Medium-size Gaussian basis sets for hydrogen through argon

Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the² P states of Li and Na, and the³ P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size.     

Semiclassical variational study of size effects in neutral and charged jellium droplets

An analytic expression for the total energy of metallic clusters composed ofN identical atoms of valencev and with net chargeQ is obtained by means of a variational solution of the Thomas-Fermi-Weizsäcker energy density functional within the spherical jellium model. The minimum energy is given as an expansion in decreasing powers of the cluster radiusR=r _s Z ^1/3, withZ=vN andr _s the radius per electron of the bulk metal. The coefficients are obtained as functions ofr _s . Terms of volume (R ³), surface (R ²), curvature (R), constant (R ⁰), (1/R) and (1/R ²) are clearly separated in the formula, as well as the different contributions (kinetic, coulombic and exchange-correlation) to each of them. The asymptotic values (R→∞) for the work functions,W(r _s ), and surface energies σ(r _s ), are compared to analogous semiclassical and Kohn-Sham calculations of jellium-like surfaces and to the experimental values. The size dependent behaviour of chemical potentials, μ(R), electron affinities,AF(R), and ionization potentials,IP(R), are easily obtained for any kind of metallic clusters. In particular we discuss the Coulomb and quantum corrections to the coefficients β, δ in the asymptotic formulae:IP?W+β/R andAF?W+δ/R.     

Nondiagonal second order intermolecular forces for interactions involving molecules

Very often only “diagonal” second order energies, varying as an even power of R^?1, occur in the multipole expansion of the interaction energy. However for many molecular interactions important “nondiagonal” second order energies, varying as an odd or even power of R^?1 can arise. This point is emphasized by a general discussion and by a detailed specific example, the interaction of an ionized dipolar molecule with a nondegenerate atom. Also some useful theorems, on the orientation average of various types of second order energies, are derived.     

Analysis of exponent values in Gaussian‐type functions for development of protonic and deuteronic basis functions

We analyzed the exponent (α) values in Gaussian‐type functions (GTF) for protons and deuterons in BH₃, CH₄, NH₃, H₂O, HF, and their deuterated molecules for the development of nuclear basis functions, which are used for molecular orbital (MO) calculations that directly include nuclear quantum effects. The optimized α (α_opt) value in the single s‐type ([1s]) GTF for protons is changed due to the difference in flexibility of the electronic basis sets. The difference between the energy obtained by using the α_opt value for each molecule and that obtained by using the average α (α_ave) value for these exponents with the 6‐31G(d,p) electronic basis function is only 2 × 10^?5 a.u. The α_ave values of protonic and deuteronic [1s] GTFs by the present calculation are 24.1825 and 35.6214, respectively. We found that the α_ave values enable the evaluation of the total energy and the geometrical changes in hydrogen bonding, such as O…H? O, O…H? N, and O…H? C, while the α_opt value became small by forming a hydrogen bond. The result using only the [1s] GTF for the protonic and deuteronic basis functions is sufficient to explain the differences of energy and geometry induced by the H/D isotope effect, although the total energy of ～5 × 10^?4 a.u. was improved by using the s‐, p‐, and d‐type ([1s1p1d]) GTFs for protons and deuterons. We clearly demonstrate that the protonic and deuteronic basis functions based on the α_ave value enable us to apply the method to other sample molecules (glycine, malonaldehyde, and formic acid dimer). The protonic and deuteronic basis functions we developed treat the quantum effects of protons and deuterons effectively and extend the application range of the MO calculation to include nuclear quantum effects. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Analysis of exponent values of Gaussian‐type functions on quantum protons and deuterons in charged or polarized systems

The optimal exponent α values (α_opt) in s‐type Gaussian‐type functions (GTFs) for quantum protons and deuterons, which are used for multicomponent molecular orbital calculations including nuclear quantum nature of protons and deuterons, are analyzed for several charged or polarized systems and their deuterated species. Ishimoto and coworkers (Ishimoto, Int. J. Quantum Chem. 2006 , 106, 1465) have already proposed the average exponent values for five neutral molecules (α_ave), and demonstrated that their α_ave enables us to evaluate the H/D isotope effect on energies and geometries of various neutral species. The differences between total energies of several charged or polarized systems with previous α_ave and our α_opt correspond to only less than 0.004% of the total energy (0.47 kcal·mol^?1) except for HeH⁺ and HeD⁺ molecules, while the difference between interaction energies of H₂OH^+…OH₂ and H₂OD^+…OH₂ systems with previous α_ave is 19% (0.22 kcal·mol^?1) smaller than that with our α_opt. Meanwhile, the difference between O? H bond lengths in H₂OH^+…OH₂ system with α_ave and α_opt values is 0.027 Å. We also found that the interaction energies with α_opt value at the geometry optimized with previous α_ave value (α_sp) well reproduce those at the geometry optimized with α_opt value. We have demonstrated that the nuclear basis functions based on s‐type GTFs with previous α_ave values enable us to evaluate the H/D isotope effect on energies and geometries of charged or polarized systems. © 2016 Wiley Periodicals, Inc.     

