Shape Of Potential Energy Curve Research Articles

The ratios of partition functions at different temperatures – Sensitivity to potential energy shape II

The ratios of partition functions at different temperatures are calculated and its dependence on potential energy shape is analyzed. The role of anharmonicity and non-rigidity of rotations is discussed in the context of the angular frequency and the shape of potential energy curve. A role of inflection point of potential energy curve for the quality of rigid rotor harmonic oscillator and rigid rotor Morse oscillator is elucidated.

A molecular dynamics study of intramolecular proton transfer reaction of malonaldehyde in solution based upon a mixed quantum-classical approximation. II. Proton transfer reaction in non-polar solvent.

The intramolecular proton transfer reaction of malonaldehyde in neon solvent has been investigated by mixed quantum-classical molecular dynamics (QCMD) calculations and fully classical molecular dynamics (FCMD) calculations. Comparing these calculated results with those for malonaldehyde in water reported in Part I [A. Yamada, H. Kojima, and S. Okazaki, J. Chem. Phys. 141, 084509 (2014)], the solvent dependence of the reaction rate, the reaction mechanism involved, and the quantum effect therein have been investigated. With FCMD, the reaction rate in weakly interacting neon is lower than that in strongly interacting water. However, with QCMD, the order of the reaction rates is reversed. To investigate the mechanisms in detail, the reactions were categorized into three mechanisms: tunneling, thermal activation, and barrier vanishing. Then, the quantum and solvent effects were analyzed from the viewpoint of the reaction mechanism focusing on the shape of potential energy curve and its fluctuations. The higher reaction rate that was found for neon in QCMD compared with that found for water solvent arises from the tunneling reactions because of the nearly symmetric double-well shape of the potential curve in neon. The thermal activation and barrier vanishing reactions were also accelerated by the zero-point energy. The number of reactions based on these two mechanisms in water was greater than that in neon in both QCMD and FCMD because these reactions are dominated by the strength of solute-solvent interactions.

A hybrid configuration interaction treatment based on seniority number and excitation schemes

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method.

Accurate Prediction of Hyperfine Coupling Constants in Muoniated and Hydrogenated Ethyl Radicals: Ab Initio Path Integral Simulation Study with Density Functional Theory Method.

We performed ab initio path integral molecular dynamics (PIMD) simulations with a density functional theory (DFT) method to accurately predict hyperfine coupling constants (HFCCs) in the ethyl radical (CβH3-CαH2) and its Mu-substituted (muoniated) compound (CβH2Mu-CαH2). The substitution of a Mu atom, an ultralight isotope of the H atom, with larger nuclear quantum effect is expected to strongly affect the nature of the ethyl radical. The static conventional DFT calculations of CβH3-CαH2 find that the elongation of one Cβ-H bond causes a change in the shape of potential energy curve along the rotational angle via the imbalance of attractive and repulsive interactions between the methyl and methylene groups. Investigation of the methyl-group behavior including the nuclear quantum and thermal effects shows that an unbalanced CβH2Mu group with the elongated Cβ-Mu bond rotates around the Cβ-Cα bond in a muoniated ethyl radical, quite differently from the CβH3 group with the three equivalent Cβ-H bonds in the ethyl radical. These rotations couple with other molecular motions such as the methylene-group rocking motion (inversion), leading to difficulties in reproducing the corresponding barrier heights. Our PIMD simulations successfully predict the barrier heights to be close to the experimental values and provide a significant improvement in muon and proton HFCCs given by the static conventional DFT method. Further investigation reveals that the Cβ-Mu/H stretching motion, methyl-group rotation, methylene-group rocking motion, and HFCC values deeply intertwine with each other. Because these motions are different between the radicals, a proper description of the structural fluctuations reflecting the nuclear quantum and thermal effects is vital to evaluate HFCC values in theory to be comparable to the experimental ones. Accordingly, a fundamental difference in HFCC between the radicals arises from their intrinsic molecular motions at a finite temperature, in particular the methyl-group behavior.

