The state-specific approach to the solution of problems of electronic structure and dynamics involving excited states

Nicolaides, Cleanthes A.

doi:10.1002/(sici)1097-461x(1996)60:1<119::aid-qua13>3.0.co;2-a

Cited by 34 publications

(26 citation statements)

References 54 publications

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“…[23][24][25][26] All of these theories are distinct from genuine multireference coupled cluster ͑MRCC͒ methods that are specifically designed for multiconfigurational zeroth-order wave functions. [35][36][37][38][39][40][41][42][43][44] Among the genuine MRCC methods, we have recently focused on the state-specific formulation of Mahapatra et al, 38,39 referred to hereafter as Mk-MRCC. [35][36][37][38][39][40][41][42][43][44] Among the genuine MRCC methods, we have recently focused on the state-specific formulation of Mahapatra et al, 38,39 referred to hereafter as Mk-MRCC.…”

Section: Introductionmentioning

confidence: 99%

Triple excitations in state-specific multireference coupled cluster theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

Evangelista

Simmonett

Allen

et al. 2008

The Journal of Chemical Physics

123

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We report the first implementation with correct scaling of the Mukherjee multireference coupled cluster method with singles, doubles, and approximate iterative triples (Mk-MRCCSDT-n, n=1a,1b,2,3) as well as full triples (Mk-MRCCSDT). These methods were applied to the classic H4, P4, BeH(2), and H8 model systems to assess the ability of the Mk-MRCCSDT-n schemes to accurately account for triple excitations. In all model systems the inclusion of triples via the various Mk-MRCCSDT-n approaches greatly reduces the nonparallelism error (NPE) and the mean nonparallelism derivative diagnostics for the potential energy curves, recovering between 59% and 73% of the full triples effect on average. The most complete triples approximation, Mk-MRCCSDT-3, exhibits the best average performance, reducing the mean NPE to below 0.6 mE(h), compared to 1.4 mE(h) for Mk-MRCCSD. Both linear and quadratic truncations of the Mk-MRCC triples coupling terms are viable simplifications producing no significant errors. If the off-diagonal parts of the occupied-occupied and virtual-virtual blocks of the Fock matrices are ignored, the storage of the triples amplitudes is no longer required for the Mk-MRCCSDT-n methods introduced here. This proves to be an effective approximation that gives results almost indistinguishable from those derived from full consideration of the Fock matrices.

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Section: Introductionmentioning

confidence: 99%

Triple excitations in state-specific multireference coupled cluster theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

Evangelista

Simmonett

Allen

et al. 2008

The Journal of Chemical Physics

123

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“…ref. [1]) is large and the overlaps in 1+2[O(coefficients 2 )] in equations 9, 10 are small: Indeed, the Hessian, and all its principal minors along the main diagonal, are, respectively, of the form: Hessian:…”

Section: The Two Methods Usedmentioning

confidence: 99%

Correct small-truncated excited state wave functions obtained via minimization principle for excited states compared/ opposed to Hylleraas-Undheim and McDonald higher ``roots''

Zhang

Zang

Liu

et al. 2017

JCM

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Abstract. We demonstrate that, if a truncated expansion of a wave function is large, then the standard excited states computational method, of optimizing one "root" of a secular equation, according to the theorem of Hylleraas, Undheim and McDonald (HUM), tends to the correct excited wave function, comparable to that obtained via our proposed minimization principle for excited states [J. Comput. Meth. Sci. Eng. 8, 277 (2008)] (independent of orthogonality to lower lying approximants). However, if a truncated expansion of a wave function is small -that would be desirable for large systems -then the HUM-based methods may lead to an incorrect wave function -despite the correct energy (: according to the HUM theorem) whereas our method leads to correct, reliable, albeit small truncated wave functions. The demonstration is done in He excited states, using truncated series "small" expansions both in Hylleraas coordinates, and via standard configuration-interaction truncated "small" expansions, in comparison with corresponding "large" expansions. Beyond that, we give some examples of linear combinations of Hamiltonian eigenfunctions that have the energy of the 1 st excited state, albeit they are orthogonal to it, demonstrating that the correct energy is not a criterion of correctness of the wave function.

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“…Detailed discussions of the theory and computations of electronic spectra and properties in the framework of the state-specific approach can be found in [7][8][9][10][11] andinrefs. We proceed with a commentary on this issue.…”

Section: The Calculation Of State-specific Wavefunctions For Use In Ementioning

confidence: 99%

Ab Initio Many-Electron Calculation of Hyperfast Time-Resolved Coherent Excitation and Decay Of Polyelectronic Atoms

Nicolaides¹,

Mercouris²,

Komninos³

2007

AIP Conference Proceedings

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Articles you may be interested inAccurate rotational constant and bond lengths of hexafluorobenzene by femtosecond rotational Raman coherence spectroscopy and ab initio calculations An ab initio study of the ground and low-lying excited states of KBe with the effect of inner-shell electrons J. Chem. Phys. 139, 074305 (2013); 10.1063/1.4818452 Time-resolved and energy-dispersed spin excitation in ferromagnets and clusters under influence of femtosecond laser pulses J. Appl. Phys. 105, 07D305 (2009); 10.1063/1.3058704Interpreting ultrafast molecular fragmentation dynamics with ab initio electronic structure calculations

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The state-specific approach to the solution of problems of electronic structure and dynamics involving excited states

Cited by 34 publications

References 54 publications

Triple excitations in state-specific multireference coupled cluster theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

Triple excitations in state-specific multireference coupled cluster theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

Correct small-truncated excited state wave functions obtained via minimization principle for excited states compared/ opposed to Hylleraas-Undheim and McDonald higher ``roots''

Ab Initio Many-Electron Calculation of Hyperfast Time-Resolved Coherent Excitation and Decay Of Polyelectronic Atoms

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