Uniform quality gaussian basis sets for molecular calculations,I. C1 hydrocarbons

The optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for atom ions, is investigated. A formal charge parameter Q is defined and used to adjust the AO basis sets to the molecular environment, by virtue of a simple quadratic expression. Calculations on a series of C₁ hydrocarbons (CH₂, CH₃, CH₃⁺, CH₃^?, CH₄) using 3G basis sets indicate considerable variations in the optimum Q value with the molecular species. The proposed method offers a simple alternative technique to a full molecular basis set optimization.     

金属Pt表面水蒸汽分子吸附的量子力学计算

基于电子与振动近似方法和密度泛函B3LYP理论, 氧和氢原子选择6-311G**基函数, Pt选择赝势基组LanL2DZ, 优化得到Pt-OH₂结构和微观性质, 稳态结构Pt-H₂O分子中, Pt与H₂O不在同一平面, Pt倾向于与O原子结合. 计算了100～898.15 K温度下, 水蒸汽分子在Pt表面吸附反应的热力学函数值和平衡压力, 拟合得到ΔS⁰,ΔH⁰, ΔG⁰, ln p与温度的函数关系. 室温以上ΔG⁰＞0 kJ•mol^－1, 水蒸汽分子在Pt表面不能稳定吸附; 200 K以下, ΔG⁰＜0 kJ•mol^－1, 能够稳定吸附. 计算了不同温度下水蒸汽分子在Pt表面发生解离反应的ΔG⁰和平衡压力, 室温以上ΔG⁰＞0 kJ•mol^－1. 100～898.15 K温度下, 水蒸汽分子在Pt表面不容易发生解离, 实际反应过程中以完整分子形式参与反应.     

The externally contracted CI method applied to N2

An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ? functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ? functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 Å for all the states. A qualitative discussion of predissociation in the a ¹Π_g and B ³Π_gstates caused by spin–orbit interaction with the ⁵Σ_g⁺ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.     

Density functional complete study of hydrogen bonding between the water molecule and the hydroxyl radical (H2O · HO)

The hydrogen bonding complexes formed between the H₂O and OH radical have been completely investigated for the first time in this study using density functional theory (DFT). A larger basis set 6‐311++G(2d,2p) has been employed in conjunction with a hybrid density functional method, namely, UB3LYP/6‐311++G(2d,2p). The two degenerate components of the OH radical ²Π ground electronic state give rise to independent states upon interaction with the water molecule, with hydrogen bonding occurring between the oxygen atom of H₂O and the hydrogen atom of the OH radical. Another hydrogen bond occurs between one of the H atoms of H₂O and the O atom of the OH radical. The extensive calculation reveals that there is still more hydrogen bonding form found first in this investigation, in which two or three hydrogen bonds occur at the same time. The optimized geometry parameter and interaction energy for various isomers at the present level of theory was estimated. The infrared (IR) spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. The estimates of the H₂O · OH complex's vibrational modes and predicted IR spectra for these structures are also made. It should be noted that a total of 10 stationary points have been confirmed to be genuine minima and transition states on the potential energy hypersurface of the H₂O · HO system. Among them, four genuine minima were located. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Development and testing of a compact basis set for use in effective core potential calculations on rhodium complexes

We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)₂μ‐Cl]₂, Rh(CO)₂ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)₂μ‐Cl]₂ with pyridine (Py) to give Rh(CO)₂ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. © 2012 Wiley Periodicals, Inc.     

Energy and density analysis on the H2 molecule from the united atom to dissociation: The Σ, Π, Δ, ϕ, and Γ manifolds

