Quantum confinement in hydrogen bond

Santos, Carlos da Silva dos; Filho, Elso Drigo; Ricotta, Regina Maria

doi:10.1002/qua.24894

Cited by 5 publications

(20 citation statements)

References 45 publications

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“…Indeed, most computational results in Ref. [ ] are qualitatively consistent with this expectation. However, the confinement introduced in Ref.…”

supporting

confidence: 61%

“…In Ref. [ ], the characteristic vibrational shift of OH and NH stretching fundamental modes engaged in hydrogen bonds is attributed to a quantum confinement effect. The latter is modeled by introducing infinite potential energy boundaries for the hydrogen motion at short and long hydride bond distances into a single‐well one‐dimensional (1D) Morse oscillator.…”

mentioning

confidence: 99%

“…However, the confinement introduced in Ref. [ ] is far from local. At the wavefunction level, it involves a multiplicative parabolic correction between the two confinement limits with substantial perturbations of the oscillator for all relevant distances.…”

mentioning

confidence: 99%

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Comment on: “Quantum Confinement in Hydrogen Bond” by Carlos da Silva dos Santos, Elso Drigo Filho, and Regina Maria Ricotta, Int. J. Quantum Chem. 2015, 115, 765-770.

Heger

Suhm

2015

Int. J. Quantum Chem.

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In Ref.[1], the characteristic vibrational shift of OH and NH stretching fundamental modes engaged in hydrogen bonds is attributed to a quantum confinement effect. The latter is modeled by introducing infinite potential energy boundaries for the hydrogen motion at short and long hydride bond distances into a single-well one-dimensional (1D) Morse oscillator. Such a confinement will necessarily lead to an increase of the gap between the ground state (quantum number v 5 0) and the first vibrationally excited state (quantum number v 5 1), if it occurs in a region of significant wavefunction amplitude. This remains valid if the onset of the confinement is somewhat smooth rather than instantaneous, although the latter case is easier to analyze. Instead of a formal variational proof, one may argue within the framework of diffusion Monte Carlo.[2]

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“…Indeed, most computational results in Ref. [ ] are qualitatively consistent with this expectation. However, the confinement introduced in Ref.…”

supporting

confidence: 61%

mentioning

confidence: 99%

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Comment on: “Quantum Confinement in Hydrogen Bond” by Carlos da Silva dos Santos, Elso Drigo Filho, and Regina Maria Ricotta, Int. J. Quantum Chem. 2015, 115, 765-770.

Heger

Suhm

2015

Int. J. Quantum Chem.

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“…Recentemente, a superálgebra tem sido empregada para auxiliar a solução da equação de Fokker-Planck [18,20] e para a obtenção de funções de onda teste (ansatz) para o estudo de interações intermoleculares [17,19].…”

Section: Introductionunclassified

“…Assim, essa abordagem tem motivado muitos estudos e estendido a compreensão sobre diversos sistemas quânticos (vide, por exemplo, Ref. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). …”

Section: Introductionunclassified

Operadores-escada generalizados para sistemas quânticos

Batael

Silva

et al. 2017

Rev. Bras. Ensino Fís.

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A superálgebra vem sendo aplicada na resolução de diversos problemas quânticos. Ela permite, por exemplo, obter soluções para potenciais exatamente solúveis e ampliar a construção de operadores de criação e destruição. Neste trabalho, o método de construção dos operadores-escada generalizadosé revisado e usado para obter os autovalores de energia e as autofunções de dois potenciais, a partícula em uma caixa unidimensional e o potencial de Rosen-Morse unidimensional. Palavras-chave: supersimetria; mecânica quântica; shape invariance; operadores-escada generalizados; partícula em uma caixa; potencial de Rosen-Morse.Supersymmetry has been applied to obtain the solution of several kinds of quantum problems. For example, it allows us to solve the Schrödinger equation and to introduce the creation and annihilation operators. In this work, the method to obtain the generalized ladder operators is revised and it is used to determine the energy eigenvalues and the eigenfunctions for two potentials, a particle in a box and the one-dimensional Rosen-Morse potential. Keywords: supersymmetry; quantum mechanics; shape invariance; ladder operators; particle in a box; RosenMorse potential. IntroduçãoEm estudos envolvendo sistemas descritos pela Mecânica Quântica, podemos fazer uso do formalismo da supersimetria para a resolução da equação de Schrödinger [1,2]. Em comparaçãoà resolução direta da equação de Schrödinger independente do tempo, este formalismo permite, por exemplo, uma simplificação dos cálculos e atacar outros tipos de problemas, como aqueles envolvendo potenciais parcialmente solúveis [3][4][5][6]. Assim, essa abordagem tem motivado muitos estudos e estendido a compreensão sobre diversos sistemas quânticos (vide, por exemplo, 11] e usando a chamada Shape Invariance do potencial [1,2,9,10,[12][13][14][15][16].Em potenciais para os quais nãoé possível determinar soluções analíticas exatas, a superálgebra aindaéútil como suporte nos métodos aproximativos, tais como perturbativo [1], aproximação WKB [13] e variacional [2,3,18]. Recentemente, a superálgebra tem sido empregada para auxiliar a solução da equação de Fokker-Planck [18,20] e para a obtenção de funções de onda teste (ansatz) para o estudo de interações intermoleculares [17,19].Problemas que envolvem sistemas quânticos em que os potenciais tratados são invariantes na sua forma funcional por transformações de supersimetria (shape invariant) podem ser resolvidos via superálgebra usando os operadores-escada generalizados [9,12] que atuam simultaneamente na coordenada espacial e no parâmetro da shape invariance.E oportuno lembrar que a construção de operadoresescada permite determinar estados coerentes [22][23][24][25] para os sistemas estudados. Em termos didáticos, os estados coerentes são discutidos na referência [26], enquanto a aplicação deste formalismo pode ser vista, por exemplo, nas referências [27] e [28]. Esses estados encontram aplicação em diferentes contextos, sendo particularmente importantes emóptica quântica [29,30].Neste trabalhoé feito uma revis...

