Double Minimum Potential Well Research Articles

Electronic vibrational problem for molecules with inversion motions

A general approach to the solution of the electronic vibrational problem with imposed conditions on possible vibrational nuclear motions in a double-minimum potential well is proposed.

Ritz assignment and Watson fits of the high-resolution ring-puckering spectrum of oxetane

Oxetane is a four-membered ring molecule exhibiting a large-amplitude ring-puckering motion. In order to analyze this vibration we recorded a rotationally resolved far-infrared spectrum between 50 and 145 cm −1. The analysis of the ring-puckering fundamental band with the assignment of 1108 lines, has been presented in a previous paper. In the present work we present a list of further 6531 assigned transitions between the five lowest excited ring-puckering states. The 4983 term values involved in the transitions assigned in this and in the preceding work have been evaluated by the “Ritz” program, and are now available. An A-reduced Watson Hamiltonian in any of the three representations I r, II r, and III r was used to perform a fit of the assigned transitions. Precise rotational constants and quartic as well as a full set of sextic centrifugal distortion constants were obtained for the investigated ring-puckering states. For the first time, high-resolution values for the vibrational G v parameters have been obtained, and we have added terms in x 6 and x 8 to the double minimum-potential well describing the ring-puckering motion, in order to reproduce their values within the experimental accuracy. The same potential still reproduces the lower resolution values of the Q-branch origins involving higher ring-puckering states up to v rp=14 found in the previous literature.

The interaction of the easily polarizable hydrogen bonds with phonons and polaritons of the thermal bath-far infrared continua

B+H⋯B⇌B⋯H+B or AH⋯B⇌−A⋯H+B hydrogen bonds, respectively, with double minimum proton potential well or broad flat potential well cause continuous absorptions in the infrared spectra. The intensity of these infrared continua is often very large, i.e. their integrated intensity is much larger than that of infrared bands. Short strong hydrogen bonds with broad flat in the average largely symmetrical proton potentials in which the protons fluctuate, show so-called proton polarizabilities. With such systems, the infrared continua extend in the far infrared region, i.e. in the region below 600cm−1. It is, however known that with such bonds no proton transitions occur in this region.It is demonstrated that the intensity of these infrared continuous absorptions is strongly increased by the coupling of the hydrogen bonds with large proton polarizability with the phonons of the thermal bath around these hydrogen bonds. Further, it is demonstrated that the pronounced absorption in the far infrared region, i.e. the region below 600cm−1, occurs due to the strong coupling of these hydrogen bonds to the polaritons. The polaritons are the quanta of the thermal bath coupled to the phonons of the thermal bath.

Fluorescence-Dip Infrared Spectroscopy of Jet-Cooled 5-Hydroxytropolone

Ground-state infrared spectra of the syn and anti conformers of jet-cooled 5-hydroxytropolone (5-HOTrOH) monomer have been recorded free from interference from one another using a fluorescence depletion method. The 5-hydroxy group “free” O−H stretch, 2-hydroxy intramolecularly hydrogen-bonded O−H stretch, and C−H stretch transitions are observed for both conformers. The assignment of these bands is clear by comparison with previous infrared studies of bare tropolone and is confirmed by MP2 and DFT level vibrational frequency and intensity calculations. Each of the conformers is predicted to have four allowed C−H stretch transitions. There is a reasonable one-for-one correspondence between calculation and experiment for the anti conformer's C−H stretch bands, while the syn conformer shows effects of Fermi resonance mixing. The 5-OH stretch bands of the syn and anti conformers are single, sharp transitions located at 3654 and 3664 cm-1, respectively. The OH stretch fundamentals of the 2-OH group involved in the intramolecular hydrogen bond are centered on 3170 and 3195 cm-1. These bands are extensively broadened in both conformers and contain reproducible substructure with irregular spacing of about 10−15 cm-1. The substructure of the intramolecularly H-bonded 2-hydroxy O−H stretch band reflects a selective first-tier vibrational-state mixing, most likely with a set of modes which are in near two-to-one resonance with it. Finally, the 249 cm-1 asymmetry in the double-minimum potential well for H atom tunneling appears to be sufficient to quench syn−anti tunneling in S0 even following excitation of the 2-OH stretch fundamental. No evidence is found for syn ↔ anti “crossover” transitions despite careful searches capable of detecting such transitions at depletion levels of about 1%.

