Locally dense basis sets for chemical shift calculations

Calculations of chemical shifts have been carried out using “locally dense” basis sets for the resonant atom of interest, and smaller, attenuated sets on other atoms in the molecule. For carbon, calculations involving a 6-311G(d) triply split valence set with polarization on the resonant atom and 3-21G atomic bases on other heavy atoms result in good agreement with experiment, and are virtually identical to those found employing the larger basis on all atoms. For species such as nitrogen, oxygen, and fluorine where standard balanced basis sets do not agree well with experiment, use of attenuated sets fail as well. The use of locally dense basis sets permits calculations previously impractical, and the successful application to carbon suggests that the chemical shift is most dependent on the local basis set, and less so on whether or not a balanced or unbalanced calculation is being carried out.     

Highly correlated particle densities and idempotent one-densities

The problem of determining idempotent one-densities which integrate to the exact or to a highly correlated particle density is considered. A method for obtaining the minimum energy idempotent one-density integrating to a given correlated particle density within a finite basis is described. The implications of this are twofold. First, Hartree–Fock accuracy can be exceeded in describing the electron density with an idempotent one-density; this is particularly relevant to the problem of constructing orbitals from experimental x-ray scattering data. Second, electron densities from analytic CI or MCSCF wave functions can be made available in a form as compact as the Hartree–Fock density by reporting the orbitals which define the correlated density via an idempotent one-density. A numerical example of the new method is given in which an accurate correlated density for He is “fitted” by an idempotent one-density represented in a finite (near Hartree–Fock) basis. Considering the deficiencies of the basis for this purpose, a technique is suggested for constructing basis sets optimized for prediction of one-electron properties rather than for energy.     

Free energy calculations,enhanced by a gaussian ansatz,for the “chemical work” distribution

The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the “chemical work” of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the “irreversible” work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible “chemical work” minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the “chemical work,” accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the “chemical work.” For a more general free energy perturbation scheme that the Gaussian ansatz may not be valid, the free energy calculation can be expressed in terms of the moment generating function of the “chemical work” distribution. © 2014 Wiley Periodicals, Inc.     

On vibrational bonding of IHI

The vibrational bond of IHI is described in analogy to the covalent bond of H₂⁺ by a Born—Oppenheimer-type separation of light (“hydrogenic” ≡ “electronic”) and heavy (“iodines” ≡ “protons”) particle degrees of freedom. Competing potential energy decreases and hydrogen zero-point energy increases (for the IHI antisymmetric stretching and bending modes) yield a minimum in the iodine symmetric stretching mode's potential energy which supports one bound vibrational IHI state.     

Improved intermolecular SCF theory and the BSSE problem

Analytical and numerical studies are performed concerning the exclusion of the basis set superposition error (BSSE ) from the SCF calculations of intermolecular interactions. Based on these studies a new procedure is proposed, which consists of the following steps: (1) determine the orbitals by the SCF scheme based on the recent “chemical Hamiltonian approach” (CHA-SCF method), i.e., excluding the delocalization effects caused by BSSE , and then (2) calculate the usual energy expectation value. (This gives results superior to those obtained by the previous nonsymmetric CHA energy formula.) The actual numerical calculations performed for different simple systems (He₂, water dimer) by using various basis sets indicate that the CHA/CE (CHA with “conventional energy” formula) potential curves are well-balanced and are close to those obtained by the Boys–Bernardi (BB ) method and usually (but not necessarily) go slightly beyond the latter. So our method gives results better than (or close to) those given by the BB method by performing only a single ～N⁴ calculation at each geometrical arrangement of the system.     

