About the Mulliken electronegativity in DFT

Putz, Mihai V.; Russo, Nino; Sicilia, Emilia

doi:10.1007/s00214-005-0641-4

Cited by 110 publications

(60 citation statements)

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“…Kleinert's variational perturbation (KP) theory [34] for the centroid density [32,70,[84][85][86][87][88][89]92] of Feynman path integrals [2,[32][33][34][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] provides a complete theoretical foundation for developing non-stochastic/non-sampling methods to systematically incorporate internuclear quantum-statistical effects in condensed phase systems. Similar to the complementary interplay between the rapidly growing quantum Monte Carlo simulations [146][147][148][149] and the well-established ab initio or density-functional theories (DFT) for electronic structure calculations [4,5,[25][26][27]29], non-sampling/non-stochastic pathintegral methods can complement the conventional Fourier or discretized path-integral Monte-Carlo (PIMC) [131,136,[139][140]…”

Section: Kleinert's Variational Perturbation Theorymentioning

confidence: 99%

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Wong

2014

Commun. comput. phys.

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Abstract. Feynman's path integral reformulates the quantum Schrödinger differential equation to be an integral equation. It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems. In this Review, the molecular Schrödinger equation will first be introduced, together with the BornOppenheimer approximation that decouples electronic and internuclear motions. Some effective semiclassical potentials, e.g., centroid potential, which are all formulated in terms of Feynman's path integral, will be discussed and compared. These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger's energy eigenvalues. As a result, path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques. To complement these techniques, we will examine how Kleinert's variational perturbation (KP) theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential. To enable the powerful KP theory to be practical for many-body molecular systems, we have proposed a new path-integral method: automated integrationfree path-integral (AIF-PI) method. Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method, we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions. The computational procedure of using our AIF-PI method, along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy (AMAZE), are also highlighted in this review.

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Section: Kleinert's Variational Perturbation Theorymentioning

confidence: 99%

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Wong

2014

Commun. comput. phys.

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“…Upon the insertion of the absolute electronegativity (394) in (399) it provides the chemical Mulliken density functional [7,100,101]

χ_{M} false(N false) = \frac{b + N - 1}{2 \sqrt{a}} arctan (\frac{N - 1}{\sqrt{a}}) - \frac{b + N + 1}{2 \sqrt{a}} arctan (\frac{N + 1}{\sqrt{a}}) + \frac{C_{A} - 1}{4} ln [\frac{a + {false(N - 1 false)}^{2}}{a + {false(N + 1 false)}^{2}}]

The exposed density functional formulation of electronegativity features reach physical contents, since the derivation appeals on fundamental quantum principles as the Hohenberg-Kohn and the chemical action theorems, while complementing somehow at the valence ( β → 0) level the previously density matrix one (263) – worked out in the context of (the fourth order) semiclassical expansion (271); nevertheless, this valence character of the chemical Mulliken electronegativity will be in the following tested for atomic scale through Feynman-Kleinert density implementation.…”

Section: Effective Classical Path Integral Of Evolution Amplitudementioning

confidence: 99%

Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

Putz

2009

IJMS

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The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

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“…[3][4][5][6][7][8][9][10][11][12][13] However as a global property, it might give insufficient insight when regioselectivity effects are of importance.…”

Section: Introductionmentioning

confidence: 98%