International Journal of Molecular Sciences

188 KiB

Open AccessArticle

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

by Pradipta Ghosh, Sudip Chattopadhyay, Debasis Jana and Debashis Mukherjee

Int. J. Mol. Sci. 2002, 3(6), 733-754; https://doi.org/10.3390/i3060733 - 30 Jun 2002

Cited by 50 | Viewed by 8152

We present in this paper two new versions of Rayleigh-Schr¨odinger (RS) and the Brillouin-Wigner (BW) state-specific multi-reference perturbative theories (SSMRPT) 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 [...] Read more.

We present in this paper two new versions of Rayleigh-Schr¨odinger (RS) and the Brillouin-Wigner (BW) state-specific multi-reference perturbative theories (SSMRPT) 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 (¹Σ⁺) and the first delta (¹Δ) 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. Full article

(This article belongs to the Special Issue Multireference Quantum Chemical Methods)

► Show Figures

Figure 1

151 KiB

Open AccessArticle

Higher Energy Derivatives in Hilbert Space Multi-Reference Coupled Cluster Theory : A Constrained Variational Approach

by K. R. Shamasundar and Sourav Pal

Int. J. Mol. Sci. 2002, 3(6), 710-732; https://doi.org/10.3390/i3060710 - 30 Jun 2002

Cited by 13 | Viewed by 8474

Abstract

In this paper, we present formulation based on constrained variational approach to compute higher energy derivatives upto third order in Hilbert Space Multi-Reference Coupled Cluster (HSMRCC) Theory. This is done through the use of a functional with Lagrange multipliers corresponding to HSMRCC method, [...] Read more.

In this paper, we present formulation based on constrained variational approach to compute higher energy derivatives upto third order in Hilbert Space Multi-Reference Coupled Cluster (HSMRCC) Theory. This is done through the use of a functional with Lagrange multipliers corresponding to HSMRCC method, as done by Helgaker, Jorgensen and Szalay. We derive explicit expressions upto third order energy derivatives. Using (2n + 1) and (2n + 2) rules, the cancellation of higher order derivatives of functional parameters that are not necessary according to these rules, is explicitly demonstated. Simplified expressions are presented. We discuss several aspects of the functional used and its potential implications. Full article

(This article belongs to the Special Issue Multireference Quantum Chemical Methods)

247 KiB

Open AccessArticle

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

by Piotr Piecuch and Karol Kowalski

Int. J. Mol. Sci. 2002, 3(6), 676-709; https://doi.org/10.3390/i3060676 - 30 Jun 2002

Cited by 59 | Viewed by 8408

Abstract

Some recent advances in the area of multi-reference coupled-cluster theory of the state-universal type are overviewed. An emphasis is placed on the following new developments: (i) the idea of combining the state-universal multi-reference coupled-cluster singles and doubles method (SUMRCCSD) with the multi-reference many-body [...] Read more.

Some recent advances in the area of multi-reference coupled-cluster theory of the state-universal type are overviewed. An emphasis is placed on the following new developments: (i) the idea of combining the state-universal multi-reference coupled-cluster singles and doubles method (SUMRCCSD) with the multi-reference many-body perturbation theory (MRMBPT), in which cluster amplitudes of the SUMRCCSD formalism that carry only core and virtual orbital indices are replaced by their first-order MRMBPT estimates; and (ii) the idea of combining the recently proposed method of moments of coupled-cluster equations with the SUMRCC formalism. It is demonstrated that the new SUMRCCSD(1) method, obtained by approximating the SUMRCCSD cluster amplitudes carrying only core and virtual orbital indices by their first-order MRMBPT values, provides the results that are comparable to those obtained with the complete SUMRCCSD approach. Full article

(This article belongs to the Special Issue Multireference Quantum Chemical Methods)

► Show Figures

Figure 1

187 KiB

Open AccessArticle

State Selective Equation of Motion Coupled Cluster Theory: Some Preliminary Results

by Marcel Nooijen

Int. J. Mol. Sci. 2002, 3(6), 656-675; https://doi.org/10.3390/i3060656 - 30 Jun 2002

Cited by 60 | Viewed by 8100

Abstract

A multireference variant of coupled cluster theory is described that applies to systems that can qualitatively be described by deleting two electrons from a closed shell determinant, for example biradicals, single bond breaking processes, or valence excited states. The theory can be generalized [...] Read more.

A multireference variant of coupled cluster theory is described that applies to systems that can qualitatively be described by deleting two electrons from a closed shell determinant, for example biradicals, single bond breaking processes, or valence excited states. The theory can be generalized to arbitrary open-shell systems and takes a form that is akin to equation-of-motion coupled cluster theory, but where all wave function parameters are explicitly optimized for the state of interest. The implementation of the present methods was accomplished in an automated fashion using the recently developed Automatic Program Generator (APG). We present benchmark results for the O₂ and F₂ molecules and investigate the behaviour of a number of closely related variants within the same general framework. Full article

(This article belongs to the Special Issue Multireference Quantum Chemical Methods)

136 KiB

Open AccessArticle

Multi-state Multireference Rayleigh–Schrödinger Perturbation Theory for Mixed Electronic States: Second and Third Order

by Isaiah Shavitt

Int. J. Mol. Sci. 2002, 3(6), 639-655; https://doi.org/10.3390/i3060639 - 30 Jun 2002

Cited by 20 | Viewed by 7895

Abstract

The formalism for multi-state multireference configuration-based Rayleigh-Schrödinger perturbation theory and procedures for its implementation for the second-order and third-order energy within a multireference configuration interaction computer program are reviewed. This formalism is designed for calculations on electronic states that involve strong mixing between [...] Read more.