Gaussian representations of charge overlap effects in intermolecular forces

The ground state H? H⁺ and H? H interactions are used as model interactions for investigating the feasibility of using Gaussian basis sets for representing charge overlap effects in intermolecular forces. The non-expanded charge-induced dipole energy and the non-expanded dipole-dipole dispersion energy, respectively, for these interactions are calculated using two types of Gaussian basis functions to represent the first order wave function, Ψ⁽¹⁾. Very good results for these interaction energies, which include charge overlap effects, are obtained for all interatomic separations by using small Gaussian basis sets to represent the interaction, that is Ψ⁽¹⁾, and/or the isolated atoms (the zeroth order wave function).     

High-quality Gaussian basis sets for fourth-row atoms

Summary Energy-optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed; (24s 16p 10d) and (26s 16p 10d) sets which we expand to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284E _H above the numerical Hartree-Fock energies.     

Isotropic C6, C8 and C10 interaction coefficients for CH4, C2H6, C3H8, n-C4H10 and cyclo-C3H6

The non-empirical generalized Kirkwood, Unsöld, and the single-Δ Unsöld methods (with double-zeta quality SCF wave-functions) are used to calculate isotropic dispersion (and induction) energy coefficients C_2n, with n ? 5, for interactions involving ground state CH₄, C₂H₆, C₃H₈, n-C₄H₁₀ and cyclo-C₃H₆. Results are also given for the related multipole polarizabilities α_l, multipole sums S₁/(0) and S₁(?1) which are evaluated using sum rules, and the permanent multipole moments. for l = 1 (dipole) to l = 3 (octupole). Estimates of the reliability of the non-empirical methods, for the type of molecules considered, are obtained by a comparison with accurate literature values of α₁S₁(?1) and C₆. This, and the asymptotic properties of the multipolar expansion of the dispersion energy, the use to discuss recommended representation for the isotropic long range interaction energies through R^?10 where R is the intermolecular separation.     

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.     

Nonempirical Atom-Atom Potentials for Main Components of Intermolecular Interaction Energy

Atom-atom potentials representing separate contributions to the nonempirical interaction energy have been derived in the SCF decomposition scheme corrected for basis set superposition error by the counterpoise method. The nontransferable long-range electrostatic multipole and classical induction terms have been evaluated directly from cumulative atomic multipole expansions, whereas the short-range exchange, charge-transfer, and electrostatic penetration contributions have been represented by simplified potentials of the form (β + δR^?1) exp(?δR) fitted to the corresponding ab initio results for 336 dimer configurations formed by HF, H₂O, NH₃, CH₄, CO, and CO₂. The dominant anisotropic character of electrostatic multipole atom-atom potentials and much more isotropic nature of the potentials representing short-range terms is illustrated in the Appendix for head-on interactions in CO ‥ OC and HF ‥ FH dimers.     

Gas-phase elimination kinetics of 1-substituted ethyl acetates. Effect of polar substituents at the α carbon of secondary acetates

