Molecule intrinsic minimal basis sets. I. Exact resolution of <i>ab initio</i> optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals

Lu, Wen‐Cai; Wang, C. Z.; Schmidt, M. W.; Bytautas, Laimutis; Ho, Kai Ming; Ruedenberg, Klaus

doi:10.1063/1.1638731

Cited by 171 publications

(154 citation statements)

References 48 publications

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“…More details about the virtual valence MO-subspace given byC v χ one can find in the original work [15]. The subspaces of occupied and virtual valence-MOs can be collectively written as |ψ and the corresponding…”

Section: Methods Detailsmentioning

confidence: 99%

“…Recently, has been proposed an efficient algorithm for determining the n v vdimensional valence-subspace |ϕ 0 v within the framework of quasi-atomic minimal basis orbitals (QUAMBO) [15,16] which constitute the molecule-intrinsic minimal basis of valence atomic orbitals, |ϕ v . However, the use of the maximum overlap criterion allows one to easily generalize the original procedure to cover also the core atomic orbitals.…”

Section: Methods Detailsmentioning

confidence: 99%

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Minimal set of molecule-adapted atomic orbitals from maximum overlap criterion

Szczepanik

Mrozek

2013

J Math Chem

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The criterion of maximum overlap with the canonical free-atom orbitals is used to construct a minimal set of molecule-intrinsic orthogonal atomic orbitals that resemble the most their promolecular origins. Partial atomic charges derived from population analysis within representation of such molecule-adopted atomic orbitals are examined on example of first-row hydrides and compared with charges from other methods. The maximum overlap criterion is also utilized to approximate the exact free-atom orbitals obtained from ab initio calculations in any arbitrary basis set and the influence of the resulting fitted canonical atomic orbitals on properties of moleculeadopted atomic orbitals is briefly discussed.

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Section: Methods Detailsmentioning

confidence: 99%

Section: Methods Detailsmentioning

confidence: 99%

Minimal set of molecule-adapted atomic orbitals from maximum overlap criterion

Szczepanik

Mrozek

2013

J Math Chem

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“…33 The present scheme for the projection of valence orbitals out of the virtual space of closed shell functions to yield atom localized orbitals was presented in 2004. 3 This algorithm is recast in a simpler form in the present paper, as an instance of the singular value decomposition (SVD). The SVD procedure (also known in quantum chemistry as the method of corresponding orbitals) consists of basis rotations in two different orbital spaces to bring the bases into maximum coincidence with each other; namely, it is a mutual projection of each space onto the other.…”

Section: Introductionmentioning

confidence: 99%

“…The poor connection between the LUMO concept and the lowest empty canonical orbital seems to be less well understood in the wider chemical community. The purpose of this paper is to demonstrate that useful, chemically relevant, and interpretable unoccupied orbitals can be obtained from MO calculations in a simple, robust, and automated way, 3 from any type of SCF or MCSCF calculation. These alternative empty MOs are called the valence virtual orbitals (VVOs).…”

Section: Introductionmentioning

confidence: 99%

Valence Virtual Orbitals: An Unambiguous ab Initio Quantification of the LUMO Concept

2015

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Many chemical concepts hinge on the notion of an orbital called the lowest unoccupied molecular orbital, or LUMO. This hypothetical orbital and the much more concrete highest occupied molecular orbital (HOMO) constitute the two "frontier orbitals", which rationalize a great deal of chemistry. A viable LUMO candidate should have a sensible energy value, a realistic shape with amplitude on those atoms where electron attachment or reduction or excitation processes occur, and often an antibonding correspondence to one of the highest occupied MOs. Unfortunately, today's quantum chemistry calculations do not yield useful empty orbitals. Instead, the empty canonical orbitals form a large sea of orbitals, where the interesting valence antibonds are scrambled with the basis set's polarization and diffuse augmentations. The LUMO is thus lost within a continuum associated with a detached electron, as well as many Rydberg excited states. A suitable alternative to the canonical orbitals is proposed, namely, the valence virtual orbitals. VVOs are found by a simple algorithm based on singular value decomposition, which allows for the extraction of all valence-like orbitals from the large empty canonical orbital space. VVOs are found to be nearly independent of the working basis set. ABSTRACT: Many chemical concepts hinge on the notion of an orbital called the lowest unoccupied molecular orbital, or LUMO. This hypothetical orbital and the much more concrete highest occupied molecular orbital (HOMO) constitute the two "frontier orbitals", which rationalize a great deal of chemistry. A viable LUMO candidate should have a sensible energy value, a realistic shape with amplitude on those atoms where electron attachment or reduction or excitation processes occur, and often an antibonding correspondence to one of the highest occupied MOs. Unfortunately, today's quantum chemistry calculations do not yield useful empty orbitals. Instead, the empty canonical orbitals form a large sea of orbitals, where the interesting valence antibonds are scrambled with the basis set's polarization and diffuse augmentations. The LUMO is thus lost within a continuum associated with a detached electron, as well as many Rydberg excited states. A suitable alternative to the canonical orbitals is proposed, namely, the valence virtual orbitals. VVOs are found by a simple algorithm based on singular value decomposition, which allows for the extraction of all valence-like orbitals from the large empty canonical orbital space. VVOs are found to be nearly independent of the working basis set. The utility of VVOs is demonstrated for construction of qualitative MO diagrams, for prediction of valence excited states, and as starting orbitals for more sophisticated calculations. This suggests that VVOs are a suitable realization of the LUMO, LUMO + 1, ... concept. VVO generation requires no expert knowledge, as the number of VVOs sought is found by counting s-block atoms as having only a valence s orbital, transition metals as having valence s and d, and main ...

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“…A related approach is the use of small adaptive basis sets. The idea of encoding chemical environment information into atomic/quasiatomic basis functions to understand chemical bonding dates back to early tools [67][68][69][70][71][72] , as well as more contemporary methods [73][74][75][76][77][78] . Apart from interpretive purposes, the merits of utilizing small adaptive bases in KS-DFT calculations have been recognized with the development of fast (especially linear-scaling) SCF algorithms, leading to renewed interest in the concept of "polarized atomic orbitals" (PAOs), first put forward by Adams in the 1960s 79,80 .…”

Section: Kohn-sham Density Functional Theorymentioning

confidence: 99%

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

Mao

Horn

Mardirossian

et al. 2016

The Journal of Chemical Physics

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Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large basis sets are used. To approach the basis set limit with potentially lower costs, a new SCF scheme with minimal adaptive basis (MAB) functions variationally optimized on each atomic site is presented, and the desired accuracy can be obtained by applying a perturbative correction (PC). Compared to exact SCF results, using this MAB-SCF (PC) approach with the same target basis set produces < 0.15 kcal/mol RMS errors for most of the tested TC datasets, and < 0.1 kcal/mol for most of the NCs. The performance of density functionals near the basis set limit can be well reproduced with slight discrepancies. With further improvement to its implementation, MAB-SCF (PC) could be a promising substitute for its conventional counterpart to viably approach the basis set limit of modern density functionals.

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Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals

Cited by 171 publications

References 48 publications

Minimal set of molecule-adapted atomic orbitals from maximum overlap criterion

Minimal set of molecule-adapted atomic orbitals from maximum overlap criterion

Valence Virtual Orbitals: An Unambiguous ab Initio Quantification of the LUMO Concept

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

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