A short dynamically symmetrical hydrogen bond in the structure of K[Mg(H0.5SO4)2(H2O)2

The Mg atoms in the title compound, magnesium potassium hydrogendisulfate(3-) dihydrate, are found at the centres of symmetry at the unit cell corners and are octahedrally coordinated by two water molecules and the O atoms from four SO 4 tetrahedra to form infinite krohnkite-like Mg(H 0.5 SO 4 ) 2 (H 2 O) 2 chains running down the a axis. The sulfate and hydrogensulfate ions are coupled to form an (SO 4 HSO 4 ) 3- group with O...O 2.478 (3) A and with the H atom disordered around a symmetric double-minimum potential well. Crossed channels along the a and b axes are filled by tenfold-coordinated K atoms

An ab-initio study of the potential energy surface for the O-H—O bond in KH2PO4

Abstract A methodology is presented for carrying out ab-initio molecular orbital calculation of the potential energy surface as a function of position of the H atom in the O-H—O bonds of KH2PO4 (KDP). The calculations employ the Hartree-Fock Self-Consistent-Field (SCF) approach utilizing the Linear Combination of Atomic Orbital for Molecular Orbital (LCAOMO) procedure with basis in Gaussian form. This approach seems to yield a reliable representation of double-minimum potential well for the O-H—O bond in KDP, as judged from the agreement between the predicted (0.3604 Ŕ) and experimental (0.3674 Ŕ) values for the separation between the two equilibrium positions of the H atom along the O—O direction. The calculated value of the barrier height (0.08 eV) helps clarify some earlier spectroscopic data on the activation energy for the motion of the H-atom in the O-H—O bond in KDP. The same methodology should be applicable for investigating the possible double-minimum wells for the heavier atoms in the KDP-type o...

Pressure dependence of zero-field splittings in organic triplets. III. Vibronic systems

We report optically detected magnetic resonance (ODMR) experiments at pressures up to 40 kbar for p-benzoquinone (BQ) in dibromobenzene (DBB) and for a deep x-trap in a BQ-d4 neat crystal. It is known from previous works that the phosphorescent triplet state (3B1g) of these systems is vibronically coupled to a nearby 3Au state, such that the former exhibits a double-minimum potential well. The zero-field splitting (ZFS) parameter D of both systems changes by several gigahertz over our pressure range. The greatest slope occurs at zero pressure, and the rate of change slows down exponentially at higher pressure. In addition, we observed a phase transition in BQ-d4 crystals at 6 kbar, which causes a huge step-discontinuity in both D and E. In contrast to the enormous change in D, the E-value is not sensitive to pressure except for the step-change during the phase transition. Triplet state kinetics and phosphorescence spectra are used to establish the existence of an in-plane distortion at least in the high-pressure phase. A model is proposed to interpret these results based on the pressure-dependent vibronic interaction, leading to a reduction of the spin–orbit coupling contribution to the ZFS.

Theoretical and experimental study of the non-s-cis form of unsaturated ethers. Molecular structure and vibrational assignment of the high-energy isomer of methylvinylether

The molecular conformation of the high-energy isomer of methylvinylether has been re-investigated. Ab initio calculations were performed using the 6–31G and 6–31G* bases at the SCF level, accounting for electron correlation by full second- and third-order Møller—Plesset perturbative treatments. The internal potential energy function, as derived from calculations at several torsional angles with complete geometry optimization, indicated the high-energy isomer in a wide double-minimum potential well at a CCOC dihedral angle between 156.7 and 159.4° from the most stable s-cis form. At every level the two equivalent minima were scarcely resolved, as expressed by a very low interconversion barrier ranging from 10.8 to 21.7 cm −. Estimates of the skeletal torsional energies in the one-vibration approximation gave aground state energy at or just above the barrier height, thus depicting the high-energy isomer as an effective s-trans form. The IR spectra of the pure liquid and the vapour were taken at several temperatures. In the mid-IR spectrum at medium-high resolution, marked fine rotational structure appeared in almost all of the gas-phase absorption envelopes of both isomers.Four bands attributed to the high-energy isomer were analyzed inthe approximation of a quasi-prolate rotor: one, of a parallel-like type, yielded B+ C=0.28 −1; the other three, of perpendicular-like type, yielded similar values, 2.38, 2.34 and 2.27 cm −1, for 2[A—(B+ C)/2]. Both these molecular parameters agree with those expected for an s-trans conformation or one very near to it. A prediction of the vibrational spectrum of the high-energy isomer was made from the harmonic force constants derived at the SCF 6–31G* level; the calculated frequencies were corrected by transferring scale factors from the s-cis isomer. With this procedure, the average difference between the eleven observed frequencies and the corresponding predicted frequencies amounted to 4.2 cm −1.

