An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

A systematic preparation of new contracted Gaussian-type orbital sets. III. Second-row atoms from Li through ne

Four minimal Gaussian basis sets are generated for the second-row atoms Li through Ne. The first one, MINI-1, consists of a 3-term contraction of primitive Gaussian-type orbitals for 1s, 2s, and 2p atomic orbitals. The convenient shorthand notation would be (3,3) for Li? Be and (3,3/3) for B? Ne. The second one, MINI-2, can be represented by (3,3/4) for B? Ne. In the same way, MINI-3 is described as (4,3) for Li? Be, and MINI-3 and MINI-4 are represented by (4,3/3) and (4,3/4) for B? Ne, respectively. Although the four basis sets are the minimal type, they give the valence shell orbital energies which are close to those of DZ. These four and other sets derived from them are tested for the hetero- and homodiatomic molecules and some organic molecules. They are found to give the orbital energies that agree well with those given by extended calculations. Atomization energies and other spectroscopic constants are also calculated and compared with those of extended calculations. The results clearly indicate that the present basis sets can be used very effectively in the molecular calculations.     

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.     

Comparison of localization and delocalization indices obtained with Hartree-Fock and conventional correlated methods: effect of Coulomb correlation

Atomic populations and localization [lambda(A)] and delocalization [delta(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree-Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6-311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values--the LIs are increased and DIs decreased--are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HC(triple bond)CH, H2C=CH2, CH3-CH3, and "protonated cyclopropane" C(3)H(7) (+), in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms.     

Kernel energy method: Basis functions and quantum methods

The kernel energy method (KEM) has been illustrated with peptides and has been shown to reduce the computational difficulty associated with obtaining ab initio quality quantum chemistry results for large biological compounds. In a recent paper, the method was illustrated by application to 15 different peptides, ranging in size from 4 to 19 amino acid residues, and was found to deliver accurate Hartree–Fock (HF) molecular energies within the model, using Slater‐type orbital (STO)‐3G basis functions. A question arises concerning whether the results obtained from the use of KEM are wholly dependent on the STO‐3G basis functions that were employed, because of their relative simplicity, in the first applications. In the present work, it is shown that the accuracy of KEM does not depend on a particular choice of basis functions. This is done by calculating the ground‐state energy of a representative peptide, ADPGV7B, containing seven amino acid residues, using seven different commonly employed basis function sets, ranging in size from small to medium to large. It is shown that the accuracy of the KEM does not vary in any systematic way with the size or mathematical completeness of the basis set used, and good accuracy is maintained over the entire variety of basis sets that have been tested. Both approximate HF and density functional theory (DFT) calculations are made. We conclude that the accuracy inherent in the KEM is not dependent on a particular choice of basis functions. The first application, to 15 different peptides mentioned above, employed only HF calculations. A second question that arises is whether the results obtained with the use of KEM will be accurate only within the HF approximation. Therefore, in the present work we also study whether KEM is applicable across a variety of quantum computational methods, characterized by differing levels of accuracy. The peptide, Zaib4, containing 74 atoms, was used to calculate its energy at seven different levels of accuracy. These include the semi‐empirical methods, AM1 and PM5, a DFT B3LYP model, and ab initio HF, MP2, CID, and CCSD calculations. KEM was found to be widely applicable across the spectrum of quantum methods tested. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Generator coordinate Hartree–Fock method applied to the choice of a contracted Gaussian basis for the second-row atoms

The generator coordinate Hartree–Fock (GCHF) method is employed as a criterion for the selection of a 18s12p Gaussian basis for the atoms Na–Ar. The role of the weight functions in the assessment of the numerical integration range of the GCHF equations is shown. The extended basis is then contracted to (10s6p) by a standard procedure and in combination with the previously contracted (7s5p) Gaussian basis for the atoms Li–Ne is enriched with polarization functions. This basis is tested for AlF, SiO, PN, BCl, and P₂. The properties of interest were HF total energies, MP2 dipolar moments, bond distances, and dissociation energies. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 927–934, 1997     

