Reduced local energy as a criterion for the accuracy of approximate Hartree–Fock wave functions. Application to H2O and CH4

The reduced local energy E_L of Rothstein and co-workers is discussed as a criterion for the local accuracy of approximate wave functions. The behavior of E_L for different approximation levels is discussed. It is shown that, for particular classes of wave functions, fluctuations of E_L reflect local inaccuracies of the wave function as compared to certain convergence limits. The applicability of this criterion is illustrated with approximate Hartree–Fock wave functions for water and methane.     

A critical local energy release rate criterion for fatigue fracture of elastomers

Using Digital Image Correlation on high‐resolution images, the full strain field near the tip of a crack propagating under cyclic loading in an elastomer was characterized. We show unambiguously, and for the first time, the existence of a strongly localized and highly oriented process zone close to the crack tip and propose a simple physical model introducing a local energy release rate g_local = W_unloadingH₀, where W_unloading is the unloading strain energy density in uniaxial tension at the maximum strain measured at the crack tip, and H₀ is the undeformed size of the highly stretched zone in the loading direction. Remarkably, the crack growth rate under cyclic loading is found to fall on a master curve as a function of g_local for three elastomers with different filler contents and crosslinking densities, while the same crack growth rate as a function of the applied macroscopic energy release rate G, differs by two orders of magnitude for the same three elastomers. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1518–1524, 2011     

Generalized quantum mechanical two-centre problems. IV. On the accuracy of simple LCAO approximations for H 2 + states and the Eckart criterion

If x denotes an exact solution of the quantum mechanical two centre Coulomb problem, we optimize a normalized LCAO approximation by making the overlap S = (x¦) a maximum. In this context we study how a weight factor (r _a r _b )^–1 in the definition of the inner product changes the approximation and the expectation value of electronic energy. Finally we compare the lower bound given by the Eckart criterion with the exact overlap. Results are reported for H ₂ ⁺ states 1s_g and 2p_u.Dedicated to Professor Hermann Hartmann on occasion of his 70th birthday on May 4th, 1984     

Analytical energy surfaces for the collinear H+H2 and Li+H2 exchange reactions

A simple four-parameter function is shown to possess adequate flexibility to fit the H + H₂ →H₂ + H and Li + H₂ → LiH + H exchange reaction energy surfaces to good accuracy along the reaction paths.     

General criteria for assessing the accuracy of approximate wave functions and their densities

Master equations for propagators in quantum open systems and their spectral resolutions are derived. The Zwanzig partitioning scheme along the superoperator algebra are used to derive equations of motion for partitioned operators in a Liouville space. The reservoir influence on the dynamical evolution of operators is shown to lead explicitly to dissipative effects arising from memory terms in the evolution equations of such operators. It is also shown that spectral representations may be written in a self-consistent analytic way by means of the self-energy fields for transition energies of the system by taking into account the lack of the complete knowledge about the reservoir. A kinematic fluid interpretation of the resultant equations is given and an explicit form of the “collision” superoperator is obtained. Finally, a simple example to illustrate the determination of self-energy fields for the system–reservoir interaction corrections is given. © 1995 John Wiley & Sons, Inc.     

Reduced dimensionality quantum calculations of resonances in H + H2

Reduced dimensionality quantum reaction probabilities are reported for the H+H₂ reaction using the ab initio potential surface of Liu, Siegbahn, Truhlar and Horowitz. Resonances are found for the ground and first two excited adiabatic bending states of H₃. Comparison of the resonance energies with the new coupled states calculations of Colton and Schatz shows good agreement. Additional resonances are reported for energies greater than those considered in the coupled states studies.     