The formalism for multi-state multireference configuration-based Rayleigh-Schrödinger perturbation theory and procedures for its implementation for the second-order and third-order energy within a multireference configuration interaction computer program are reviewed. This formalism is designed for calculations on electronic states that involve strong mixing between different zero-order contributions, such as avoided crossings or mixed valence-Rydberg states. Such mixed states typically display very large differences in reference-configuration mixing coefficients between the reference MCSCF wave function and an accurate correlated wave function, differences that cannot be reflected in state-specific (diagonalize-then-perturb) multireference perturbation theory through third order. A procedure described in detail applies quasidegenerate perturbation theory based on a model space of a few state-averaged MCSCF functions for the states expected to participate strongly in the mixing, and can be characterized as a “diagonalize-then-perturb-thendiagonalize” approach. It is similar in various respects to several published methods, including an implementation by Finley, Malmqvist, Roos, and Serrano-Andrés [Chem. Phys. Lett. 1998, 288, 299–306]. Full article

(This article belongs to the Special Issue Multireference Quantum Chemical Methods)

801 KiB

Open AccessArticle

Implicit and Explicit Coverage of Multi-reference Effects by Density Functional Theory

by Dieter Cremer, Michael Filatov, Victor Polo, Elfi Kraka and Sason Shaik

Int. J. Mol. Sci. 2002, 3(6), 604-638; https://doi.org/10.3390/i3060604 - 30 Jun 2002

Cited by 115 | Viewed by 13744

Abstract

Multi-reference effects can be covered by density functional theory (DFT) either implicitly via the exchange-correlation functional or explicitly via the form of the Kohn-Sham wave function. With the help of the exchange hole it is shown that the self-interaction error of the exchange [...] Read more.

Multi-reference effects can be covered by density functional theory (DFT) either implicitly via the exchange-correlation functional or explicitly via the form of the Kohn-Sham wave function. With the help of the exchange hole it is shown that the self-interaction error of the exchange functional will mimic long-range electron correlation effects if restricted Kohn-Sham theory is used. Functionals based on Slater or Becke exchange have a relatively large self-interaction error and, therefore, lead to a relatively large implicit coverage of long-range correlation, which, because of the possibility of doublecounting of electron correlation, has to be considered when using these functionals in connection with two- or multi-configurational descriptions based on ensemble DFT methods such as REKS (spin-Restricted Ensemble-referenced KS-DFT). Arguments are given that a REKS description of a multireference problem avoids a double-counting of long-range correlation effects, in particular as in this situation the self-interaction error of the exchange functional simulates more short- rather than longrange correlation effects. There is, however, no guarantee that the short-range effects are not doublecounted, namely once via the exchange and once via the correlation functional. Therefore, one should use hybrid functionals such as B3LYP in connection with multi-reference DFT methods because for hybrid functionals the self-interaction error and by this the implicit coverage of long(short)-range correlation effects is reduced due to the admixture of exact exchange. This rule applies also to broken-symmetry UDFT, which performs better with hybrid rather than GGA functionals. A way of avoiding the implicit coverage of multi-reference effects is given by the combination of wave function theory and DFT methods. The advantages and disadvantages of CAS-DFT are discussed and it is shown that an effective reduction of a double-counting of correlation effects is possible within this method. Full article

(This article belongs to the Special Issue Multireference Quantum Chemical Methods)

► Show Figures

Figure 1

471 KiB

Open AccessArticle

To Multireference or not to Multireference: That is the Question?

by Rodney J. Bartlett

Int. J. Mol. Sci. 2002, 3(6), 579-603; https://doi.org/10.3390/i3060579 - 30 Jun 2002

Cited by 79 | Viewed by 10575

Abstract

I present a personal viewpoint on multi-reference coupled-cluster theory, its pros and cons. I also suggest some criteria that should be satisfied by multi-reference CC, not the least of which is to develop a tool that will be (almost!) as easy to apply [...] Read more.

I present a personal viewpoint on multi-reference coupled-cluster theory, its pros and cons. I also suggest some criteria that should be satisfied by multi-reference CC, not the least of which is to develop a tool that will be (almost!) as easy to apply as today’s powerful array of single reference coupled-cluster methods. Some approaches like the equation of motion CC method offers a multi-reference description of some target states, while being entirely single reference in execution. Perhaps it offers a model for further generalization to a wider array of multi-reference problems. Full article

(This article belongs to the Special Issue Multireference Quantum Chemical Methods)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Int. J. Mol. Sci., Volume 3, Issue 6 (June 2002) – 7 articles , Pages 579-754

Further Information

Guidelines

MDPI Initiatives

Follow MDPI