The effect of basis set superposition error on the convergence of intermolecular interaction energies for deprotonated complexes

The intermolecular interaction energies of the deprotonated hydrogen-bonded complexes F(-)(HF), F(-)(H(2)O), F(-)(NH(3)), Cl(-)(HF), SH(-)(HF), H(2)P(-)(HF), OH(-)(H(2)O), OH(-)(H(2)O)(2), OH(-)(NH(3)), Cl(-)(H(2)O), SH(-)(H(2)O), H(2)P(-)(H(2)O), Cl(-)(NH(3)), SH(-)(NH(3)), H(2)P(-)(NH(3)), Cl(-)(HCl), Cl(-)(H(2)S), Cl(-)(PH(3)), SH(-)(H(2)S), SH(-)(PH(3)), and H(2)P(-)(PH(3)) were calculated with correlation consistent basis sets at the MP2, MP4, QCISD(T), and CCSD(T) levels. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are closer to the complete basis set limit than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies obtained at the MP2/aug-cc-pVDZ level of theory are close to the interaction energies obtained at the extrapolated complete basis set limit in most of the complexes. Also, we investigate the accuracy of the other levels.     

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted ¹³C and ¹H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for ¹³C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.     

Hartree-Fock exchange fitting basis sets for H to Rn

For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree–Fock treatments (RI-JK-HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI-JK approximation are below ∼1 meV per atom in molecular compounds. Accuracy of RI-JK-approximated HF wave functions is sufficient for being used for post-HF treatments like Møller–Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI-JK-HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008     

Polarization consistent basis sets. 4: the elements He, Li, Be, B, Ne, Na, Mg, Al, and Ar

Polarization consistent basis sets, optimized for density functional calculations, are proposed for the elements He, Li, Be, B, Ne, Na, Mg, Al, and Ar. The basis sets for He, B, Ne, Al, and Ar are assigned based on the previously proposed basis sets for H, C-F, and Si-Ar. The basis sets for Li, Be, Na, and Mg are defined based on energetic analysis along the lines used in previous work and the performance for molecular systems. The performance for atomization energies is comparable to those for systems composed of the elements H, C-F, and Si-Ar.     

Basis set limits of the second order Moller-Plesset correlation energies of water, methane, acetylene, ethylene, and benzene

We report second order Moller-Plesset (MP2) and MP2-F12 total energies on He, Ne, Ar, H(2)O, CH(4), C(2)H(2), C(2)H(4), and C(6)H(6), using the correlation consistent basis sets, aug-cc-pVXZ (X=D-7). Basis set extrapolation techniques are applied to the MP2 and MP2-F12/B methods. The performance of the methods is tested in the calculations of the atoms, He, Ne, and Ar. It is indicated that the two-point extrapolation of MP2-F12/B with the basis sets (X=5,6) is the most reliable. Similar accuracy is obtained using two-point extrapolated conventional MP2 with the basis sets (X=6,7). For the molecules investigated the valence MP2 correlation energy is estimated within 1 mE(h).     

A polynomial version of the generator coordinate Dirac-Fock method

A polynomial version of the Generator Coordinate Dirac-Fock (p-GCDF) method is introduced and applied to develop Adapted Gaussian Basis Sets (AGBS) for helium- and beryllium-like atomic species (He, Ne +8, Ar +16, Sn +48, Be, Ne +6, Ar +14, and Sn +46) and for Kr and Xe atoms. The Dirac-Fock-Coulomb and Dirac-Fock-Breit energies obtained with these basis sets are in excellent agreement with numerical finite-difference calculations. Moreover, the sizes of the AGBS generated here with the p-GCDF method are significantly smaller than the size of previous relativistic Gaussian basis sets.     

The Challenge of ab Initio Calculations in Small Neon Clusters

Weakly bound neon dimer, trimer and tetramers are studied at HF and CCSD(T) levels using Dunning, ANO and SIGMA-s basis sets. Their ground-state binding energies are studied along with some structural properties. SIGMA-s basis sets have been developed explicitly for this issue but in a manner that can be readily applied to other atoms for the study of larger weakly bound systems. The difficulties for attaining accurate results on these systems are assessed by the computation of total, atomization and correlation energies, as well as equilibrium distances, with several basis sets of increasing size, ranging from non-augmented to double-augmented versions. Extrapolations are proposed to predict stabilization energies and the results are compared with previously published data.     