Refractive index gratings in rare-earth-doped alkaline earth glasses

Four-wave-mixing techniques were used to produce permanent laser-induced refractive index gratings in Eu3+ -doped silicate glasses. These gratings are associated with a thermally induced change in the local glass structure at the site of the Eu3+ ions, leading to a double-minimum potential well for the electronic energy levels of the Eu3+ ions. The effects on the characteristics of the permanent laser-induced gratings produced by changing the divalent modifier ions of the glass host are reported and a theoretical model is presented to explain the physical origin of the change in the refractive index of the material.

High‐resolution solid‐state NMR study of reversible 1,5‐proton shifts in organic solids

AbstractHigh‐resolution CP‐MAS NMR analyses of solid organic samples where fast 1,5‐proton shifts occur between tautomeric structures are described. Attention is focused on the available techniques to establish the existence of such reactions. Dynamic interconversion is unambiguously characterized where complete line shape study involving multiple sites is possible. Reconciliation between this information and that provided by diffraction methods is stressed, the latter often suggesting the presence of unique, static structures in crystals. In cases in which reactions are in the fast limit at all accessible temperatures, the combination of CP‐MAS spectra, x‐ray or neutron diffraction data at variable temperatures and theoretical calculations of molecular properties may be helpful in establishing double minimum potential wells for the proton motion. Among these, porphyrins, arylazonaphthols and 1,3‐diketones in rigid and non‐rigid skeletons are interesting examples of current interest.

ChemInform Abstract: Theoretical and Experimental Study of the Non‐s‐cis Form of Unsaturated Ethers: Molecular Structure and Vibrational Assignment of cis‐Methyl‐1‐propenylether

Abstract Ab initio calculations of the internal potential energy function of cis -methyl-1-propenylether, with complete optimization of the structural parameters, have been performed at the SCF level using the 6–31G and 6–31G* bases. By keeping the SCF-optimized geometries, electron correlation was accounted for using the MP2 Moller-Plesset perturbation theory. The most stable isomer was found to occur in a wide double-minimum potential well at a torsional angle o = 152° about the C( sp 2 )O bond; the interconversion barrier between the two skew enantiomers was predicted as low as 53 cm −1 . The s- cis form of the molecule (o=0°) appeared at a relative energy of 1286 cm −1 , in a shallow potential well, only 135 cm −1 deep. The Raman spectra of the solid and liquid phases and the complete IR spectrum of the vapour phase have been recorded. They yield evidence that the molecule occurs in a single, non-planar isomer. An assignment of the vibrational spectrum has been made from the harmonic force constants derived at the SCF 6–31G* level; the calculated frequencies have been corrected by transferring scale factors from propene, methylvinylether and methylisopropenylether, for which parallel calculations of the same accuracy have been made. The average difference between observed and predicted frequencies amounted to 5.7 cm −1 . Structureless gas-phase IR bands observed at 100 and 58 cm −1 are assigned to the skeletal torsion vibration. In a model calculation using the one-vibration approximation and the computed MP2 potential only two closely spaced levels, corresponding to a genuine skew conformation, appear below the interconversion barrier; the 1←0 and 2←0 torsional transitions have frequencies of 40 and 72 cm −1 , while single- and double-jump transitions between higher levels converge to frequencies of about 45 and 90 cm −1 , respectively.

Intramolecular Na + bonds with double minimum potential wells

Four Na + salts of (4-R-6-tert-butyl-pyridyl-N-oxide) acetic acids are studied by FTIR spectroscopy. An intramolecular ( I) COO −Na +...ON⇌COO −...Na +ON ( II) bond is present. Within the series of compounds R = NO 2, Br, H, CH 3 the ν CO character of the carbonyl vibration in structure I decreases and the equilibrium shifts more and more to the right.