A numerical integration scheme for the evaluation of correlation energy functionals

A numerical integration scheme is presented for three-dimensional integrals occurring in electronic structure calculations, concentrating attention on the evaluation of the correlation energy through a density-functional expression. The scheme is based on the choice of density-based weight functions that naturally partition the space into “atomic” volumes (in which the integration is performed in terms of spherical coordinates) and “diatomic” volumes (in which the integration is performed in terms of confocal elliptical coordinates). Such a choice is justified on the basis of the analytical behavior of the integrand. The attainable accuracy and the required computational effort within the proposed scheme are discussed in detail in a test application on the C₆₀ molecule in the symmetrical configuration. Finally, a comparison with previously proposed schemes is presented. © 1993 John Wiley & Sons, Inc.     

eaq− hydration energy and photoemission threshold potentials for mercury in contact with aqueous electrolytes

The meaning of the “red limit” potential in photoemission experiments is discussed. For mercury in contact with aqueous electrolytes, the energy of a photoemitted electron at the “red limit” is 0.6 eV higher than the solvation energy of e_aq^?. This difference is attributed to the solvent reorganization energy contribution to the hydration energy of e_aq^?.     

Folding Lattice HP Model of Proteins Using the Bond‐Fluctuation Model

In this paper, we find ‘good’ amino acid sequences that fold to a desired “target” structure as a ground state conformation of lowest accessible free energy using the modified bond‐fluctuation lattice model. In our protein lattice model, bond lengths are set to vary between one and √2 in three dimensions. Our results agree well with the native state energies E_N. Comparisons with the “putative native state” (PNS) energy E_PNS and the “hydrophobic zippers” (HZ) energy E_HZ are made. For every sequence, the global energy minimum is found to have multiple degeneracy of conformations, which is the same result as for the constraint‐based hydrophobic core construction (CHCC) method. The interior conformations of the ground states are also discussed.     

Application of the Kelvin equation to vaporization of silver and gold in electrothermal atomic absorption spectrometry

In order to obtain additional insight into the release mechanism of the metals in electrothermal atomization atomic absorption spectrometry, a quantitative relation between the heat of vaporization and the size of the released particles is proposed on the basis of the Kelvin equation. The applicability of the equation for the investigation of silver and gold vaporization is demonstrated and the limits in which the model is valid are determined.According to the present considerations the activation energy could be equal to the heat of vaporization of the silver and gold droplets. An explanation of the observed dependence of activation energy on analyte mass is given. The proposed relation provides a possibility for definition and evaluation of an “effective” radius/size of the droplets on the basis of their heat of vaporization. A correlation between the mass of the injected sample and the “effective” radius of the droplets, obtained at higher temperature is found. The minimum and maximum “effective” radii of the droplets, following the proposed equation are calculated for Ag on pyrolytic graphite coated electrographite (PGC) and Au on PGC, uncoated electrographite (EG) and glassy carbon (GC) tubes. The results obtained are indirect evidence for the island structure of precursor metal layer and for the existence of silver and gold microdroplets on the graphite support.     

Equilibrium structure and harmonic force field of the known PH3 and the unknown PH5

The equilibrium geometries and harmonic force fields of PH₃ and PH₅ are calculated in an ab initio way including electron correlation. The results for PH₃ are in very good agreement with experimental values, whereas those for PH₅ have to be regarded as predictions. We find for PH₅ in its equilibrium D _3h structure r _ax = 1.47 Å, r _eq = 1.42 Å and the harmonic vibration frequencies in Table 7 given under the heading “CEPA”. The barrier for Berry inversion is 2 kcal/mol. The ab initio calculation of phosphoranes such as PH₅ not only requires the inclusion of polarization functions (d on P and p on H) but is also very sensitive to the choice of these polarization functions. This problem is taken care of by a detailed comparison of various basis sets. It is confirmed that a (10/6) basis for P in “double zeta contraction” is better balanced than a (12/9) basis in “double zeta contraction” and that the total energy is not a good criterion for the quality of a basis.     

