A hybrid stochastic-deterministic approach for computing the second-order perturbative contribution $E^{(2)}$ within multireference perturbation theory (MRPT) is presented. The idea at the heart of our hybrid scheme --- based on a reformulation of $E^{(2)}$ as a sum of elementary contributions associated with each determinant of the MR wave function --- is to split $E^{(2)}$ into a stochastic and a deterministic part. During the simulation, the stochastic part is gradually reduced by dynamically increasing the deterministic part until one reaches the desired accuracy. In sharp contrast with a purely stochastic MC scheme where the error decreases indefinitely as $t^{-1/2}$ (where $t$ is the computational time), the statistical error in our hybrid algorithm displays a polynomial decay $\sim t^{-n}$ with $n=3-4$ in the examples considered here. If desired, the calculation can be carried on until the stochastic part entirely vanishes. In that case, the exact result is obtained with no error bar and no noticeable computational overhead compared to the fully-deterministic calculation. The method is illustrated on the F$_2$ and Cr$_2$ molecules. Even for the largest case corresponding to the Cr$_2$ molecule treated with the cc-pVQZ basis set, very accurate results are obtained for $E^{(2)}$ for an active space of (28e,176o) and a MR wave function including up to $2 \times 10^7$ determinants.

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Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory

The recently proposed approach to multireference dynamic correlation energy based on the adiabatic connection (AC) is extended to an arbitrary spin symmetry of the reference state. We show that bot...

Capturing the Dynamic Correlation for Arbitrary Spin-Symmetry CASSCF Reference with Adiabatic Connection Approaches: Insights into the Electronic Structure of the Tetramethyleneethane Diradical.

The Distinguishable Cluster (DC) approximation to the coupled cluster (CC) doubles, proposed by Kats and Manby [J. Chem. Phys. 139, 021102 (2013)], can semiquantitatively describe multiple bond dissociation (which is traditionally considered a paradigm of strongly correlated electronic structure methods based on the multideterminant approach) without leaving the single-reference coupled cluster framework. DC is just one of many internally corrected (CC) methods that improve on the parent CC method by approximation. To build on the success of the DC methods, it is important to probe whether they can be systematically improved. To answer this question, we considered a set of methods in the distinguishable cluster family, culminating in the DC singles, doubles, and triples (DCSDT), a DC modification of the parent CC singles, doubles, and triples that maintains exactness for 3-electron systems. Inclusion of the complete treatment of triples leads to systematic improvement over the DCSD for equilibrium correlation energy estimates. However, this improvement is not matched by enhanced accuracy for multiple bond breaking processes.

Can the distinguishable cluster approximation be improved systematically by including connected triples

Modified coupled-cluster (CC) methods such as linearized coupled-cluster doubles (LinCCD), approximate coupled pair (ACP D14), 2CC (from nCC family), parameterized CCSD (pCCSD) and distinguishable ...

Behind the success of modified coupled-cluster methods: addition by subtraction

A central difficulty of state-specific Multi-Reference Coupled Cluster (MR-CC) formalisms concerns the definition of the amplitudes of the single and double excitation operators appearing in the exponential wave operator. If the reference space is a complete active space (CAS) the number of these amplitudes is larger than the number of singly and doubly excited determinants on which one may project the eigenequation, and one must impose additional conditions. The present work first defines a state-specific reference-independent operator $\hat{\tilde{T}}^m$ which acting on the CAS component of the wave function $|\Psi_0^m \rangle$ maximizes the overlap between $(1+\hat{\tilde{T}}^m)|\Psi_0^m \rangle$ and the eigenvector of the CAS-SD CI matrix $|\Psi_{\rm CAS-SD}^m \rangle$. This operator may be used to generate approximate coefficients of the Triples and Quadruples, and a dressing of the CAS-SD CI matrix, according to the intermediate Hamiltonian formalism. The process may be iterated to convergence. As a refinement towards a strict Coupled Cluster formalism, one may exploit reference-independent amplitudes provided by $(1+\hat{\tilde{T}}^m)|\Psi_0^m \rangle$ to define a reference-dependent operator $\hat{T}^m$ by fitting the eigenvector of the (dressed) CAS-SD CI matrix. The two variants, which are internally uncontracted, give rather similar results. The new MR-CC version has been tested on the ground state potential energy curves of 6 molecules (up to triple-bond breaking) and a two excited states. The non-parallelism error with respect to the Full-CI curves is of the order of 1 m$E_{\rm h}$.