Water line lists close to experimental accuracy using a spectroscopically determined potential energy surface for H2(16)O, H2(17)O, and H2(18)O

Line lists of vibration-rotation transitions for the H(2) (16)O, H(2) (17)O, and H(2) (18)O isotopologues of the water molecule are calculated, which cover the frequency region of 0-20 000 cm(-1) and with rotational states up to J=20 (J=30 for H(2) (16)O). These variational calculations are based on a new semitheoretical potential energy surface obtained by morphing a high accuracy ab initio potential using experimental energy levels. This potential reproduces the energy levels with J=0, 2, and 5 used in the fit with a standard deviation of 0.025 cm(-1). Linestrengths are obtained using an ab initio dipole moment surface. That these line lists make an excellent starting point for spectroscopic modeling and analysis of rotation-vibration spectra is demonstrated by comparison with recent measurements of Lisak and Hodges [J. Mol. Spectrosc. (unpublished)]: assignments are given for the seven unassigned transitions and the intensity of the strong lines are reproduced to with 3%. It is suggested that the present procedure may be a better route to reliable line intensities than laboratory measurements.     

Spin-spin coupling constant 3 J H,F as a reliable criterion for recognition of individual regioisomeric and tautomeric pairs of H(CF2)2-containing isoxazoles and pyrazoles

The spin-spin coupling constant ³ J _H,F of the H(CF₂)₂ group varies within 1.6—3.5 Hz for 5-R^F- and 3.8—4.5 Hz for 3-R^F-isoxazoles and pyrazoles in CDCl₃ and can serve as a reliable criterion for recognition of regioisomeric and tautomeric structures of H(CF₂)₂-containing heterocyclic compounds.     

Efficient evaluation of the accuracy of molecular quantum dynamics on an approximate analytical or interpolated ab initio potential energy surface

Ab initio electronic structure methods have reached a satisfactory accuracy for the calculation of static properties, but remain too expensive for quantum dynamical calculations. Recently, an efficient semiclassical method was proposed to evaluate the accuracy of quantum dynamics on an approximate potential without having to perform the expensive quantum dynamics on the accurate potential. Here, this method is applied for the first time to evaluate the accuracy of quantum dynamics on an approximate analytical or interpolated potential in comparison to the quantum dynamics on an accurate potential obtained by an ab initio electronic structure method. Specifically, the vibrational dynamics of H₂ on a Morse potential is compared with that on the full CI potential, and the photodissociation dynamics of CO₂ on a LEPS potential with that on the excited ¹Π surface computed at the EOM‐CCSD/aug‐cc‐pVDZ level of theory. Finally, the effect of discretization of a potential energy surface on the quantum dynamics is evaluated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2426–2435, 2010     

Zeroth-order exchange energy as a criterion for optimized atomic basis sets in interatomic force calculations. Application to He2

A suggestion is made for using the zeroth-order exchange term, at the one-exchange level, in the perturbation development of the interaction energy as a criterion for optimizing the atomic basis sets in interatomic force calculations. The approach is illustrated for the case of two helium atoms.     

Boundary conditions for the Swain-Schaad relationship as a criterion for hydrogen tunneling

Hydrogen quantum mechanical tunneling has been suggested to play a role in a wide variety of hydrogen-transfer reactions in chemistry and enzymology. An important experimental criterion for tunneling is based on the breakdown of the semiclassical prediction for the relationship among the rates of the three isotopes of hydrogen (hydrogen -H, deuterium -D, and tritium -T). This is denoted the Swain-Schaad relationship. This study examines the breakdown of the Swain-Schaad relationship as criterion for tunneling. The semiclassical (no tunneling) limit used hereto (e.g., 3.34, for H/T to D/T kinetic isotope effects), was based on simple theoretical considerations of a diatomic cleavage of a stable covalent bond, for example, a C-H bond. Yet, most experimental evidence for a tunneling contribution has come from breakdown of those relationship for a secondary hydrogen, that is, not the hydrogen whose bond is being cleaved but its geminal neighbor. Furthermore, many of the reported experiments have been mixed-labeling experiments, in which a secondary H/T kinetic isotope effect was measured for C-H cleavage, while the D/T secondary effect accompanied C-D cleavage. In experiments of this type, the breakdown of the Swain-Schaad relationship indicates both tunneling and the degree of coupled motion between the primary and secondary hydrogens. We found a new semiclassical limit (e.g., 4.8 for H/T to D/T kinetic isotope effects), whose breakdown can serve as a more reliable experimental evidence for tunneling in this common mixed-labeling experiment. We study the tunneling contribution to C-H bond activation, for which many relevant experimental and theoretical data are available. However, these studies can be applied to any hydrogen-transfer reaction. First, an extension of the original approach was applied, and then vibrational analysis studies were carried out for a model system (the enzyme alcohol dehydrogenase). Finally, the effect of complex kinetics on the observed Swain-Schaad relationship was examined. All three methods yield a new semiclassical limit (4.8), above which tunneling must be considered. Yet, it was found that for many cases the original, localized limit (3.34), holds fairly well. For experimental results that are between the original and new limits (within statistical errors), several methods are suggested that can support or exclude tunneling. These new and clearer criteria provide a basis for future applications of the Swain-Schaad relationship to demonstrate tunneling in complex systems.     