Spectral interferences in inductively coupled plasma atomic emission spectrometry-I: A theoretical and experimental study of the effect of spectral bandwidth on selectivity,limits of determination,limits of detection and detection power

This article links up with recent work on high resolution spectroscopy in this laboratory [1] and primarily deals with the effect of the spectral resolution on the “selectivity” in the case of samples that emit line-rich spectra. The concept of selectivity, as developed by KAISER [8] on the basis of the set of calibration equations for a multicomponent system, is considered as a useful starting-point but is rejected as a meaningful analytical figure of merit. Instead the concept of “line selectivity” is introduced as a criterion and related to the analytical error. This approach leads to a definition of the limit of determination such that its dependence on the spectral resolution can be clearly and unambiguously revealed in any concrete situation, that is, once the sample type has been specified. Such a specification is necessary since the numerical values of quantities related to selectivity are inherently linked with sample composition.Thus the theory is illustrated with practical examples including the results of a multiplicity of simulated line overlap situations using representative experimental line profiles measured at two extreme levels of resolution, referred to as “medium” and “high” resolution.It is shown that in the case of line overlap the limit of determination may exceed the limit of detection by one or even two orders of magnitude, unless line selection is based on a selectivity criterion so that the limit of detection is inherently coupled to the limit of determination. It is also shown that the prime benefit of high resolution spectroscopy is the reduction of the limit of determination, not that of the limit of detection. This benefit is found only if the spectral resolution can improve the selectivity, thus if there exist situations of line overlap.     

The Pyrolysis of Azides in the Gas Phase

The chemistry of the non-metallic elements has in recent years passed through a period of rapid development, often referred to as its “renaissance”. To emphasize just one of the key facets: numerous short-lived molecules containing multiple bonds to elements of the third and higher periods have been discovered, often accompanied by the planned synthesis of derivatives which are sterically shielded by bulky groups and thus kinetically stabilized. Thus today molecules such as silabenzenes H₆C_6?nSi_n and silaethenes H₂Si?CH₂ or R₂Si?CR₂, disilenes R₂Si?SiR₂ and diphosphenes RP?PR, silaphenylisonitrile H₅C₆? N?Si, or methylidyne-phosphanes R? C?P, are all well-known species. Sandwich compounds with P₆ rings or silicon centers demonstrate that there are now hardly any barriers to impede the imagination of the non-metal chemist. In sharp contrast is our lack of knowledge regarding the “microscopic” pathways of chemical reactions: thus apart from information provided for example by molecular beam experiments, or from exact numerical calculations involving species consisting of only a few atoms, it remains largely unknown from which directions medium-sized molecules must approach each other to successfully collide and form a “reaction complex”, in which way their structures are changed in such a process or which role is played by molecular dynamics in the energy transfer.–The pyrolysis of azides X? N₃, i.e. compounds which tend to explode violently when ignited in the condensed phase but can be heated in low-pressure gas flow systems without much risk, illustrates that studies of reactive intermediates are of interest not only because novel molecules may be discovered and isolated, and thereby possibilities for synthesis expanded. Moreover, some aspects of the “microscopic” pathways of these azide pyrolyses can be described satisfactorily on the basis of calculated energy hypersurfaces, and the influence of molecular dynamics becomes experimentally visible in the “chemical activation” of intermediates which leads to their “thermal explosion”.     

Stability conditions for the solutions of the hartree-fock equations. VII. Stability of some closed-shell nonalternant systems

The instabilities of the solutions to the Hartree-Fock equations for the nonalternants in the pentalene, heptalene, etc., series and in the azulene, etc., series are examined. The systems are found to have symmetry-adapted solutions which are unstable for values of the core integral β close to the standard (spectroscopic) value; for example, the pentalene solution is unstable with β equal to 75% of its standard value. The “broken” symmetry solutions although exhibiting only a very slightly lower energy (0.01 eV) may exhibit dramatically different values for other properties, e.g., 30% changes in bond orders. The off-diagonal charge-density wave (CDW ) appearing in the “broken” symmetry solutions at the onset of instability is amplified as the cooperative phenomena dominate, until in the “fully correlated” limit, the linked-ethylenic (bond alternating) structure is obtained.     