On the viability of small endohedral hydrocarbon cage complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12, AND X@C16H16

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and ions (X = H(+), H, He, Ne, Ar, Li(0,+), Be(0,+,2+), Na(0,+), Mg(0,+,2+)) have been studied at the B3LYP/6-31G(d) hybrid HF/DFT level of theory. No tetrahedrane (C(4)H(4), T(d)()) endohedral complexes are minima, not even with the very small hydrogen atom or beryllium dication. Cubane (C(8)H(8), O(h)()) and bicyclo[2.2.2]octane (C(8)H(14), D(3)(h)()) minima are limited to encapsulating species smaller than Ne and Na(+). Despite its intermediate size, adamantane (C(10)H(16), T(d)()) can enclose a wide variety of endohedral atoms and ions including H, He, Ne, Li(0,+), Be(0,+,2+), Na(0,+), and Mg(2+). In contrast, the truncated tetrahedrane (C(12)H(12), T(d)()) encapsulates fewer species, while the D(4)(d)() symmetric C(16)H(16) hydrocarbon cage (see Table of Contents graphic) encapsulates all but the larger Be, Mg, and Mg(+) species. The host cages have more compact geometries when metal atoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into C-C bonding and C-H antibonding cage molecular orbitals. The relative stabilities of endohedral minima are evaluated by comparing their energies (E(endo)) to the sum of their isolated components (E(inc) = E(endo) - E(cage) - E(x)) and to their exohedral isomer energies (E(isom) = E(endo) - E(exo)). Although exohedral binding is preferred to endohedral encapsulation without exception (i.e., E(isom) is always exothermic), Be(2+)@C(10)H(16) (T(d)(); -235.5 kcal/mol), Li(+)@C(12)H(12) (T(d)(); 50.2 kcal/mol), Be(2+)@C(12)H(12) (T(d)(); -181.2 kcal/mol), Mg(2+)@C(12)H(12) (T(d)(); -45.0 kcal/mol), Li(+)@C(16)H(16) (D(4)(d)(); 13.3 kcal/mol), Be(+)@C(16)H(16) (C(4)(v)(); 31.8 kcal/mol), Be(2+)@C(16)H(16) (D(4)(d)(); -239.2 kcal/mol), and Mg(2+)@C(16)H(16) (D(4)(d)(); -37.7 kcal/mol) are relatively stable as compared to experimentally known He@C(20)H(20) (I(h)()), which has an E(inc) = 37.9 kcal/mol and E(isom) = -35.4 kcal/mol. Overall, endohedral cage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small, highly charged guest species are the most viable synthetic targets.     

HF分子与惰性气体二聚体的分子形貌的理论研究

采用Gaussian-03程序中的MP2/6-311++G(2d,2p)方法,优化了FH- Rg(Rg=He,Ne,Ar)二聚体的结构.使用MELD精密从头计算中的CISD方法,结合我们自编的程序,计算了这些二聚体的单电子作用势(PAEM),并绘出了它们的分子形貌图象.分子形貌所提供的形貌特征、前沿电子密度的特征等,可以直观地揭示He,Ne和Ar等原子与HF分子相互作用时2种相互作用的差别,即共价相互作用与非共价相互作用区分的直观形象的表征.从二聚体的内禀特征信息可以看出,F,H和Rg原子都发生了不同程度的变形,HF分子对惰性气体原子有一定影响,而惰性气体原子对HF分子的影响较小.     