The gas-phase elimination of several polar substituents at the α carbon of ethyl acetates has been studied in a static system over the temperature range of 310–410°C and the pressure range of 39–313 torr. These reactions are homogeneous in both clean and seasoned vessels, follow a first-order rate law, and are unimolecular. The temperature dependence of the rate coefficients is given by the following Arrhenius equations: 2-acetoxypropionitrile, log k₁ (s^?1) = (12.88 ± 0.29) – (203.3 ± 2.6) kJ/mol (2.303RT)^?1; for 3-acetoxy-2-butanone, log ±₁(s^?1) = (13.40 ± 0.20) – (202.8 ± 2.4) kJ/mol (2.303RT)^?1; for 1,1,1-trichloro-2-acetoxypropane, log ?₁ (s^?1) = (12.12 ± 0.50) – (193.7 ± 6.0) kJ/mol (2.303RT)^?; for methyl 2-acetoxypropionate, log ?₁ (s^?1) = (13.45 ± 0.05) – (209.5 ± 0.5) kJ/mol (2.303RT)^?1; for 1-chloro-2-acetoxypropane, log ?₁ (s^?1) = (12.95 ± 0.15) – (197.5 ± 1.8) kJ/mol (2.303RT)^?1; for 1-fluoro-2-acetoxypropane, log ?₁ (s^?1) = (12.83 ± 0.15)– (197.8 ± 1.8) kJ/mol (2.303RT)^?1; for 1-dimethylamino-2-acetoxypropane, log ?₁ (s^?1) = (12.66 ± 0.22) –(185.9 ± 2.5) kJ/mol (2.303RT)^?1; for 1-phenyl-2-acetoxypropane, log ?₁ (s^?1) = (12.53 ± 0.20) – (180.1 ± 2.3) kJ/mol (2.303RT)^?1; and for 1-phenyl?3?acetoxybutane, log ?₁ (s^?1) = (12.33 ± 0.25) – (179.8 ± 2.9) kJ/mol (2.303RT)^?1. The C_α? O bond polarization appears to be the rate-determining process in the transmition state of these pyrolysis reactions. Linear correlations of electron-releasing and electron-withdrawing groups along strong σ bonds have been projected and discussed. The present work may provide a general view on the effect of alkyl and polar substituents at the C_α? O bond in the gas-phase elimination of secondary acetates.     

Designing Novel Contrast Agents for Magnetic Resonance Imaging. Synthesis and Relaxometric Characterization of three Gadolinium(III) Complexes Based on Functionalized Pyridine‐Containing Macrocyclic Ligands

The three novel pyridine‐containing 12‐membered macrocyclic ligands 1 – 3 were synthesized. The coordinating arms are represented by three acetate moieties in 1 and 3 and by one acetate and two phosphonate moieties in 2 . In all three ligands, the acetate arm in the distal position is substituted, with a benzyl group in 1 and 2 and with an arylmethyl moiety in 3 . The relaxivities r_1p (20 MHz, 25°) of Gd^III complexes are: GD?1 , r_1p=8.3 mM ^?1 s^?1; GD?2 , r_1p8.1 mM ^?1 s^?1; Gd?3 , r_1p10.5 mM ^?1 s^?1. ¹H‐NMRD and ¹⁷O‐NMR T₂ data show that Gd?1 and Gd?3 contain two H₂O molecules in the inner sphere, whereas the presence of two phosphonate arms allows the coordination of only one H₂O molecule in Gd?2 . Interestingly, the exchange lifetime of coordinated H₂O in the three complexes is similar in spite of the difference in the coordination number of the Gd^III ion (i.e., 9 in Gd?1 and Gd?3 , and 8 in Gd?2 ). ¹H‐Relaxometric measurements at different pH and in the presence of lactate and oxalate were carried out to get some insight into the formation of ternary complexes from Gd?1 and Gd?3 . Finally, it was found that binding to human‐serum albumin (HSA) of Gd?1 and Gd?2 , though weak, yields limited relaxivity enhancements, likely as a consequence of effects on the hydration sphere caused by donor atoms on the surface of the protein.     

Ab initio calculation of spin–orbit interaction in polyatomic molecules using Gaussian-type wavefunctions

A set of programs has been developed to calculate molecular spin–orbit interaction with Gaussian-type wavefunctions in connection with the popular GAUSSIAN 76 program. The spin–orbit contributions to the fine structure of O₂ (X³∑_g^?), NH (X³∑^?), and CH₂ (X³B₁) are evaluated with the standard STO -3G and 6-31G basis sets; for NH the influence of bond functions added to the latter basis set is also investigated. The results are compared to values previously obtained with other types of basis sets.     

