Monohydration selectivity mechanism of alkali cations in the potassium channel of excitable biomembranes

Nonempirical quantum chemical method Hartree–Fock–Roothan LCAO SCF MO in a two-exponent Dunning basis with the use of an extended set of Gaussian functions by Huzinaga–Dunning with consideration of electron correlation according to the Meller–Plesset theory of excitations of the second order was used to study monohydrates of Li⁺, Na⁺, K⁺, and HCOO^? ions. The indicated basis was supplemented with polarization functions of d-type on the O atom and of p-type on the hydrogen atom as well as with diffusion functions of p-type on the oxygen atom. It has been found that binding energies of the water molecule with Li⁺, Na⁺ appeared to be higher and with K⁺ lower than with HCOO^? · H₂O. Potential curve shapes of K⁺ + H₂O and HCOO^? + H₂O reactions are shown to be similar. The molecular mechanism of K⁺ channel selectivity of an excitable membrane is explained on the basis of the obtained calculations.     

Uniform quality gaussian basis sets for molecular calculations. II. C2 hydrocarbons

This investigation is a continuation of a study on the optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for ions. A formal charge parameter Q is used to adjust AO basis sets to the molecular environment, by virtue of a simple quadratic equation. Calculations are performed on a series of seven C₂ hydrocarbons (C₂H₂, C₂H₄, C₂H₆, C₂H₃⁺ (open), C₂H₃⁺ (bridged), C₂H₅⁺ (bridged), and C₂H₄^? radical anion). A simple rule is formulated to give approximate values of the charge parameter Q.     

Matrix elements for Ĵ2 and Ĵz operators over explicitly correlated Cartesian Gaussian functions

General formalism for evaluation of multiparticle integrals involving J?² and J?_z operators over explicitly correlated Cartesian Gaussian functions is presented. The integrals are expressed in terms of the general overlap integrals. An explicitly correlated Cartesian Gaussian function is a product of spherical orbital Gaussian functions, powers of the Cartesian coordinates of the particle, and exponential Gaussian factors, which depend on interparticular distances. This development is relevant to both adiabatic and nonadiabatic calculations of energy and properties of multiparticle systems. © 1995 John Wiley & Sons, Inc.     

Analytical gradients for Singer's multicenter n‐electron explicitly correlated Gaussians

Analytical gradients for Singer's basis of n‐electron multicenter explicitly correlated Gaussian functions are derived and implemented to variationally optimize the energy and wave function of molecular systems within the Born–Oppenheimer approximation. Wave functions are optimized with respect to (½n(n+1)+3n) nonlinear variational parameters and one linear coefficient per term in the basis set. Preliminary results for the ground states of H₃⁺ and H₃ suggest that the method can be more flexible and can achieve lower energies than previously reported calculations. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 151–159, 2001     

Molecule‐adapted basis sets optimized with a quantum Monte Carlo method

The Monte Carlo simulated annealing method is adapted to optimize correlated Gaussian‐type functions in nonrelativistic molecular environments. Starting from an atom‐centered atomic Gaussian basis set, the uncontracted functions are reoptimized in the molecular environments corresponding to the H₂O, CN^?, N₂, CO, BF, NO⁺, CO₂, and CS systems. These new molecular adapted basis sets are used to calculate total energies, harmonic vibrational frequencies, and equilibrium geometries at a correlated level of theory. The present methodology is a simple and effective way to improve molecular correlated wave functions, without the need to enlarge the molecular basis set. Additionally, this methodology can be used to generate hierarchical sequences of molecular basis sets with increasing size, which are relevant to establish complete basis set limits. © 2014 Wiley Periodicals, Inc.     

Gaussian expansions of hydrogenic functions involving few variational parameters

Fully optimized lengthy Gaussian expansions of hydrogenic 1s and 2p_z functions have been practically reproduced by generating the variational parameters by means of suitably chosen functions involving only few parameters. Hydrogenic 3d_xy and 4f_xyz functions have been approximated in a similar way. The usefulness of such generating functions is briefly discussed.     

