Double Minimum Research Articles

Excess molar enthalpies of mixtures containing 1,3-dichloropropane

Excess molar enthalpies H m E of [(1− x){C 6H 14 or CH 3C(CH 3) 2CH 2CH 3 or c-C 6H 12 or CCl 4 or C 6H 6} + xCH 2ClCH 2CH 2Cl] at four temperatures ranging from 288.15 to 318.15 K, and of {(1− x)C 16H 34 + xCH 2ClCH 2CH 2Cl} between 298.15 and 328.15 K, were measured. With alkanes, the curves of the excess molar heat capacity C p,m E obtained from the H m Es show a double minimum.

Proton transfer in intramolecular hydrogen bonds with large proton polarizability in 1-piperidinecarboxylic acids. Temperature, solvent and concentration dependence

1-Piperidinecarboxylic acids C5H10N(CH2)nCO2H (n= 1–4)(PCA) solutions have been studied by NMR and IR spectroscopy as well as by osmometric measurements. NMR measurements have shown that with the compounds n= 2–4 relatively strong intramolecular hydrogen bonds are formed. The osmometric measurements demonstrate that compound n= 4 is always dimerized owing to dipole–dipole interactions. At low concentrations in relatively polar solvents the compound with n= 2 is present as a monomer. With increasing concentration it also dimerizes. Because of this dimerization the equilibrium OH⋯N(I)⇌ O–⋯H+N(II) is shifted in favour of the polar structure. In the case of the compound with n= 4, from temperature-dependent measurements the enthalpy ΔH° and the entropy ΔS° have been determined with two solvents. Both quantities are large and negative, in agreement with all other systems with AH⋯B ⇌ A–⋯H+B equilibria studied up to now. For the compound with n= 4 the strong influence of the CH acidity of the solvent is illustrated. This specific interaction effect is responsible for the double minimum in the proton potential.

Description of adsorption phenomena within the framework of the embedded atom method

We have calculated and compared the self-adsorption parameters (desorption energy, activation energy of adatom surface migration, vibration frequencies of adsorbed atoms, and truncated Fourier representation of the adatom-substrate interaction) for a W adatom on a W {110} surface using embedded-atom methods (EAM) introduced by Gollisch (G), by Finnis and Sinclair (FS) and by Johnson and Oh (JO), using the fitting parameters of the authors for bulk crystals. A small modification noticeably improved the results from the FS model. The equilibrium adsorbate-substrate binding energy, and height were mapped within a unit cell to generate the necessary data. The G and FS models both display double minima.

1H relaxation study in (NH4)2SbF5

1H spin-lattice relaxation rate (T 1 −1 ) has been measured using inversion recovery technique in polycrystalline (NH4)2SbF5 system in the temperature range 140–400 K. From the plot of log (M 0−M) againstτ, we have estimated two differentT 1 corresponding to two inequivalent ammonium ions in the unit cell. Temperature-dependence ofT 1 in each case exhibits features of double minima indicating the influence of different correlation times corresponding to different types of motion. Activation energies at different temperature regions have been estimated. Some features of dynamics of motion of the different groups of ions across the phase transitions have been discussed.

IR continua of hydrogen bonds and hydrogen-bonded systems, calculated proton polarizabilities and line spectra

Homoconjugated B +H·B⇌B·H +B hydrogen bonds cause intense continua in the IR spectra. Continua are also observed in the case of heteroconjugated (I) AH·B⇌A −·H +B (II) bonds if the two proton limiting structures have noticeable weight. In this case, with the exception of extreme systems, the double minimum of the proton potentials is created by the interactions of these hydrogen bonds with their environments. Finally, structurally symmetrical or largely structurally symmetrical hydrogen-bonded chains or chains which are built up by the above mentioned hydrogen bonds cause continua by collective proton motion. Theory proves that all these three types of hydrogen bonds and hydrogen-bonded systems show so-called proton polarizabilities due to proton shifts. These proton polarizabilities are two orders of magnitude larger than usual polarizabilities due to distortion of electron systems, and with hydrogen-bonded chains they may be much larger still. The calculated line spectra of all these systems show many lines which shift as a function of the electrical field strength at the hydrogen bonds (simulating their environments). In the whole region some lines vanish, some arise with changes of the electrical field strength. The IR continua occur due to strong interaction effects of these hydrogen bonds or hydrogen-bonded systems with their environments which are caused by the large proton polarizability. Hydrogen bonds with large proton polarizability are of great significance with the electrochemistry of acid and base solutions. Furthermore, it is proved that a large number of hydrogen bonds and hydrogen-bonded systems occurring in biochemistry show large proton polarizability. Their hypothetical importance for biological functions is discussed. Finally, it is shown that at surfaces hydrogen bonds and hydrogen-bonded systems with large proton polarizability may be present and should be taken into account, when studying reactions at surfaces in which protons are involved.