Theoretical and experimental study of the non-S- cis form of unsaturated ethers: Molecular structure and vibrational assignment of cis-methyl-1-propenylether

Ab initio calculations of the internal potential energy function of cis-methyl-1-propenylether, with complete optimization of the structural parameters, have been performed at the SCF level using the 6–31G and 6–31G* bases. By keeping the SCF-optimized geometries, electron correlation was accounted for using the MP2 Møller-Plesset perturbation theory. The most stable isomer was found to occur in a wide double-minimum potential well at a torsional angle ø = 152° about the C( sp 2)O bond; the interconversion barrier between the two skew enantiomers was predicted as low as 53 cm −1. The s- cis form of the molecule (ø=0°) appeared at a relative energy of 1286 cm −1, in a shallow potential well, only 135 cm −1 deep. The Raman spectra of the solid and liquid phases and the complete IR spectrum of the vapour phase have been recorded. They yield evidence that the molecule occurs in a single, non-planar isomer. An assignment of the vibrational spectrum has been made from the harmonic force constants derived at the SCF 6–31G* level; the calculated frequencies have been corrected by transferring scale factors from propene, methylvinylether and methylisopropenylether, for which parallel calculations of the same accuracy have been made. The average difference between observed and predicted frequencies amounted to 5.7 cm −1. Structureless gas-phase IR bands observed at 100 and 58 cm −1 are assigned to the skeletal torsion vibration. In a model calculation using the one-vibration approximation and the computed MP2 potential only two closely spaced levels, corresponding to a genuine skew conformation, appear below the interconversion barrier; the 1←0 and 2←0 torsional transitions have frequencies of 40 and 72 cm −1, while single- and double-jump transitions between higher levels converge to frequencies of about 45 and 90 cm −1, respectively.

ChemInform Abstract: Rotational Isomerism, Structure and Vibrational Assignment of Methoxyallene: Joint IR and Raman Investigation and Non‐Empirical MO‐SCF and Valence Force Field Calculations.

Abstract The rotational isomerism of methoxyallene has been studied both by ab initio calculations and vibrational analysis. The internal potential energy function, calculated at the 6-31G**//3-21G level, indicates the occurrence of two isomers. The more stable one has a planar s- cis structure; the other is predicted at a torsional angle of 140.0° ( skew form), with a relative energy of 2.68 kcal mol −1 . The enantiomers corresponding to the latter are indicated in a double-minimum potential well with a central barrier height of only 0.34 kcal mol −1 (119 cm −1 ). From IR and Raman spectra evidence it was found that methoxyallene exists predominantly in the s- cis form; by measurements of the temperature dependence of the relative band intensities, the enthalpy difference between the skew and the s- cis isomers was found to be 1.96 ± 0.14 kcal mol −1 . The vibrational assignment was based on ab initio derivation, at the 3-21G level, of the harmonic force constants. The calculated frequencies were scaled by factors obtained from analogous calculations for the strictly related molecules allene and methylvinylether. The accord between the normal frequencies predicted by this procedure and the observed ones was quite satisfactory, the differences ranging between 0 and 18 cm −1 for twenty-four out of the twenty-seven fundamentals. From the assigned torsional frequency, the derived barrier to internal rotation of the methyl group was 3.1 kcal mol −1 (1048 cm −1 ).

Rotational isomerism, structure and vibrational assignment of methoxyallene: joint IR and Raman investigation and non-empirical MO-SCF and valence force field calculations

The rotational isomerism of methoxyallene has been studied both by ab initio calculations and vibrational analysis. The internal potential energy function, calculated at the 6-31G**//3-21G level, indicates the occurrence of two isomers. The more stable one has a planar s- cis structure; the other is predicted at a torsional angle of 140.0° ( skew form), with a relative energy of 2.68 kcal mol −1. The enantiomers corresponding to the latter are indicated in a double-minimum potential well with a central barrier height of only 0.34 kcal mol −1 (119 cm −1). From IR and Raman spectra evidence it was found that methoxyallene exists predominantly in the s- cis form; by measurements of the temperature dependence of the relative band intensities, the enthalpy difference between the skew and the s- cis isomers was found to be 1.96 ± 0.14 kcal mol −1. The vibrational assignment was based on ab initio derivation, at the 3-21G level, of the harmonic force constants. The calculated frequencies were scaled by factors obtained from analogous calculations for the strictly related molecules allene and methylvinylether. The accord between the normal frequencies predicted by this procedure and the observed ones was quite satisfactory, the differences ranging between 0 and 18 cm −1 for twenty-four out of the twenty-seven fundamentals. From the assigned torsional frequency, the derived barrier to internal rotation of the methyl group was 3.1 kcal mol −1 (1048 cm −1).