Evaluation of one-electron integrals for arbitrary operators V(r) over Cartesian Gaussians: Application to inverse-square distance and Yukawa operators

A general procedure is presented for generating one-electron integrals over any arbitrary potential operator that is a function of radial distance only. The procedure outlines that for a nucleus centered at point C integrals over Cartesian Gaussians can be written as linear combinations of 1-D integrals. These Cartesian Gaussian functions are expressed in a compact form involving easily computed auxiliary functions. It is well known that integrals over the Coulomb operator can be expressed in terms of F_n(T) integrals, where By means of a substitution for F_n(T) by other simple functions, algorithms that form integrals over an arbitrary function can be generated. Formation of such integrals is accomplished with minor editing of existing code based on the McMurchie–Davidson formalism. Further, the method is applied using the inverse-square distance and Yukawa potential operators V(r) over Cartesian Gaussian functions. Thus, the proposed methodology covers a large class of one-electron integrals necessary for theoretical studies of molecular systems by ab initio calculations. Finally, by virtue of the procedure's recursive nature it provides us with an efficient scheme of computing the proposed class of one-electron integrals. © 1993 John Wiley & Sons, Inc.     

Comparative study of unconventional 1s basis functions for the 1Σ ground state of H2 and He

We investigated various nonstandard 1s basis functions (generalized Slater-Gaussian, ellipsoidal Gaussian, floating spherical and ellipsoidal Gaussian, rational function, Hulthén approximation, two-Slater-type orbital, generalized Guillemin–Zener function, and various noninteger-n elliptical orbitals) for approximating the ¹Σ ground state of H₂ and He₂⁺⁺. A CI trial wave-function including Σ_g-type MO's is adopted and molecular integrals are evaluated numerically. The energy improvement on the 1s STO is small except for noninteger-n orbitals which closely approach the “SCF limit”.     

Constrained self-consistent-field wave functions with improved long-range behavior

The recent suggestion that the long-range behavior of energy-optimized Gaussian basis sets can be improved by augmenting them with a Gaussian chosen to satisfy a constraint involving a linearly averaged position moment is explored. Calculations indicate that the high-order moments 〈r^k〉, with k > 4, in He, Be, and Li^?, and 〈x^kz^L?k〉, with L > 4 and k ≤ L, in H₂ are improved by the constraint, but that lower-order moments and dipole polarizabilities are not. In H₂, the higher moments with a given L improve by different amounts for different k, and, hence, the multipole moments do not improve. The basis-set superposition error in He? He and Be? Be interaction energy calculations decreases if the internuclear distance is large enough. Thus, the constraint procedure improves the very long range behavior of the self-consistent-field wave functions. © 1992 John Wiley & Sons, Inc.     

Structure and stability of ion pairs A−·K+·H2O with a strong anion

Characteristics of the ion pairs HCOO^–·Na⁺·H₂O, HCOO^–·K⁺·H₂O, and also Na⁺·H₂O and K⁺·H₂O were calculated by the nonempirical Hartree—Fock—Roothan linear-combination-of-atomic-orbitals self-consistent-field (SCF) molecular-orbital method in a two-exponent Dunning basis using an extended set of Huzinaga—Dunning Gaussian functions. The basis was supplemented by polarization functions ofd type for the oxygen atom andp type for the H atom and also by diffusion functions ofp type for the oxygen atom. Characteristics of the ion pairs HCOO^–·Li⁺ and HCOO^–·Na⁺ were calculated taking into account the electronic correlation according to the Möller — Plesset second-order perturbation theory. Significant quantitative difference was observed in the hydration of ionogens and free cations. The stability of the ionogens HCOOMe in aqueous solutions, increasing from Li⁺ to Cs⁺, is not explained by the difference between the energies of complexation and the energies of hydration of the cations. The better solubility of the salt molecule with a cation of smaller radius is due to the higher degree of hydration of that ionogen.N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 117977 Moscow. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 12, pp. 2700–2707, December, 1992.     

Completeness of Gaussian orbital and geminal basis sets for linear molecules in L2 and in the first and second Sobolev spaces

Completeness theorems for Gaussian orbital and geminal basis sets of axial symmetry are proved in the space L² of square integrable functions and in the first and second Sobolev spaces H¹ and H². © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 357–384, 1998     

Prediction of hydrocarbon enthalpies of formation by various thermochemical schemes