Change of the proton potential from a single to a double minimum in intramolecular hydrogen bonds with increasing p Ka of the phenolic group in 4-R-Mannich base N-oxides

Nine 4-R-Mannich base N-oxides have been studied by FTIR spectroscopy. The intramolecular hydrogen bonds formed between the phenolic and the N-oxide group show proton polarizability. If the phenolic group is relatively acidic a broad flat single minimum proton potential with the well at the NO group is found, whereas if the phenolic group is more basic a double minimum proton potential is observed. An analogous change of the shape of the proton potential was observed earlier in the case of carboxylic acid/trimethylammonium N-oxide systems if the acidity of the carboxylic acid increases. The reasons for this change of the proton potential are explained.

Excess molar enthalpies of mixtures containing 1,2-dichloropropane

Excess molar enthalpies H m E of (1,2-dichloropropane + n-hexane or 2,2-dimethylbutane or cyclohexane or tetrachloromethane or benzene) at four temperatures ranging from 288.15 to 318.15 K, and of (1,2-dichloropropane + n-hexadecane) between 298.15 and 328.15 K, were measured. With alkanes, the values of the excess molar heat capacity C p, m E obtained from those of H m E are all negative and the corresponding curves show a double minimum.

MRD CI study on the low-lying states of AlP

Large-scale MRD CI calculations assign to AlP the ground state X 3Σ− (9σ23π2) and a close-lying state 1 3Π (9σ3π3) (Te = 0.08 eV). Up to transition energies of 2.0 eV, other states are described by the configurations 9σ3π3 (11Π), 8σ23π4 (1 1Σ+), 9σ23π2 (1 1Δ and 2 1Σ+) and 9σ3π24π (1 5Π). The 2 3Π state, located at ≈ 2.30 eV, shows a shallow double minimum. Numerous perturbations are expected to induce predissociation upon 2 3Π. Multiplets arising from the occupation 8σ23π34π are clustered in the 3.25–3.50 eV region. Quintet states with the configuration 8σ9σ3π34π are bound, with Te values (in eV) of 3.80 (1 5Σ+), 4.44 (1 5Δ) and 4.88 (3 5Σ−), respectively. The 9σ → 4s Rydberg members 5Σ− and 3Σ− lie in the 4.58–4.72 eV energy region. The first ionization potential (ionization to X4Σ− of AlP+, 9σ → ∞) is estimated to be 7.65 eV. Ionization to the 1 2Σ− and 1 2Π states of AlP+ is suggested to occur between 8.0 and 8.8 eV. The dipole moments of X 3Σ−, 1 1Δ and 2 1Σ+ are close to 1.0 D, whereas the 1 1Σ+ state has μ = 3.49 D; 1 3Π and 1 1Π have dipole moments from 2.45 to 2.91 D. All low-lying states show a polarity Al+P−. Finally, the electronic structure and transition energies of AlP are compared with those of the isoelectronic species BN, AIN, and SiP+.

Application of the higher order finite‐element method to one‐dimensional Schrödinger equation

AbstractThe accuracy and applicability of the finite‐element method of the higher order interpolation functions to the one‐dimensional Schrödinger equation were examined. When the fifth‐order Lagrange and Hermite interpolation functions were used as the basis functions, practically exact solutions were obtained for all eigenvalues of several model potential energy functions. It was demonstrated that the appropriate analytical integration over the potential energy function within each element is important in the matrix element evaluation. The accuracy of the method was examined for the potential functions with a double minimum, which has a large classically forbidden region. The method was also applied to evaluate the Franck‐Condon factors of the transitions between the 1 1Σ and 2 1Σ states of Na2; the latter state having a double minimum in its potential energy function.