An approximate potential energy surface for HeI2 collisions

We have calculated the interaction potential for HeI₂ in T-shaped geometries using Hartree—Fock and Møller—Plesset third-order perturbation t     

Al-doped B80 fullerene as a suitable candidate for H2, CH4, and CO2 adsorption for clean energy applications

Dispersion-corrected density functional theory method was performed to report on a high-performance adsorbent for removal of CO₂ from the precombustion and natural gases. At first, the effect of Al atom impurity on the structural and electronic properties of B₈₀ fullerene is studied. Then, the adsorption geometries and energies of gases (H₂, CH₄, or CO₂) on the B₈₀ and AlB₇₉ (amphoteric adsorbents) are explored. The Al atom enhances reactivity of the cage toward the gases and the adsorption processes are more exothermic with low and high energy barriers for chemisorption of H₂ and CO₂, respectively. Stable chemisorption of CO₂ on the AlB₇₉ is validated by the high adsorption energy and large charge transfer, while the CH₄ is just physically adsorbed on the AlB₇₉. Further, the physisorbed gases can enhance field emission current of the AlB₇₉ and in the continuous capturing of the gases, the magnetic moment of the cage is quenched. Furthermore, dependency of the electronic structure of the adsorbent on the gas adsorption is intensively studied. We suggest that the AlB₇₉ could be a promising material for capture, storage, and separation of the gases and as a novel material for sustainable energy and sweetening process in the petroleum industry.     

Local energy as an indicator of the accuracy of wave functions and probability densities for helium

The local energy is examined as an indicator of the accuracy of approximate wave functions for the ground state of helium. It is observed that at a given point (1) an inaccurate local energy may or may not correspond to an inaccurate value of the wave function or probability density, but (2) a value of the local energy within 0.1 a.u. of the ground-state energy corresponds to a value of the approximate wave function or probability density within about 10% of that for the ground-state wave function.     

Kinetic isotope effects for the H2 + C2H ↔ C2H2 + H reaction based on the ab initio calculations and a global potential energy surface

In the present paper, kinetic isotope effects of the title reaction are studied with canonical variational transition state theory on the modified Wang Bowman (MWB) potential energy surface (PES) (Chem Phys Lett 2005, 409, 249) and the ab initio calculations at the quadratic configuration interaction (QCISD (T, full))/aug‐cc‐pVTZ//QCISD (full)/cc‐pVTZ level. The calculated rate constants for the isotopic variants of this title reaction on the MWB PES have good agreement with those of the present ab initio calculations over the temperature range of 20–5000 K for the forward reactions and 800–5000 K for the reverse reactions, respectively. In particular, the forward rate constants for the title reaction and its isotopically substituted reactions have negative temperature dependences at about 40 K. Rate expressions are presented for all the studied reactions. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 289–298, 2010     

Exact quantum mechanical reaction probabilities for the collinear H + H2 reaction on a porter-karplus potential energy surface

Exact quantum mechanical calculation of the reaction probability for the collinear H + H₂ reaction on a Porter-Karplus potential energy surface are carried out by the finite-difference boundary value method at 6 energes in the threshold region and compared to close coupling, distorted wave, classical S matrix, transition state theory, and vibrational adiabatic calculations.     

On the accuracy of the many-points local procedures

As until now proposed in the literature, in the local energy calculations we can distinguish “few-points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many-points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many-points” calculation M points/N functions (M > N) can be connected in a simple way with the errors of the (^M_N) partial calculations N points/N functions. This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.