We present 140 accurate potential energy curves, PECs, for the Σ, Π, Δ, ?, and Γ manifolds for the H₂ molecule, mapping all the states with energy below the H ground state. The full configuration interaction, nonrelativistic Born–Oppenheimer computations are performed with large and optimized basis sets of Slater‐type and spherical Gaussian functions; these new basis sets are somewhat larger than those used in recent published studies on the 60 Σ state PECs. The full CI computations are performed twice, with Hartree–Fock and with Heitler–London‐type functions, allowing the identification of the ionic component in the total energy. The computed energies are within 10^?5 hartree from the most accurate PECs in literature. We aim (a) at the evaluation of the PECs starting at very short and unexplored internuclear distances (0.01 bohrs) and ending at full dissociation, (b) at the systematic prediction of high excited state PECs dissociating as 1s + 4l and 1s + 5l, and (c) at the characterization of the evolution of the 140 PEC electronic densities from united atom to dissociation. With this work we fill a gap in today literature, which has dealt mainly with low excited states, generally excluding short internuclear distances. The electronic configuration at the united atom persists as dominant configuration well beyond the equilibrium separation, and it switches to that at dissociation often with energy patterns seemingly irregular, in particular when the values of the principal quantum number at dissociation and at the united atom differ by one or more unit. The Hund's singlet‐triplet splitting, which propagates from the united atom to the molecule, is discussed. The singlet and triplet states are rather close in energy in the Π manifolds, and approach degeneracy in the Δ and ? manifolds, to become fully degenerate in the Γ manifolds. Discussions on the correlation energy correction, adiabatic correction, spectroscopic constants and on general features of the H₂ excited states are presented. The H₂ molecule is a system, which—to be understood—needs consideration of both the very short internuclear distances in approaching the united atom and of the very high excited states below H. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Conformational analysis of vitamin K<Subscript>1</Subscript> model molecule: a theoretical study

Isomerism, conformations, and molecular structure of a model molecule of vitamin K₁ with a truncated side chain have been studied by the density functional theory calculations using B3LYP method and double- and triple-ζ correlation consistent basis sets. The conformations of two possible (E and Z) isomers, formed by the rotations around three single C–C bonds closest to the naphthoquinone ring, have been studied. The lowest energy conformers are stabilized by additional hydrogen bonds between hydrogen atoms of the side chain and an oxygen atom in the naphthoquinone subunit. It is interesting to note that the structure of the energetically preferred conformer of the E-isomer (3c) has been found to be similar to the solid state structures of phylloquinones in the photosystem I of cyanobacterium Synechococcus elongatus. The excited electronic states of two lowest energy conformers have also been investigated.     

Reliability of atomic natural orbital basis sets in calculations involving pseudopotentials

The performance of Atomic Natural Orbital (ANO) basis sets for calculations involving nonempirical core pseudopotentials has been studied by comparing the results for atomic and molecular nitrogen obtained using contracted ANO basis sets with those obtained using both the primitive set and a segmented one. The primitive set has been optimized at the SCF level for atomic N treated as a five-electron pseudo-atom, and consists of 7s and 7p primitive GTOs supplemented by 2d and 1f GTOs optimized at the CI level. From this primitive set three contracted [3s 3p 2d 1f] sets have been obtained. The first one has been derived from the ANOs of the neutral atom, the second has been obtained from an averaged density matrix and the third one is a segmented set. For the atom, the segmented set gives a zero contraction error at the SCF level as it must be in valence-only calculations. The ANO basis sets show some small contraction error at the SCF level but perform better in CI calculations. However, for the diatomic N₂ molecule the ANO basis sets exhibit a rather large contraction error in the calculated SCF energy. A detailed analysis of the origin of this error is reported, which shows that the conventional strategy used to derive ANO basis sets does not work very well when pseudopotentials are involved.     

Ab initio calculations on sulfur-containing compounds. I. Uniform quality basis sets for sulfur: Total energies and geometries of H2S

Uniform quality basis sets (UQ-NG ; N=3, 4, 5), with s = p and s ≠ p, and a 6-31 G^* basis set have been optimized for the sulfur atom. These uniform quality basis sets in their uncontracted and contracted forms were used, together with other basis sets reported in the literature (a total of 40 basis sets), to study their accuracy in predicting the bond length and bond angle of H₂S.     

Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree–Fock method

We have applied a discretized version of the generator coordinate Hartree–Fock method to generate adapted Gaussian basis sets for atoms Cs (Z=55) to Lr (Z=103). Our Hartree–Fock total energy results, for all atoms studied, are better than the corresponding Hartree–Fock energy results attained with previous Gaussian basis sets. For the atoms Cs to Lr we have obtained an energy value within the accuracy of 10⁻⁴ to 10⁻³ hartree when compared with the corresponding numerical Hartree–Fock total energy results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 858–865, 1998     

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     

Gaussian basis sets for first‐, third‐, and fourth‐row positive and negative ions

An improved generator coordinate Hartree–Fock (HF) method is used to generate accurate triple‐optimized Gaussian basis sets for the cations from He⁺ (Z=2) through Ne⁺ (Z=10) and from K⁺ (Z=19) through Xe⁺ (Z=54), and for the anions from H⁻ (Z=1) through F⁻ (Z=9) and from K⁻ (Z=19) through I⁻ (Z=53). For all ions here studied, our ground‐state HF total energies are better than those calculated with the generator coordinate HF method, using optimized Gaussian basis sets of the same size. For all ions studied, the largest difference between our total energy values and the corresponding results obtained with a numerical HF method is equal to 3.434 mhartrees for Te⁺. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 126–130, 2001     

Quantum study on the electrocyclic reactions of CH2CHCHCHX (XH,F, Cl)

The microscopic mechanisms of the electrocyclic reactions for cis‐1,3‐butadiene and its monofluoro‐, monochloroderivatives have been studied by density functional theory (DFT), using the B3LYP method and 6‐311++G** basis sets. We optimized the geometric configurations of reactants, transition states, and products; verified all the probable transition states through vibrational analysis; and calculated the relative single‐point energies at the QCISD(T)/6‐311++G**//B3LYP/6‐311++G**. The results show that the monofluoro‐, monochloroderivatives of cis‐1,3‐butadiene both have two conformers; the reactant favors the electrocyclic reaction when one outboard hydrogen atom of the CH₂ groups is substituted by the fluorine or chlorine atom. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Dual-level direct dynamics calculations of deuterium kinetic isotope effects for the Cl(2P)+C2H6 abstraction reaction

 Kinetic isotope effects, KIEs, for hydrogen abstraction from C₂H₆ and C₂D₆ by chlorine atom have been studied by the dual-level direct dynamics approach. A low-level potential energy surface is obtained with the MNDO-SRP method. High-level structural properties of the reactants, transition state, and products were obtained at the MP2 level with the cc-pVDZ, aug-cc-pVDZ, and the cc-pVTZ basis sets. Using the variational transition state theory with microcanonical optimized multidimensional tunneling, the values of deuterium KIE, at 300 K, range from 2.28 to 3.27, in good agreement with the experimental values (2.69–5.88). Received: 6 June 2001 / Accepted: 12 July 2001 / Published online: 19 November 2001     

Long range interaction energies using Gaussian basis sets and a one center method

A one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R^?8), for the H(ls) – H⁺ interaction employing two types of Gaussian basis sets constructed from functions of the form {r^je^?αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) – H(ls) interaction, through O(R^?10), and the R^?9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.     

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.     

LCGTO-LSD calculations for CH2

LCGTO-LSD calculations for ground (³B₁) and excited (¹A₁) states of methylene, CH₂, have been performed. Various exchange-correlation potentials and a variety of basis sets (including f functions) have been used. For both states the LSD optimized geometry agrees well with both experimental and the most advanced ab initio results. The correct ground state is found, and the ¹A₁-³B₁ energy separation was found to be ～ 15 kcal/mol, using the “best” local exchange-correlation potential (VWN ), the experimental value being ～ 9 kcal/mol. This result compares favorably with the Hartree-Fock limit separation of 25 kcal/mol. The Kohn-Sham exchange potential leads to a gap of ～26 kcal/mol.     

On the convergence properties of the Rayleigh–Schrödinger and the Hirschfelder–Silbey perturbation expansions for molecular interaction energies

By applying the powerful direct optimization technique of conjugate gradients as adapted for the optimization of an open shell energy functional, a uniformly balanced (15^s 10^p) Gaussian basis set was obtained for the silicon atom. The quality of this basis set, as defined in terms of “exponent forces” or energy gradient |g|, is compatible with the quality of suitably chosen (10^s 5^p) carbon and (5^s) hydrogen basis sets. Contractions better than double zeta were determined for all three bases of Si, C, and H. Using the primitive and contracted bases, ab initio SCF MO calculations were carried out on molecules of SiH₄, CH₄, and H₂. Some of the computed results obtained for H₂C = SiH₂ are also included as an illustration for organo-silicon compounds.