Water–hydrocarbon interactions: Rotational spectroscopy and structure of the water–acetylene complex

The radiofrequency and microwave spectra of C2H2–H2O, C2H2–D2O, C2D2–H2O, and C2D2–D2O have been measured by molecular beam electric resonance spectroscopy. Rotational constants and dipole moments are reported. The structure is effectively planar with the acetylene hydrogen bonded to the oxygen of the water. The hydrogen-bond length and stretching force constant are calculated to be. 2.229 Å and 0.065 mdyn/Å, respectively. Considering the lone pair orbital structure of the water molecule, an equilibrium structure having the water plane tilted away from the a axis of the complex is expected. Even so, a comparison of the dipole moments for the different isotopically substituted species shows that the height of the barrier hindering an inversion motion is low enough that no vibrational levels lie below the top of the barrier in the double-minimum potential well.

Proton Magnetic Relaxation Study of Phase Transition in Crystalline p-Terphenyl

Proton spin-lattice relaxation time T 1 was measured at 19.5 MHz of p -terphenyl in the vicinity of its solid-solid phase transition point. A sharp decrease in T 1 was observed near the transition point and was attributed to the critical fluctuation associated with the phase transition. The T 1 was interpreted successfully in terms of the order-disorder mechanism by which the central phenylene ring jumps between two stable sites in a double minimum potential well and its motion undergoes a critical slowing down in the phase transition region. The possibility of displacive phase transition was also discussed.

Coulomb spectrum in crossed electric and magnetic fields: Eigenstates of motion in double-minimum potential wells

Two-dimensional electron layers when placed in perpendicular electric and magnetic fields can have a potential well with two minima for the electronic motion normal to the surface. Such double-minimum potential wells also arise for highly excited Rydberg states of atoms in crossed electric and magnetic fields and in certain molecular potential curves. We develop and apply a WKB formalism to such double-minimum wells and calculate the energy splittings that arise when one is near degeneracy, that is, when either well, considered independently, can support a bound state at the same energy.

Domain-wall-like excitations in a discrete one-dimensional anharmonic lattice model

In the discrete chain of harmonically coupled particles moving in double-minimum potential wells (the discrete Phi 4 model), static and dynamical domain-wall-type solutions are studied. In the static case, no translationally invariant solutions exist, but rather two special discrete-ones. The energy difference between the two determines the pinning of the domain wall to a lattice site and is shown to be exponentially small for larger coupling parameters. The authors also present a non-trivial dynamical permanent profile solution, which corresponds to the propagating domain wall with a vanishing average velocity.

Calculation of Raman intensities for the ring-puckering vibrations of 2,5-dihydropyrrole and trimethyleneimine. Electrical versus mechanical anharmonicity in asymmetric potential wells

Raman intensities are calculated for the ring-puckering transitions of 2,5-dihydropyrrole (DHP) and trimethyleneimine (TMI) using an anisotropic atom–point dipole interaction model to evaluate the elements of the molecular polarizability tensor. The calculated relative intensities for the members of the Δv = 1 and Δv = 2 ring-puckering progressions for DHP are in good agreement with those observed. The calculations predict that the observed Δv = 2 overtones of DHP occur not because of the first-order allowedness expected for these transitions in the asymmetric double-minimum potential well which governs the ring-puckering motion, but rather because of unusually large second-order terms in the expansions of the polarizability tensor elements in the puckering coordinate [‖(∂2αμν/∂Z2)0‖≫0]. Raman intensities are calculated for the ring-puckering transitions of TMI using the two different potential functions which have been proposed for the puckering motion. It is found that the intensities calculated for the slightly asymmetric double-minimum potential V(Z) = (0.922 05×106)Z4−(0.379 44×105)Z2+(0.159 13×105)Z 3 proposed by Carreira and Lord [J. Chem. Phys. 51, 2735 (1969)] cannot be reconciled with experiment. On the other hand, the intensities calculated for the highly asymmetric single-minimum potential V(Z) = (0.7553×105)Z2−(0.4336×106)Z3+(0.7035×106)Z4 proposed by Robiette et al. [Mol. Phys. 42,1519 (1981)] are in excellent agreement with experiment. Our calculations confirm that the three most intense ring-puckering transitions observed in the Raman (and far-infrared) spectrum of TMI are the lowest members of a Δv = 1 rather than a Δv = 2 progression. The calculations further indicate that high-order electrical terms in the polarizability expansions contribute significantly to the Raman intensities of both the Δv = 1 and Δv = 2 ring-puckering progressions. Neglect of the electrically anharmonic terms in the intensity calculation for the single-minimum well results in a significant disparity between calculation and experiment.