Accurate Quantum Chemical Calculations

Bauschlicher, Charles W.; Langhoff, Stephen R.; Taylor, Peter R.

doi:10.1002/9780470141267.ch3

Cited by 155 publications

(23 citation statements)

References 175 publications

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“…II). An alternative strategy is given by so-called direct methods, 30,31,32,33,34,35,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58 where required matrix elements are computed on the fly during each step of recursive diagonalization of the many-electron Hamiltonian. The latter approach constitutes an interesting direction for future work, together with possible interfaces with other CI codes.…”

Section: Discussionmentioning

confidence: 99%

“…The main limitations within the CI approach, when applied to the strongly correlated regimes attainable in artificial atoms, are that truncation of the Fock space -one of the standard procedures in traditional CI methods of quantum chemistry (the so-called CI with singles, doubles, etc. 30,31,32,33,34,35 ) -generally gives large errors or even qualitatively wrong results, and that the Fock space dimension grows exponentially with N .…”

mentioning

confidence: 99%

“…The implementation is independent of the SP orbital basis and, therefore, of the details of the device. We do not assume any truncation of the Fock space of SDs generated from the chosen SP basis [full-CI 30,31,32,33,34,35 (FCI)]. The large eigenvalue problem is reduced to its minimal size by exploiting the symmetry of the effective-mass interacting Hamiltonian (1), including square total spin (S 2 ).…”

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confidence: 99%

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Full configuration interaction approach to the few-electron problem in artificial atoms

Rontani¹,

Cavazzoni

Bellucci

et al. 2006

The Journal of Chemical Physics

183

202

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We present a new high-performance configuration interaction code optimally designed for the calculation of the lowest energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a singleparticle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted up to the Wigner regime, where correlations become dominant. Comparison with previous Quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Full configuration interaction approach to the few-electron problem in artificial atoms

Rontani¹,

Cavazzoni

Bellucci

et al. 2006

The Journal of Chemical Physics

183

202

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“…This is the basis of the so-called Full Configuration Interaction (FCI) method which provides the most accurate possible solution [40]. Indeed, for a finite basis set this is the exact solution and has extensively been used as a benchmark for quantum chemical methods [42][43][44][45][46]. Equation (6) is the starting point of DFT which aims to replace both γ 1 (r 1 ; r 1 ) and γ 2 (r 1 , r 2 ) by the one-electron density, γ 1 (r 1 ) or ρ(r).…”

Section: Remarks On Wave Function and Density Functional Theory Appromentioning

confidence: 99%

Spin Symmetry Requirements in Density Functional Theory: The Proper Way to Predict Magnetic Coupling Constants in Molecules and Solids

et al. 2006

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Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract In this paper it is argued that the use of density functional theory (DFT) to solve the exact, non-relativistic, many-electron problem, for magnetic systems requires imposing space and spin symmetry constraints exactly in the same way as it is currently done in ab initio wave function theory. This strong statement is supported on pertinent calculations for selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids. These calculations include several wave function methods of increasing accuracy and different forms of the exchangecorrelation functional. The comparisons of numerical results carried out always within the same standard Gaussian Type Orbital atomic basis set show that imposing or not the spin and space constraints (restricted or unrestricted formalisms) leads to contradictory results. Therefore, it appears that, in the case of the Heisenberg magnetic constant, the present exchange-correlation functionals may provide reasonable numerical results although for the wrong physical reasons thus evidencing the failure of the current DFT methods to properly describe magnetic systems.

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“…It is important to understand the role of d electrons in chemical bond formation and cleavage, [8][9][10][11][12][13][14][15][16][17][18][19][20][21] and relativistic effects often play dominant roles in such processes. To enable an entry level of theory, we have proposed effective nuclear charges for the first-through sixth-row main-group elements, as well as those for the first-through third-row transition elements, to estimate spin-orbit splittings within the one-electron (Z eff ) approximation.…”

Section: Introductionmentioning

confidence: 99%

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. 3. Hydrides of Groups 6 and 7

2006

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The dissociation energy curves of low-lying spin-mixed states for Group 5 hydrides (VH, NbH, and TaH), as well as Group 3 hydrides (ScH, YH, and LaH), have been calculated by using both effective core potential (ECP) and all-electron (AE) approaches. The two approaches are based on the multiconfiguration selfconsistent field (MCSCF) method, followed by second-order configuration interaction (SOCI) calculations: the first method employs an ECP basis set proposed by Stevens and co-workers (SBKJC) augmented by a set of polarization functions, and spin−orbit coupling effects are estimated with a one-electron approximation, using effective nuclear charges. The second method employs a double-ζ basis set developed by Huzinaga (MIDI) and three sets of p functions are added to both transition element and hydrogen and one set of f functions is also added to the transition element. The relativistic elimination of small components (RESC) scheme and full Breit−Pauli Hamiltonian are employed in the AE approaches to incorporate relativistic effects. The present paper reports a comprehensive set of theoretical results including the dissociation energies, equilibrium distances, electronic transition energies, harmonic frequencies, anharmonicities, and rotational constants for several low-lying spin-mixed states in the hydrides, filling a considerable gap in available data for these molecules. Transition moments are also computed among the spin-mixed states, and qualitative agreement is obtained for Group 3 hydrides in comparison with the experimental results reported by Ram and Bernath. Peak positions of emission spectra in Group 5 hydrides are also predicted. Disciplines Chemistry CommentsReprinted ( ReceiVed: January 13, 2004; In Final Form: March 13, 2004 The dissociation energy curves of low-lying spin-mixed states for Group 5 hydrides (VH, NbH, and TaH), as well as Group 3 hydrides (ScH, YH, and LaH), have been calculated by using both effective core potential (ECP) and all-electron (AE) approaches. The two approaches are based on the multiconfiguration self-consistent field (MCSCF) method, followed by second-order configuration interaction (SOCI) calculations: the first method employs an ECP basis set proposed by Stevens and co-workers (SBKJC) augmented by a set of polarization functions, and spin-orbit coupling effects are estimated with a one-electron approximation, using effective nuclear charges. The second method employs a double-basis set developed by Huzinaga (MIDI) and three sets of p functions are added to both transition element and hydrogen and one set of f functions is also added to the transition element. The relativistic elimination of small components (RESC) scheme and full Breit-Pauli Hamiltonian are employed in the AE approaches to incorporate relativistic effects. The present paper reports a comprehensive set of theoretical results including the dissociation energies, equilibrium distances, electronic transition energies, harmonic frequencies, anharmonicities, and rotational constants for sever...

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Accurate Quantum Chemical Calculations

Cited by 155 publications

References 175 publications

Full configuration interaction approach to the few-electron problem in artificial atoms

Full configuration interaction approach to the few-electron problem in artificial atoms

Spin Symmetry Requirements in Density Functional Theory: The Proper Way to Predict Magnetic Coupling Constants in Molecules and Solids

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. 3. Hydrides of Groups 6 and 7

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