Orthogonality constrained calculations of MC SCF excited states in non-adiabatic regions

Matsumoto, Shiro; Toyama, Masayuki; Yasuda, Yuki; Uchide, Takayuki; Ueno, R.

doi:10.1016/0009-2614(89)87223-9

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…Moreover, an orthogonality constrained energy minimization of Ref. [20][21][22], as explained and demonstrated here (cf. below), leads to an incorrect wave function lying below the exact eigenfunction.…”

Section: Previous Attemptsmentioning

confidence: 99%

“…(3) may become negative. This actually happens in MCSCF calculations when variational collapse occurs due to the so called MCSCF "rootflipping" [15,21,[25][26][27]29,31,[35][36][37][38][39][40][41][42][43]: In MCSCF, as mentioned above, improvement of the n th root, by improving its orbitals, deteriorates the lower roots; If these deteriorated roots were used in n F (whose derivation, like MCSCF, also demands flatness and "saddleness" of the energy at n n   ), then root-flipping would be rather unavoidable (in both methods MCSCF and n F ). However, contrary to MCSCF (which unavoidably computes the desired higher root orthogonal to the deteriorated lower roots), n F does not need the deteriorated lower roots.…”

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confidence: 99%

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Minimization principle for non degenerate excited states (independent of orthogonality to lower lying known approximants)

Bacalis¹

2016

JCM

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The computation of small concise and comprehensible excited state wave functions is needed because many electronic processes occur in excited states. But since the excited energies are saddle points in the Hilbert space of wave functions, the standard computational methods, based on orthogonality to lower lying approximants, resort to huge and incomprehensible wave functions, otherwise, the truncated wave function is veered away from the exact. The presented variational principle for excited states, F n , is demonstrated to lead to the correct excited eigenfunction in necessarily small truncated spaces. Using Hylleraas coordinates for He 1 S 1s2s, the standard method based on the theorem of Hylleraas -Unheim, and MacDonald, yields misleading main orbitals 1s1s' and needs a series expansion of 27 terms to be "corrected", whereas minimizing F n goes directly to the corect main orbitals, 1s2s, and can be adequately improved by 8 terms. F n uses crude, rather inaccurate, lower lying approximants and does not need orthogonality to them. This reduces significantly the computation cost. Thus, having a correct 1 st excited state ψ 1 , a ground state approximant can be immediately improved toward an orthogonal to ψ 1 function. Also higher lying functions can be found that have the energy of ψ 1 , but are orthogonal to ψ 1 . F n can also recognize a "flipped root" in avoided crossings: The excited state, either "flipped" or not, has the smallest F n . Thus, state average is unnecessary. The method is further applied via conventional configuration interaction up to three lowest singlet states of He. The problem and the purposeThe study of excited states is already imperative especially as it concerns reactions, after activation, of stable species, like CO 2 or alkanes. First principles studies can only be utilized in truncated Hilbert spaces. Unfortunately, the standard methods of computing excited states in truncated spaces, although perhaps adequate for the energy and for spectroscopy, may yield incorrect wave functions (perhaps with correct energy), misleading for desired proper excitations. Thus, a method is needed (such as the present demonstrated) to yield excited state truncated wave functions that are not veered away from the exact Hamiltonian eigenfunctions. The ability to extend the variational principle to any excited state (without knowledge of the lower-lying exact eigenfunctions) has long been proven to be an inherent property of the Hamiltonian. The excited state truncated wave function based on the standard method of the Hylleraas and Undheim / MacDonald (HUM) theorem, is in principle incorrect in a more fundamental manner than just being truncated: Its accuracy must be strictly less than the accuracy of the ground state truncated approximant. On the other hand, an energy minimization orthogonally to all lower approximants ["orthogonal optimization" (OO)] must lead to a wave function lying lower than, and veered away from, the exact. A minimization principle for excited electronic states of a nondegenerate ...

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Section: Previous Attemptsmentioning

confidence: 99%

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confidence: 99%

Minimization principle for non degenerate excited states (independent of orthogonality to lower lying known approximants)

Bacalis¹

2016

JCM

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“…Non-orthogonal CI (NOCI) provides a strategy for doing just this. [34][35][36][37][38][39][40][41] As a CI method, the NOCI wavefunction is defined as a linear combination of determinants, the weights of which are variationally optimized. However, in contrast to conventional CI, the determinantal basis used in NOCI needn't refer to a common set of orbitals.…”

Section: Non-orthogonal CImentioning

confidence: 99%

Spin–flip non-orthogonal configuration interaction: a variational and almost black-box method for describing strongly correlated molecules

Mayhall

Horn

Sundstrom

et al. 2014

Phys. Chem. Chem. Phys.

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In this paper, we report the development, implementation, and assessment of a novel method for describing strongly correlated systems, spin-flip non-orthogonal configuration interaction (SF-NOCI). The wavefunction is defined to be a linear combination of independently relaxed Slater determinants obtained from all possible spin-flipping excitations within a localized orbital active-space, typically taken to be the singly occupied orbitals of a high-spin ROHF wavefunction. The constrained orbital optimization of each CI basis configuration is defined such that only non-active-space orbitals are allowed to relax (all active space orbitals are fixed). A number of simplifications and benefits arise due to the fact that only a restricted number of orbital rotations are permitted, (1) basis states cannot coalesce during SCF, (2) basis state optimization is better conditioned due to a larger effective HOMO-LUMO gap, (3) smooth potential energy surfaces are easily obtained, (4) the Hamiltonian coupling between two basis states with non-orthogonal orbitals is greatly simplified. To illustrate the advantages over a conventional orthogonal CI expansion, we investigate exchange coupling constants of bimetallic complexes, the avoided crossing of the lowest singlet states during LiF dissociation, and ligand non-innocence in an organometallic complex. These numerical examples indicate that good qualitative agreement can be obtained with SF-NOCI, but dynamical correlation must be included to obtain quantitative accuracy.

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If Truncated Wave Functions of Excited State Energy Saddle Points Are Computed as Energy Minima, Where Is the Saddle Point?

Bacalis

2020

Theoretical Chemistry for Advanced Nanomaterials

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Orthogonality constrained calculations of MC SCF excited states in non-adiabatic regions

Cited by 3 publications

References 10 publications

Minimization principle for non degenerate excited states (independent of orthogonality to lower lying known approximants)

Minimization principle for non degenerate excited states (independent of orthogonality to lower lying known approximants)

Spin–flip non-orthogonal configuration interaction: a variational and almost black-box method for describing strongly correlated molecules

If Truncated Wave Functions of Excited State Energy Saddle Points Are Computed as Energy Minima, Where Is the Saddle Point?

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