the Hamiltonian with canonical Van Vleck perturbation theory leads to a Hermitian variant of quasidegenerate N-electron valence perturbation theory.
TLDR
The result is a Hermitian variant of multipartitioning quasidegenerate N-electron valence state perturbation theory, which is shown to give good results for the calculation of electronic transitions of the [CuCl4]2 -complex and of electron paramagnetic resonance parameters, which are two examples where the balance between ligand field and charge transfer configurations is of utmost importance.
N-Electron Valence State Perturbation Theory Based on a Density Matrix Renormalization Group Reference Function, with Applications to the Chromium Dimer and a Trimer Model of Poly(p-Phenylenevinylene).
TLDR
A combination of the DMRG and strongly contracted NEVPT 2 (DMRG-SC-NEVPT2) is presented that uses an efficient algorithm to compute high-order reduced-density matrices from D MRG wave functions.
...
...

References

SHOWING 1-10 OF 66 REFERENCES
High-performance ab initio density matrix renormalization group method: applicability to large-scale multireference problems for metal compounds.
TLDR
The authors have found that a large number of renormalized basis states are required to represent high entanglement of the electron correlation for metal compound applications, and it is crucial to adopt auxiliary perturbative correction to the projected density matrix during the DMRG sweep optimization in order to attain proper convergence to the solution.
Higher excitations in coupled-cluster theory
The viability of treating higher excitations in coupled-cluster theory is discussed. An algorithm is presented for solving coupled-cluster (CC) equations which can handle any excitation. Our method
The CIPT2 method: Coupling of multi-reference configuration interaction and multi-reference perturbation theory. Application to the chromium dimer
The potential energy function of is computed using the MRCI+Q (multi-reference configuration interaction with Davidson correction) and CASPT2 (complete active space second-order multi-reference
Large-scale parallel uncontracted multireference-averaged quadratic coupled cluster: the ground state of the chromium dimer revisited.
  • T. Müller
  • Physics
    The journal of physical chemistry. A
  • 2009
TLDR
A detailed basis set study of the potential energy function of the X1Sigmag+ state of Cr2 is presented, adopting a variational method, and relevant details on implementation and general performance of the parallel program code are discussed.
A review of canonical transformation theory
TLDR
It is argued that many multireference dynamic correlation methods display unsatisfactory characteristics, including lack of size-consistency, a low-order treatment of correlation, and a poor computational scaling, and CT theory is based on an exponential ansatz that is rigorously size- Consistent.
Third-order multireference perturbation theory The CASPT3 method
Rayleigh-Schrodinger perturbation theory is applied to compute second and third-order correlation energies using complete active space self-consistent field (CASSCF) zeroth-order wavefunctions. The
Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.
TLDR
The joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry provides the ability to describe static correlation in large active spaces, and provides a high-order description of the dynamic correlation effects.
Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.
TLDR
The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals and addressed the problems of why the dissociation energy is largely overestimated by CASPT2, and also is oversensitive to the choice of the zeroth-order Hamiltonian.
Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly.
TLDR
The internally contracted multireference coupled cluster (icMRCC) method allows a highly accurate description of both static and dynamic correlation with a computational scaling similar to single reference coupled cluster theory and is in excellent agreement with CCSDTQ.
Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states.
TLDR
A formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS) and can be used to compute the third order energy with little overhead.
...
...