The Structure of Cellulose by Conformational Analysis. 1. Cellobiose and Methyl-β-cellobioside

Conformational analysis studies on the tertiary structure of cellobiose and methyl-β-cellobioside were carried out by using calculations of van der Waals, H-bond, electrostatic, and torsional energy interactions between the atoms and groups of the molecules. Energy maps as functions of the rotational anglesΨo and Φ° of the glucosidic bond were obtained in increments of 20° and refined in increments of 1°. Two “primary” and one “secondary” conformations of minimum energy were obtained for both cellobiose and methyl-β-cellobioside, some of which are equivalent to results obtained by x-ray diffraction. The H-bond forces are shown to be, together with the van der Waals forces, the predominant factors in the fixation of the conformations of minimum energy. The position and energy contributions of the H-bonds patterns for the favored conformations are identified.     

A conformational analysis of the six isomers of oxybispyridine

Conformational energy contour maps of the six isomers of oxybispyridine have been constructed using the ab initio STO-3G molecular orbital method. The calculations (employing a partial rigid rotor) for all six isomers indicate that the minimum energy conformers are not planar and that energy barriers between 70–1000 kJ mol^?1 restrict interconversion to planar structures, thereby preventing conjugation between the p-electrons of the oxygen atom with the π system of the pyridine rings. It is postulated that of the three mechanisms used to explain conformer interconversion about the C? O bond, the disrotatory one-ring flip mechanism is the most appropriate, since the “Morino's” structures are all within 2.5 kJ mol^?1 of the minimum. Furthermore, room temperature accessibility of the “Morino's” structures suggests that the Smiles rearrangement would be possible for suitably substituted derivatives of these isomers.     

Inhomogeneous polymer solutions: Theory of the interfacial free energy and the composition profile near the consolute point

The Flory–Huggins formulation of the combinatorial entropy, supplemented with residual free energy, is applied locally to obtain the interfacial free energy and the concentration profile of polymer in the interface between two demixed polymer solution phases. Two choices were investigated for the residual free energy: a “regular solution” formulation and an empirical formulation of Koningsveld for polystyrene in cyclohexane. Asymptotic, analytical solutions of the equations near the critical solution point and solutions obtained by numerical calculations are given as a function of temperature for several molecular weights. At temperatures farther below the critical temperature the equations have no solutions. The reason for this is not entirely clear. The local formulation of the free energy used here is an improved version of a previous one, which gave wrong results for asymmetric systems (polymer in a low molecular weight solvent). This newer version is consistent with our theory of critical opalescence and gives a relation between the interface “thickness” and the correlation range of the concentration fluctuations. The calculated correlation ranges were in good accord with those found experimentally by Debye, Chu, and Woerman. That the newer version of our equations for an interface gives no acceptable solutions at lower temperatures could be caused by a “collapse” of a diffuse to a sharp interface as suggested by Nose.     

A metropolis Monte Carlo method for computing microcanonical statistical rate constants

A new method of computing microcanonical statistical rate constants is presented. The method utilizes the Metropolis Monte Carlo algorithm in a manner which circumvents some of the numerical inefficiency associated with other Metropolis and “shot-gun” Monte Carlo based schemes. It is therefore expected to be useful in studies of many degree of freedom systems where numerical efficiency is crucial. Optimization of the method efficiency with respect to its adjustable parameters is examined in detail, both theoretically and in a numerical study of the T-shaped Ar₃ “inversion” process. The energy dependence of the T-shaped Ar₃ inversion rate is studied in a sample application of the method. An application to full three dimensional Ar₃ will be presented in a future study.     

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.     

Toward a prediction of the phase behavior of polyamide blends

As we have reported recently, the application of association models has provided a theoretical basis for the calculation of the free energy changes and phase diagrams of binary polymer blends in which hydrogen bonding plays a significant role. Here we report theoretical calculations of spinodal phase diagrams of a series of polyisophthalamide-polyether blends and compare the predictions with experimental observations of the miscibility of these polymer blend systems. The general agreement between theory and experiment is very encouraging and has important ramifications to discussions of polymer-induced crystallnity, the minimum number of hydrogen bonding sites necessary to ensure significant molecular mixing, and the effect of hydrogen bonding on the breadth of “miscibility windows.”