HX体系电子对内、对间相关研究

在6-311+G^*基组水平上用CISD（configurationinteractionwithsinglyanddoublyexcitedconfigurations)方法研究HX(X=Li-F,HBe)体系电子对内、对间的相关能。计算结果表明不同元素形成的HX(X=Li-F,HBe^+,HBe)体系,其价层电子对内、对间相关能的变化较大,它们之间存在着轨道差别,不宜将其相关贡献归为简单的常数。在使用相同理论方法和相同质量基组的前提下,电子数将直接影响到电子对间相关能的大小。对于多电子体系,电子对间相关在总相关中占有优势,若将其忽略会引起较大误差。     

Orbitals expanded in slater functions with single-exponent by shell and by subshell

Slater-type orbitals (STO s) with a single-exponent by shell or by subshell have been constructed to reduce the number of integrals evaluated in the electronic calculations. The expansion of orbitals in these new basis sets has been carried out in detail for the ground state of the Ne atom. We have carried out a study of STO basis sets with a different size for this atom that could help to propose empirical rules for the selection of these basis sets for other atoms. The usefulness of STO s with single-exponent by shell and subshell and the splitting of s and p functions are discussed. © 1994 John Wiley & Sons, Inc.     

A systematic preparation of new contracted Gaussian- type orbital sets. VII. MINI-3, MINI-4, MIDI-3, and MIDI-4 sets for transition metal atoms

Two minimal contracted Gaussian-type orbital (CGTO ) sets are developed for the transition metal atoms. The expansion terms for the first set, MINI -3, are 4, 3, 3, and 3 for s-type CGTO s and others are all three. The abbreviation would be (4333/33/3) where the slash divides symmetry. The expansion terms for the other set, MINI -4, is (4333/43/4). The split-type basis sets, MIDI -3 and MIDI -4, are derived directly from MINI -3 and MINI -4, MINI -3 and MIDI -3 provide the outer-shell orbital energies which are far better than those by single-zeta (SZ ) STO s. MINI -4 and MIDI -4 provide the outer-shell orbital energies which are almost as good as those by double-zeta (DZ ) STO s. The total energies given by the present sets are better than those of SZ except for MINI -3 for Sc and Ti: the energies by MINI -4 and MIDI -4 are only 0.8–1.7 a.u. higher than DZ . The basis sets were tested on the Cu₂ molecule, where a large basis set was also used.     

Extrapolating to the one-electron basis-set limit in electronic structure calculations

A simple, yet reliable, scheme based on treating uniformly singlet-pair and triplet-pair interactions is suggested to extrapolate atomic and molecular electron correlation energies calculated at two basis-set levels of ab initio theory to the infinite one-electron basis-set limit. The novel dual-level method is first tested on extrapolating the full correlation in single-reference coupled-cluster singles and doubles energies for the closed-shell systems CH2((1)A1), H2O, HF, N2, CO, Ne, and F2 with correlation-consistent basis sets of the type cc-pVXZ (X=D,T,Q,5,6) reported by Klopper [Mol. Phys. 6, 481 (2001)] against his own benchmark calculations with large uncontracted basis sets obtained from explicit correlated singles and doubles coupled-cluster theory. Comparisons are also reported for the same data set but using both single-reference Moller-Plesset and coupled-cluster doubles methods. The results show a similar, often better, accordance with the target results than Klopper's extrapolations where singlet-pair and triplet-pair energies are extrapolated separately using the popular X(-3) and X(-5) dual-level laws, respectively. Applications to the extrapolation of the dynamical correlation in multireference configuration interaction calculations carried out anew for He, H2, HeH+, He2 ++, H3+(1 (1)A'), H3+(1 (3)A'), BH, CH, NH, OH, FH, B2, C2, N2, O2, F2, BO, CO, NO, BN, CN, SH, H2O, and NH3 with standard augmented correlation-consistent basis sets of the type aug-cc-pVXZ (X=D,T,Q,5,6) are also reported. Despite lacking accurate theoretical or experimental data for comparison in the case of most diatomic systems, the new method also shows in this case a good performance when judged from the results obtained with the traditional schemes which extrapolate using the two largest affordable basis sets. For the Hartree-Fock and complete-active space self-consistent field energies, a simple pragmatic extrapolation rule is examined whose results are shown to compare well with the ones obtained from the best reported schemes.