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Reply to the Comment on: “Quantum Confinement in Hydrogen Bond” by Carlos da Silva dos Santos, Elso Drigo Filho, and Regina Maria Ricotta, Int. J. Quantum Chem. 2015, 115, 765-770

Santos

Filho

Ricotta

2015

Int. J. Quantum Chem.

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Recently, we have presented a study that describes the use of an analytical technique to provide the shift on the frequency of the OH and NH groups present in a series of biological macromolecules. The shift in the vibrational frequency occurs because of the formation of hydrogen bonds between the group and a donor atom of the macromolecule, inducing quantum confinement. [1] To describe such proposition, we have used the variational method associated with Supersymmetric Quantum Mechanics which is essentially an algebraic method of quantum mechanics, to provide the energy spectra of the system before the hydrogen bond formation (system unconfined) and after the hydrogen bond formation (confined system). The main virtue of our method is its simplicity.The Schr€ odinger equation was written with the Morse potential, notably a phenomenological potential with exact analytical solution, introduced in 1929 by Morse to treat molecular problems. [2] The unconfined problem is, therefore, exact whereas the confined problem (with the hydrogen bond) has to have an approximation method to solve the Schr€ odinger equation in a region surrounded by infinite walls, characterizing the confinement space where the hydrogen vibrates. The infinite walls are settled at the edges of the two atoms around the hydrogen, meaning that the hydrogen cannot penetrate inside them. The main point is the use of the cut-off terms (y max 2 y) (y 2 y min ), which multiply the unconfined (exact) wave function to describe the confined wave function, where (y max 2 y min ) is the region of space where the hydrogen vibrates. These two parameters, y min and y max , are related to the covalent radius of the atom for which the hydrogen is chemically bound and the van der Waals radius complementary of hydrogen bond, respectively. The other parameters involved are the equilibrium distance, the energy dissociation, and the reduced mass, which are characteristic of the Morse potential.The variational functions imply an approximation of what would be the actual functions for the studied problem and thus imply the assumption that the function would be close to the real one. The variational parameters used to minimize the energy eigenvalues must also reflect the correction of any distortions that alienate such a solution from the real solution of the problem. There is no evidence that this does not occur in this study. Rather, the convergence between experimental and theoretical values indicates that the suggested wave functions are appropriate for describing the desired system.It should be remarked that the Morse potential is not a first principles potential but a potential constructed from the phenomenology. Seeking a conceptual reach the same potential is used for different environmental conditions where the hydrogen bonds appear. The quantitative results presented in the literature confirm this practice. There are no arguments or strong evidence at the moment to abandon this attitude in the incorporation of confinement to the description of hydrogen bonds in d...

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Quantum confinement in hydrogen bond

Cited by 5 publications

References 45 publications

Comment on: “Quantum Confinement in Hydrogen Bond” by Carlos da Silva dos Santos, Elso Drigo Filho, and Regina Maria Ricotta, Int. J. Quantum Chem. 2015, 115, 765-770.

Comment on: “Quantum Confinement in Hydrogen Bond” by Carlos da Silva dos Santos, Elso Drigo Filho, and Regina Maria Ricotta, Int. J. Quantum Chem. 2015, 115, 765-770.

Operadores-escada generalizados para sistemas quânticos

Reply to the Comment on: “Quantum Confinement in Hydrogen Bond” by Carlos da Silva dos Santos, Elso Drigo Filho, and Regina Maria Ricotta, Int. J. Quantum Chem. 2015, 115, 765-770

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