Multiconfiguration wavefunctions obtained by application of the generalized Brillouin theorem

Grein, Friedrich; Chang, Tse‐Chiang

doi:10.1016/0009-2614(71)80612-7

Cited by 134 publications

(37 citation statements)

References 15 publications

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“…For the orbital optimization, a Super-CI method [8] was implemented and discussed in T2, a Newton-Raphson method was implemented in T3, and the formal aspects of the two methods were compared in T1.…”

Section: The Development Of the Casscf Methodsmentioning

confidence: 99%

“…In the MCSCF method, the orbitals and expansion coefficients are simultaneously optimized. Through the seventies, the work of in particular Wahl and Das [7], Grein and Chang [8], Hinze [9], and Ruedenberg and coworkers [10] had led to MCSCF methods that were applicable to atoms and small molecules. However, these methods were in general only used in the developers' own groups and did not explore the many insights and advances in the area of optimization methods made by the numerical mathematicians [11].…”

Section: Olsenmentioning

confidence: 98%

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The CASSCF method: A perspective and commentary

Olsen

2011

Int J of Quantum Chemistry

202

165

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ABSTRACT:The CASSCF method of Roos and coworkers is reviewed and compared to other approaches. It is argued that the implementation of the CASSCF method marks the beginning of large scale multiconfigurational self consistent field calculations and thus has been important in many fields of the molecular sciences. It is further argued that CASSCF and related approaches will continue to play an important role in the development of a molecular understanding of structures and processes in many fields of science, as these approaches constitute the appropriate starting point for wave function descriptions of molecules and complexes containing transition metals. This development will, however, require a way to avoid the exponential scaling of the complexity of the underlying wave function and several ways to eliminate this scaling is reviewed.

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Section: The Development Of the Casscf Methodsmentioning

confidence: 99%

Section: Olsenmentioning

confidence: 98%

The CASSCF method: A perspective and commentary

Olsen

2011

Int J of Quantum Chemistry

202

165

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“…113,114 It is well known that the bottleneck of this algorithm is the evaluation of the non-orthogonal matrix elements, however a number of improvements for speeding up this evaluation have been proposed. Thus, orthogonalization of orbitals is automatically invoked, wherever this procedure leaves the wave function unaltered, and is exploited in the algorithm by generalizing the Slater-Condon rules to cases where not all orbitals are orthogonal.…”

Section: Pure Vb Methods That Use Localized Orbitalsmentioning

confidence: 99%

A survey of recent developments in ab initio valence bond theory

Hiberty

Shaik

2006

J Comput Chem

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Starting from the 1980s and onwards, Valence Bond theory has been enjoying renaissance that is characterized by the development of a growing number of ab initio methods, and by many applications to chemical reactivity and to the central paradigms of chemistry. Owing the increase of computational power of modern computers and to significant advances in the methodology, valence bond theory begins to offer a sound and attractive alternative to Molecular Orbital theory. This review aims at summarizing the most important developments of ab initio valence bond methods during the last two or three decades, and is primarily devoted to a description of what the various methods can actually achieve within their specific scopes and limitations. Key available softwares are surveyed.

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“…Such wave functions have proven very useful for the elucidation of chemical reaction paths and they have also lead to illuminating analyses of chemical bonding. 1 Early methods for optimizing MCSCF wave functions, the so-called first-order approaches, include the Fock-operator diagonalization method 2 and the super-CI method, [3][4][5] which is based on the generalized Brillouin theorem. 6 These approaches were largely superceded by the development of the Newton-Raphson secondorder methods.…”

Section: Introductionmentioning

confidence: 99%

A MCSCF method for ground and excited states based on full optimizations of successive Jacobi rotations

Ivanic

Ruedenberg

2003

J Comput Chem

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A new multiconfigurational self-consistent field (MCSCF) method based on successive optimizations of Jacobi rotation angles is presented. For given one- and two-particle density matrices and an initial set of corresponding integrals, a technique is developed for the determination of a Jacobi angle for the mixing of two orbitals, such that the exact energy, written as a function of the angle, is fully minimized. Determination of the energy-minimizing orbitals for given density matrices is accomplished by successive optimization and updating of Jacobi angles and integrals. The total MCSCF energy is minimized by alternating between CI and orbital optimization steps. Efficiency is realized by optimizing CI and orbital vectors quasi-simultaneously by not fully optimizing each in each improvement step. On the basis of the Jacobi-rotation based approach, a novel MCSCF procedure is formulated for excited states, which avoids certain shortcomings of traditional excited-state MCSCF methods. Applications to specific systems show the practicability of the developed methods.

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Multiconfiguration wavefunctions obtained by application of the generalized Brillouin theorem

Cited by 134 publications

References 15 publications

The CASSCF method: A perspective and commentary

The CASSCF method: A perspective and commentary

A survey of recent developments in ab initio valence bond theory

A MCSCF method for ground and excited states based on full optimizations of successive Jacobi rotations

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