The correlation consistent composite approach (ccCA) has been used to compute the enthalpies of formation (ΔH_f′s) for 60 closed‐shell, neutral hydrocarbon molecules selected from an established set (Cioslowski et al., J. Chem. Phys. 2000 , 113, 9377). This set of thermodynamic values includes ΔH_f's for hydrocarbons that span a range of molecular sizes, degrees of aromaticity, and geometrical configurations, and, as such, provides a rigorous assessment of ccCA's applicability to a variety of hydrocarbons. The ΔH_f's were calculated via atomization energies, isodesmic reactions, and hypohomodesmotic reactions. In addition, for 12 of the aromatic molecules in the set that are larger than benzene, the energies of ring‐conserved isodesmic reactions were used to calculate the ΔH_f′s. Using an atomization energy approach to determine the ΔH_f′s, the lowest mean absolute deviation (MAD) from experiment achieved by ccCA for the 60 hydrocarbons was 1.10 kcal mol^?1. The use of the mixed Gaussian/inverse exponential complete basis set extrapolation scheme (ccCA‐P) in conjunction with hypohomodesmotic reaction energies resulted in a MAD of 0.87 kcal mol^?1. This value is compared with MADs of 1.17, 1.18, and 1.28 kcal mol^?1 obtained via the Gaussian‐4 (G4), Gaussian‐3 (G3), and Gaussian‐3(MP2) [G3(MP2)] methods, respectively (using the hypohomodesmotic reactions). © 2012 Wiley Periodicals, Inc.     

Correlation of the position of the bond functions in H-X with electronegativity

S type Gaussian bond functions are optimized for HF, H₂O, NH₃, and CH₄. The optimization is carried out with respect to the exponent and position in the H-X bond. The position is found to correlate well with the electronegativity of Pauling and Allred-Rochow.     

SCF calculations for H 2 + , Li 2 + and LiH+ with atomic basis sets enlarged by bond functions

To simulate the charge distortion in the formation of a molecule from the separated atoms, a set of concentrics-type Gaussian functions is placed on the internuclear axis in addition to thes-type atomic basis functions to construct the molecular orbital for the one valence-electron systems H ₂ ⁺ , Li ₂ ⁺ and LiH⁺. This simple model gives 90.1%, 75.2% and 61.7%, respectively, of the improvement over minimal basis relative to Hartree-Fock energies.Supported in part by a research grant to Rice University from the Robert A. Welch Foundation.     

Unimolecular reactions of the isolated immonium ions CH3CH = NH+C4H9, CH3CH2Ch = NH+C4H9 and (CH3)2C = NH+C4H9

The reactions of ten metastable immonium ions of general structure R¹R²C?NH⁺C₄H₉ (R¹ = H, R² = CH₃, C₂H₅; R¹ = R² = CH₃) are reported and discussed. Elimination of C₄H₈ is usually the dominant fragmentation pathway. This process gives rise to a Gaussian metastable peak; it is interpreted in terms of a mechanism involving ion-neutral complexes containing incipient butyl) cations. Metastable immonium ions ontaining an isobutyl group are unique in undergoing a minor amount of imine (R¹R²C?NH) loss. This decomposition route, which also produces a Gaussian metastable peak, decreases in importance as the basicity of the imine increases. The correlation between imine loss and the presence of an isobutyl group is rationalized by the rearrangement of the appropriate ion-neutral complexes in which there are isobutyl cations to the isomeric complexes containing the thermodynamically more stable tert-butyl cations. A sizeable amount of a third reaction, expulsion of C₃H₆, is observed for metastable n-C₄H₉ ⁺NH?CR¹R² ions; in contrast to C₄H₈ and R¹R²C?NH loss, C₃H₆ elimination occurs with a large kinetic energy release (40–48 kJ mol^?1) and is evidenced by a dish-topped metastable peak. This process is explained using a two-step mechanism involving a 1,5-hydride shift, followed by cleavage of the resultant secondary open-chain cations, CH₃CH⁺ CH₂CH₂NHCHR¹R².     

Small-angle electron scattering by formaldehyde and ketene: Effects of electron correlation and chemical binding

The total (elastic plus inelastic) intensities of 51 keV electrons scattered by H₂CO and H₂CCO have been measured over a range of K = (4π/λ) sin(θ/2) = 1–9.5 Å^?1 and compared with the theoretical intensities calculated with SCF and CI wave functions. Significant discrepancies are found between the experimental intensities and the theoretical ones based on the SCF wave functions. Most of the chemical binding and electron correlation effects observed in the total scattered intensities are reproduced by the theoretical intensities based on the CI wave functions calculated with the basis set including polarization functions on all atoms. © 1992 John Wiley & Sons, Inc.     