Reversible proton transfer phenomenon in the 2,4-dichlorophenol-triethylamine hydrogen-bonded complex studied by low-temperature 1H NMR spectroscopy

Low-temperature 1H NMR studies of the bridging OHN signal in the hydrogen-bonded complex formed between 2,4-dichlorophenol and triethylamine in C 2H 5Cl solution have demonstrated for the first time that separate signals for the molecular and ion-pair forms of this type of system can be observed. The temperature dependence of these signals leads to thermodynamic and kinetic quantities which suggest that the potential energy profile of the hydrogen bond is roughly symmetric with a double minimum.

Electronic and structural properties of elemental copper: A pseudopotential-local-orbital calculation.

We have examined the electronic and structural properties of elemental copper using pseudopotentials and a local-orbital basis consisting of Gaussians. We find we can use a much weaker ionic pseudopotential to describe accurately the measured band structure, cohesive energy, lattice constant, and compressibility of copper than previous pseudopotential work. Our potential should be more amenable than existing ones to momentum-space evaluations of the total crystalline energy. In addition, we have examined the equation of state for copper in both the fcc and bcc structures. Unlike a recent pseudopotential--mixed-basis calculation, we find that the energy-versus-volume curve for copper in the bcc structure does not exhibit a double minimum.

Classical partition functions for two-dimensional hindered rotations. Application to the combination of H with CH 3

An exact analytic expression has been derived for the classical partition function, Q c, of a two-dimensional rotation hindered by a sinusoidal potential with a double minimum. The expression transforms smoothly between the classical partition function for free rotation, Q fc, valid where the barrier to rotation, V 2, is much less than the thermal energy, k B T, and the classical partition function for doubly degenerate harmonic vibrations, valid where V 2 is greater than k B T. Numerical results have been compared to exact and approximate calculations of the quantal partition function. An approximate quantal expression, Q b, generally agrees with the exact quantal results within 10% when V 2 is greater than 4 k B T. Q c agrees better with the exact quantal results when V 2 is less than 4 k B T. However, when Q fc is unity or less and the barrier is small, both Q b and Q c diverge from the exact quantal results. The Pitzer-Gwinn interpolation method gives satisfactory results when Q fc is greater than five, but does not work as well as Q c itself for low barriers. Q c has been applied to a variational transition state theory calculation of the rate constant for H + CH 3→CH 4. Quantum chemical electronic energies have been fitted to a sinusoidal function for the rocking motion and to Morse and Lippincott functions for the C…H stretching motion. Analytic expressions have been deduced for the critical C…H distance and for the rate constant. The results have been compared with previous theoretical work and with experiment.

Role of Valence Fluctuation in High-TcSuperconductors

The role of the valence fluctuation in high- T c superconductors is investigated from the viewpoint that the frequency of valence fluctuation is slower than the frequency of lattice vibration (the breathing mode) so that the lattice displacement manifests two possible valence states of atoms showing double minima in the atomic potential. This can lead to a large electron-phonon interaction suggesting that the high- T c superconductors are inherent structural instability superconductors.

Spectroscopic properties and potential energy surfaces of In2

Complete active space MCSCF (CASSCF) followed by first-order configuration interaction (FOCI) and relativistic configuration interaction (RCI) calculations are carried out on 29 electronic states of In2. Spectroscopic properties of 19 electronic states below 34 000 cm−1 are calculated. The ground state of In2 is found to be 3Πu(0−u). The experimentally observed electronic absorption spectra of In2 are reassigned to A(3Πg)←X(3Πu) (13 000 cm−1) and B(3Πg)←X(3Πu) (27 700 cm−1) transitions. The observed emission spectrum in the King furnace is assigned to the 3Σ−u–3Σ−g system. Spectroscopic properties and potential energy surfaces of 15 more electronic states are reported which are yet to be observed. The 0+g electronic states of In2 exhibit considerable spin–orbit contaminations and avoided crossings resulting in double minima in the 0+g and 0+g(III) surfaces. The 3Σ+u(II) curve also undergoes an avoided crossing. The Mulliken population analyses of the electronic states of In2 are reported.

ChemInform Abstract: Theoretical Study of the Properties of BC and Its Positive Ion in Their Ground and Excited Electronic States

Potential curves have been calculated for the ground and low‐lying states of the BC molecule and its positive ion by employing the MRD (multireference through double excitation)‐CI method. Spectroscopic constants for 14 states are given, and the results are compared with those of the isoelectronic C+2 and BN+ molecules. Of particular technical interest is the occurrence of an artificial double minimum in the SCF treatment of the X 4Σ− ground state, corresponding to two different electronic configurations with quite distinctive dipole moment curves; use of natural orbitals in a subsequent CI treatment is shown to give a consistent description of the true dipole moment dependence on the BC internuclear distance.

