Analytic treatment of IR-spectroscopy data for double well potential

Abstract

A theoretical scheme for the analysis of experimental data on IR spectroscopy for a quantum particle in a double well potential (DWP) is suggested. The analysis is based on the trigonometric DWP for which the exact analytic solution of the Schrödinger equation is available. The corresponding energy levels along with their wave functions are expressed via special functions implemented in Mathematica (spheroidal function and its spectrum of eigenvalues). As a result trigonometric DWP makes the calculation of the energy levels an extremely easy procedure. It contains three parameters allowing one to model the most important characteristics of DWP (barrier height and the distance between the minima of the potential) along with the required asymmetry. Our approach provides an accurate calculation of the energy spectrum for hydrogen bonds in chromous acid (CrOOH) and potassium dihydrogen phosphate (KH 2 PO 4 ) along with their polarizability in agreement with available experimental data.

Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart

“…On the other hand, hyperbolic and trigonometric type potentials are used in molecular physics and quantum chemistry, modeling inter-atomic and inter-molecular forces, ranging from Razavy [17], Pöschl-Teller [18], Rosen-Morse [19,20], and Scarf [21] potentials to their modified counterparts [9,[22][23][24][25][26][27]. In quantum chemistry, the area of IR-spectroscopy is particularly interesting, since double-well potentials (DWP) could describe the ammonia molecule (NH 3 ) [28], chromous acid (CrOOH) [29] and potassium dihydrogen phosphate (KH2PO4) experimental data [29][30][31].…”

“…In their work, they only develop the case k > 0 which corresponds to values 0 < η < 1, but in our case both cases, k < 0 and k > 0, are included, making ours a more general treatment. Furthermore, Sitnitsky [29] has shown applications to IR spectroscopy for a particle in a DWP potential to describe the proton energy states in hydrogen bonds. The model potential is a DW trigonometric potential, with an asymmetric term whose zero limit is used to describe thermodynamic features of the experimental data.…”

Exactly solvable double-well potential in Schrödinger equation for inversion mode of phosphine molecule

“…This circumstance makes TDWP to be an extremely convenient and efficient tool for usage. Earlier TDWP was applied to an asymmetric hydrogen bond in KHCO 3 [24], inversion of an ammonia molecule NH 3 [25], [45], ring-puckering vibration in 1,3-dioxole and 2,3-dihydrofuran [23], the calculations of the polarizability of hydrogen bonds in chromous acid (CrOOH) and potassium dihydrogen phosphate (KH 2 PO 4 ) [42] and the calculation of IR absorption intensities for a hydrogen bond in the Zundel ion H 5 O + 2 (oxonium hydrate) [43]. In the present article we construct with the help of TDWP a modified phenomenological DWP for the exactly solvable SE with the position-dependent mass that yields the description of the energy levels structure for the inversion mode of PH 3 .…”

Calculation of IR absorption intensities for hydrogen bond from exactly solvable Schrödinger equation

“…therein). In a commonly used approach the proton position in HB is modeled by the Schrödinger equation (SE) with a double-well potential (DWP) [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. In particular it is applied to the investigation of IR-absorption by HB [7], [8], [9], [17], [18].…”

“…As a result the calculation of the energy levels becomes an automatic (at a click) procedure. Earlier trigonometric DWP was applied to an asymmetric hydrogen bond in KHCO 3 [15], inversion of an ammonia molecule NH 3 [25], [26], ring-puckering vibration in 1,3-dioxole and 2,3-dihydrofuran [27] and calculations of the polarizability of HB in chromous acid (CrOOH) and potassium dihydrogen phosphate (KH 2 PO 4 ) [16]. The aim of the present article is to show that the above solution enables one to calculate conveniently the IR absorption intensities of HB.…”