Supramolecular architectures in the salt trimethoprimium ferrocene‐1‐carboxylate and the cocrystal 4‐amino‐5‐chloro‐2,6‐dimethylpyrimidine–ferrocene‐1‐carboxylic acid (1/1)

In the salt trimethoprimium ferrocenecarboxylate [systematic name: 2,4‐diamino‐5‐(3,4,5‐trimethoxybenzyl)pyrimidin‐1‐ium ferrocene‐1‐carboxylate], (C₁₄H₁₉N₄O₃)[Fe(C₅H₅)(C₆H₄O₂)], (I), of the antibacterial compound trimethoprim, the carboxylate group interacts with the protonated aminopyrimidine group of trimethoprim via two N—H…O hydrogen bonds, generating a robust R ₂²(8) ring motif (heterosynthon). However, in the cocrystal 4‐amino‐5‐chloro‐2,6‐dimethylpyrimidine–ferrocene‐1‐carboxylic acid (1/1), [Fe(C₅H₅)(C₆H₅O₂)]·C₆H₈ClN₃, (II), the carboxyl–aminopyrimidine interaction [R ₂²(8) motif] is absent. The carboxyl group interacts with the pyrimidine ring via a single O—H…N hydrogen bond. The pyrimidine rings, however, form base pairs via a pair of N—H…N hydrogen bonds, generating an R ₂²(8) supramolecular homosynthon. In salt (I), the unsubstituted cyclopentadienyl ring is disordered over two positions, with a refined site‐occupation ratio of 0.573 (10):0.427 (10). In this study, the two five‐membered cyclopentadienyl (Cp) rings of ferrocene are in a staggered conformation, as is evident from the C…Cg …Cg …C pseudo‐torsion angles, which are in the range 36.13–37.53° for (I) and 22.58–23.46° for (II). Regarding the Cp ring of the minor component in salt (I), the geometry of the ferrocene ring is in an eclipsed conformation, as is evident from the C…Cg …Cg …C pseudo‐torsion angles, which are in the range 79.26–80.94°. Both crystal structures are further stabilized by weak π–π interactions.     

有机-无机杂化配位聚合物{[C12H28N2][(Pb3I8) (DMF)2]•2DMF}n的晶体及电子结构

合成了一种新颖有机-无机杂化配位聚合物{[C₁₂H₂₈N₂] [(Pb₃I₈)(DMF)₂]•2DMF}_n, 并进行了红外、紫外、热重表征, 采用X射线衍射方法确定了晶体结构. 结构解析表明, 整个分子由阳离子(双质子化的N,N'-二丁基哌嗪)及聚阴离子链([(Pb₃I₈)(DMF)₂]_n^2-)组成, 它们之间由静电作用结合在一起形成一维链状配位聚合物. 依据晶体结构数据, 采用Gaussian03程序对产物进行量子化学计算.     

Theoretical Study on the Intermolecular Interactions between 1,1‐Diamino‐2,2‐Dinitroethylene and H2O

The density functional method was applied to the study of 1,1‐diamino‐2,2‐dinitroethylene (Fox‐7)/H₂O dimer. All the possible dimers ( 1, 2 and 3 ), as well as the monomers, were fully optimized with the DFT method at the B3LYP/6‐311++G^** level. The basis set superposition errors (BSSE) are 4.62, 4.07 and 3.45 kJ/mol, and the zero point energy (ZPE) corrections for the interaction energies are 7.94, 5.66 and 6.40 kJ/mol for 1, 2 and 3 , respectively. Dimer 1 is the most stable, judged by binding energy. After BSSE and ZPE corrections, the greatest corrected intermolecular interaction energy of dimer 1 was predicted to be ?29.36 kJ/mol. The charge redistribution mainly occurs on the adjacent N–H··· O atoms and N–O··· H atoms between submolecules. The oxygen in the nitro group acts as a moderate hydrogen acceptor as compared to water oxygen. Based on the statistical thermodynamic method, the standard thermodynamic functions, heat capacities (C⁰_P), entropies (S⁰_T) and thermal corrections to enthalpy (H⁰_T), and the changes of thermodynamic properties on going from monomer to dimer over the temperature range 200.00‐700.00 K were predicted. It is energetically or thermodynamically favorable for Fox‐7 to bind with H₂O and to form dimer 1 at room temperature.