Gaussian multipoles in practice: Electrostatic energies for intermolecular potentials

A method is presented for calculating the total electrostatic interaction energies between molecules from ab initio monomer wave functions. This approach differs from existing methods, such as Stone's distributed multipole analysis (DMA), in including the short-range penetration energy as well as the long-range multipolar energy. The monomer charge densities are expressed as distributed series of atom-centered functions which we call Gaussian multipoles; these are analogous to the distributed point multipoles used in DMA. Our procedure has been encoded in the GMUL program. Calculations have been performed on the formamide/formaldehyde complex, a model system for N? H …? O hydrogen bonding in biological molecules, and also on guanidinium/benzene, modeling amino/aromatic interactions in proteins. We find that the penetration energy can be significant, especially in its contribution to the variation of the electrostatic energy with interaction geometry. A hybrid method, which uses Gaussian multipoles for short-range atom pair interactions and point multipoles for long-range ones, allows the electrostatic energies, including penetration, to be calculated at a much reduced cost. We also note that the penetration energy may provide the best route to an atom–atom anisotropic model for the exchange-repulsion energy in intermolecular potentials. © 1994 by John Wiley & Sons, Inc.     

Relaxivity and Transmetallation Stability of New Benzyl‐Substituted Derivatives of Gadolinium?DTPA Complexes

In our efforts of finding new specific contrast agents of higher relaxivity and selectivity, we have prepared the two new benzyl‐functionalized DTPA (‘diethylenetriamine pentaacetate’) gadolinium complexes (S)‐ 3 and (R,S)‐ 4 , and compared their properties with those of the known regioisomers (S)‐ 2 and (S)‐ 1 . The theoretical fitting of the reduced transverse relaxation rates of the ¹⁷O‐nucleus of H₂O gave values for the water‐residence time (τ_M) of 86–143 ns at 310 K, values that are not limiting the proton relaxivity at body temperature. ¹H‐NMRD (nuclear magnetic‐relaxation dispersion) Profiles showed that the relaxivity of 1 – 4 (r₁=4.3–5.1 s^?1 mM ^?1 at 20 MHz and 310 K) is higher than for the Gd? DTPA parent compound 5 . Transmetallation assessment demonstrated that all substituted compounds, except for (S)‐ 2 , are more stable than 5 . The highest stability towards Zn²⁺‐induced transmetallation was achieved with complexes 3, 1 , and 4 (in decreasing order). Apparently, the steric hindrance of the benzyl substituents in positions 5, 4, and 2, respectively, favorably reduces the accessibility of Zn ions. From a synthetic point of view, 4‐substituted DTPA complexes of type 1 are more readily accessible than 5‐substituted compounds of type 3 . Therefore, the former seem to be superior for linking substituted DTPA complexes to macromolecules or specific vectors.     

Modified Gaussian functions and their use in quantum chemistry. I. Integrals

A modified Gaussian function g(u, v, w, a, R ) = const s(a, R ) is considered where l = u + v + w, s (a, R ) is a 1s-type Gaussian function centered at R , a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R . General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.     

基态PuOH分子的多体展式分析势能函数

Using the density functional method B3LYP with relativistic effective core potential(RECP)for Pu atom,thelow-lying excited states(~4Σ~ ,~6Σ~ ,~8Σ~ )for three structures of PuOH molecule were optimized.The results showthat the ground state is X~6Σ~ of the linear Pu-O-H(C_(∞v)),its corresponding equilibrium geometry and dissociationenergy are R_(Pu-O)=0.20595 nm,R_(O-H)=0.09581 nm and —8.68 eV,respectively.At the same time,two other me-tastable structures [PuOH(C_s)and H-Pu-O(C_(∞v)] were found.The analytical potential energy function has alsobeen derived for whole range using the many-body expansion method.This potential energy function represents theconsiderable topographical features of PuOH molecule in detail,which is adequately accurate in the whole potentialsurface and can be used for the molecular reaction dynamics research.     

A mass formula for the energy of metal clusters

We obtain an analytic expression for the total energy of a metallic cluster formed by N atoms of valence v and with net charge Q, by solving variationally the extended Thomas–Fermi version of density functional theory within the spherical jellium model. The energy is expressed as an expansion (mass formula) in decreasing powers of the cluster radius R_I = r_sZ^1/3, with Z = _vN, and r_s, the one electron radius of the bulk, and the coefficients of this mass formula are functions of r_s. Contributions of volume (R_I³), surface (R_I²), curvature (R_I), constant (R_I⁰), (1/R_I), and (1/R_I²) are clearly separated in the formula. The Chemical potential, work function, electron affinity, and ionization potential are easily obtained for neutral and charged clusters of any electronic density in the metallic range. A general estimation of the critical size for stability against electron detachment of negatively charged clusters is also obtained. The stability of highly charged clusters against fragmentation is also studied. © John Wiley & Sons, Inc.