Parametric two-electron reduced-density-matrix method applied to computing molecular energies and properties at nonequilibrium geometries

A parametric approach to the variational calculation of the two-electron reduced density matrix (2-RDM) for many-electron atoms and molecules has recently been developed in which the 2-RDM is parametrized to be both size consistent and nearly N-representable [C. Kollmar, J. Chem. Phys. 125, 084108 (2006); A. E. DePrince and D. A. Mazziotti, Phys. Rev. A 76, 049903 (2007)]. The parametric variational 2-RDM method is applied to computing ground-state molecular energies and properties at nonequilibrium geometries in significantly larger basis sets than previously employed. We study hydrogen abstraction from the hydroxide groups of H(2)O, NH(3)OH, and CH(3)OH. The 2-RDM method, parametrized by single and double excitations, shows significant improvement over coupled-cluster methods with similar excitations in predicting the shape of potential energy curves and bond-dissociation energies. Previous work completes the parametrization of the energy and 2-RDM by a system of n(2)h(2) normalization constraints, where n and h are the number of occupied and unoccupied orbitals, respectively. In the present paper, however, we show that the constraints can be eliminated by incorporating them into the energy and 2-RDM functions and, hence, the constrained optimization of the ground-state energy can be reformulated as an unconstrained optimization. The 2-RDMs from the parametric method are very nearly N-representable, and as measured by an l(2) norm, they are more accurate than the 2-RDMs from configuration interaction truncated at single and double excitations by an order of magnitude.

High-temperature mass spectrometry: Instrumental techniques, ionization cross-sections, pressure measurements, and thermodynamic data (IUPAC Technical Report)

Abstract An assessment of high-temperature mass spectrometry and of sources of inaccuracy is made. Experimental, calculated, and estimated cross-sections for ionization of atoms and inorganic molecules typically present in high-temperature vapors are summarized. Experimental cross-sections determined for some 56 atoms are generally close to theoretically calculated values, especially when excitation–autoionization is taken into account. Absolute or relative cross-sections for formation of parent ions were measured for ca. 100 molecules. These include homonuclear diatomic and polyatomic molecules, oxides, chalcogenides, halides, and hydroxides. Additivity of atomic cross-sections supplemented by empirical corrections provides fair estimates of molecular cross-sections. Causes of uncertainty are differences in interatomic distances and in shapes of potential energy curves (surfaces) of neutral molecules and of molecular ions and tendency toward dissociative ionization in certain types of molecules. Various mass spectrometric procedures are described that render the accuracy of measured thermodynamic properties of materials largely independent of ionization cross-sections. This accuracy is comparable with that of other techniques applicable under the conditions of interest, but often only the mass spectrometric procedure is appropriate at high temperatures.

Potential Energy Curves for the Isomerization of Protonated Schiff Base of Retinal on the Triplet State Surface

Potential energy curves (PECs) for the trans–cis isomerization of protonated Schiff base of retinal (PSBR) have been calculated by means of the time-dependent density functional theory (TD-DFT) method at the B3LYP/3-21G* level. The isomerization from all trans to 13-cis forms of PSBR in bacteriorhodopsin (bR) in the ground state (S 0) and low-lying triplet states (T 1–T 10) were considered in the present calculation. The excitation energies from S 0 to T 1 in all trans and 13-cis forms were calculated to be 1.16 and 1.17 eV, respectively. The shape of PEC for the ground state (S 0) showed that the activation barrier is located in where θ13–14 is twist angle around the double bond of PSBR. The shape of PEC for the triplet state (T1) was very similar to that of S 0. In the first excited triplet state, PEC (T2 state), two potential barriers are located at and 112°, while the energy minimum is located at The mechanism of the photo-isomerization on the low-lying triplet states is discussed on the basis of theoretical results.

Comments on the ``Hildebrand Rule''

According to the ``Hildebrand rule,'' normal liquids should have the same entropy of vaporization at temperatures at which their vapors have the same molal volume. Pitzer has shown that liquids which obey the theory of corresponding states should have equal entropies of vaporization at temperatures at which their ratio of vapor volume to liquid volume is the same. He pointed out, however, that this rests upon several assumptions, including, ``potential energy depending only on intermolecular distances and universal shape of potential energy curve.'' In this paper, two pairs of liquids with widely different liquid molal volumes but otherwise closely similar, are compared with the result that the former rule is more closely obeyed, supporting the suggestion that it is an oversimplification to regard the molecular fields of polyatomic molecules as radial from the center of the molecule. The entropy of vaporization of a van der Waals liquid, R[1n(V—b)−1n(v—b)], where V refers to vapor and v to liquid, indicates that equal V and equal v—b should give equal entropy of vaporization. In comparing ethane and diisopropyl, for example, the separation of the methyl groups is more significant than the separation of the molecular centers.