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Alternative definition of excitation amplitudes in Multi-Reference state-specific Coupled Cluster

To obtain even qualitatively correct results of potential energy surfaces (PESs) of the ground and two lowest-lying excited singlet states of C2 is a difficult task due to the strong geometry-dependent closeness of these PESs leading to real and avoided crossings. Our IVO-SSMRPT method in which the nondynamical correlation is simplified with IVO-CASCI has been applied to these states. IVO-SSMRPT provides comparable results with reference theoretical and experimental data indicating all components of the approach work in harmony for a correct representation of the surfaces including the locations of the challenging crossing points between the states.

Description of C2 dissociation using a naive treatment of dynamical correlation in the presence of quasidegeneracy of varying degree

To compute the electronic excitation energies, a state-specific multireference Moller-Plesset perturbation theory (SSMRPT) with a complete active space configuration interaction reference function constructed using the orbitals obtained by the density functional theory (DFT) is presented as an accurate, as well as computationally affordable, and efficient protocol at the level of second order. The global hybrid B3LYP (Becke, 3-parameter, Lee-Yang-Parr) functional has been used to generate orbitals. The present method, called DFT-SSMRPT, uses perturbers that are individual Slater determinants and accounts for the coupling between the nondynamical and dynamical correlation effects. We have applied the new method to compute excitation energies in conjugated systems of π-electrons such as trans-1,3-butadiene, trans,trans-1,3,5-hexatriene, and all-trans-1,3,5,7-octatetraene. The ordering of the excited states is correctly reproduced by the DFT-SSMRPT calculations. The relative ordering of low-lying excited 1Bu and 1Ag states alters when the length of the polyene changes. The results match reasonably well with the literature including experimental and best theoretical findings. The accuracy of the method is sufficient to discern the energy gap between the close low-lying singlet and triplet states. The DFT-SSMRPT appears as an affordable computational ab initio avenue for a qualitatively correct description of excitation energies.

Taming the excited states of butadiene, hexatriene, and octatetraene using state specific multireference perturbation theory with density functional theory orbitals.

Adaptation of improved virtual orbital complete active space configuration interaction functions in state-specific multireference perturbation theory motivated by the Brillouin-Wigner perturbation scheme using Moller-Plesset multipartitioning is examined. The method, denoted as IVO-BWMRPT, focuses on only the root of principal interest at a time using single-root parameterization of Jeziorski-Monkhorst ansatz within the frame of an effective Hamiltonian. This approach yields size-extensive energy and avoids intruder-state problems in a natural manner. It allows relaxation of the reference space wave function in the presence of the perturbation which produces an important differential effect on the energy and cannot be neglected for quasidegenerate electronic states. The method has been tested against nontrivial situations such as the Be + H2 insertion profile along with the energy surfaces of FH and X2 (X = F, Cl, and Br), in which conventional single-reference methods generally fail, exhibiting very encouraging findings. We also consider the energy surfaces of ethylene (by breaking the π bond as well as the CC bond) and for the twisting of tetramethyleneethane. IVO-BWMRPT represents a rather balanced protocol for the description of molecules at a wide range of geometries, including stretched or dissociating bonds. Close agreement of our estimates with the reference values provides a useful measure for the success of the IVO-BWMRPT method to treat strongly correlated systems. Our results for TME show that the singlet state always lies below the triplet state for different conformations. The IVO-BWMRPT furnishes a compact and correct representation of the MR-wave function, and hence, a large variety of quasidegenerate situations can be accommodated within the method.

A simplified account of the correlation effects to bond breaking processes: The Brillouin-Wigner perturbation theory using a multireference formulation

Multireference perturbation theory with improved virtual orbitals for radicals: More degeneracies, more problems

Despite the enormous biological significance, the structure-stability relationship in S-Nitrosothiols (RSNOs) that govern their activity in vivo is not well understood We provide useful structural

Shovan Manna

Papers

Description of C2 dissociation using a naive treatment of dynamical correlation in the presence of quasidegeneracy of varying degree

Taming the excited states of butadiene, hexatriene, and octatetraene using state specific multireference perturbation theory with density functional theory orbitals.

A simplified account of the correlation effects to bond breaking processes: The Brillouin-Wigner perturbation theory using a multireference formulation

Multireference perturbation theory with improved virtual orbitals for radicals: More degeneracies, more problems

Structural properties and isomerisation of simple S-nitrosothiols: ab initio studies with a simplified treatment of correlation effects