Theoretical study of the properties of BC and its positive ion in their ground and excited electronic states

Potential curves have been calculated for the ground and low-lying states of the BC molecule and its positive ion by employing the MRD (multireference through double excitation)-CI method. Spectroscopic constants for 14 states are given, and the results are compared with those of the isoelectronic C+2 and BN+ molecules. Of particular technical interest is the occurrence of an artificial double minimum in the SCF treatment of the X 4Σ− ground state, corresponding to two different electronic configurations with quite distinctive dipole moment curves; use of natural orbitals in a subsequent CI treatment is shown to give a consistent description of the true dipole moment dependence on the BC internuclear distance.

Non-orthogonal basis functions in the solution of diffusional problems

The diffusion equation in presence of strong potential gradients can be conveniently solved by means of a suitable set of non-orthogonal basis functions that mimic the asymptotic behaviour of the eigensolutions of the time evolution operator. This method is discussed in the context of the calculation of spectroscopic observables by means of the Lanczos algorithm, that is by representing the spectral density as a continued fraction. The modified Lanczos algorithm, which takes into account the non-orthogonality of the basis functions, is analysed in detail. In order to test the performance of the new procedure, the planar rotor subject to a cosine potential is considered, and the set of non-orthogonal functions having the correct asymptotic behaviour is derived in both cases of single and double minimum. The results of the numerical calculations clearly show the advantages of the proposed method when dealing with systems characterized by hindered motions.

Study of internal motions and phase transitions in (NH4)2ZnCl4 and [(N(CH3)4)]2 ZnCl4 by proton magnetic resonance and relaxation

Proton second moment (M2) and spin-lattice relaxation time (T1 at 10 MHz have been measured in polycrystalline ammonium tetrachlorozincate (ATC-Zn) and tetramethyl ammonium tetrachlorozincate (TMATC-Zn) as a function of temperature, covering the phase transitions. In ATC-Zn, the motion of NH+4 ion is fast in all phases as seen by a small and temperature independent proton second moment. Two types of chemically inequivalent NH+4 ions have been identified from the observed double minima in proton T1. Proton T1 shows a discontinuous jump and change of slope at 319 K, probably due to a phase transition. In addition, T1 shows a maximum around the reported ferroelectric phase transition (270 K), indicating the presence of spin-rotation interaction. In TMATC-Zn, the lowest temperature transition seems to be related to the slowing down of CH3 groups as revealed by the proton second moment. In this system also, two kinds of [N(CH3)4] ions have been found to be present from the proton T1 studies. Proton T1 shows ch...

Towards an understanding of stacked base interactions: non-equilibrium phase transitions as a probable model

The distances of stacked bases of DNA in different conformations can-not be calculated by equilibrium potentials, since they exhibit not more than only one minimum. However, a double potential minimum is obtained by considering the most simple semiclassical model of excitons that are coupled adiabatically to lattice vibrations, hence forming polaritons. By use of Danilov's extended Huckel approximation of DNA excitons, stacked base distances can be calculated that agree fairly well with the experimental data. The errors of this approach are small as compared to the differences of the distances in various conformations. Consequently, this model may work as a first base of understanding molecular interactions in DNA.

Photoinduced intramolecular proton transfer in methyl salicylates: a theoretical study with spectroscopic support

Intramolecular proton transfer processes in the ground and excited state of methyl calicylate, methyl 4-hydroxysalicylate and methyl 5-hydroxysalicylate have been studied by CNDO-CI and INDO semiempirical methods in order to determine the existence of a single or a double energy minimum in the corresponding potential curves, as well as to interpret thier photophysical behaviour. Hydrogen-bonding strenghts of ground state and local energy-minized geometries of ground and excited states are also discussed. These studies, combinded with IR and 1H HMR spectral data from methyl 4-methoxysalicylate and methyl 5-methoxysalicylate, support the existence of two different intramolecular hydrogen-bonded forms in the ground state and, at the same time, show that the photphysical behaviour of all these salicylic acid derivatives closely depends on the distance between the two oxygen atoms supporting the bond.