Definitive ab initio studies of model SN2 reactions CH(3)X+F- (X=F,Cl, CN,OH, SH,NH(2), PH(2))

The energetics of the stationary points of the gas-phase reactions CH(3)X+F(-)-->CH(3)F+X(-) (X=F, Cl, CN, OH, SH, NH(2) and PH(2)) have been definitively computed using focal point analyses. These analyses entailed extrapolation to the one-particle limit for the Hartree-Fock and MP2 energies using basis sets of up to aug-cc-pV5Z quality, inclusion of higher-order electron correlation [CCSD and CCSD(T)] with basis sets of aug-cc-pVTZ quality, and addition of auxiliary terms for core correlation and scalar relativistic effects. The final net activation barriers for the forward reactions are: E (b/F,F)=-0.8, E (b/F, Cl)=-12.2, E (b/F,OH)=+13.6, E b/F,OH=+16.1, E b/F,SH=+2.8, Eb/F, NH=+32.8, and E b/F,PH =+19.7 kcal x mol(-1). For the reverse reactions E b/F,F= -0.8, Eb/Cl,F =+18.3, E b/CN,F=+12.2, E b/OH,F =-1.8, E b/SH,F =+13.2, E b/NH(2),=-1.5, and E b/PH(2) =+9.6 kcal x mol(-1). The change in energetics between the CCSD(T)/aug-cc-pVTZ reference prediction and the final extrapolated focal point value is generally 0.5-1.0 kcal mol(-1). The inclusion of a tight d function in the basis sets for second-row atoms, that is, utilizing the aug-cc-pV(X+d)Z series, appears to change the relative energies by only 0.2 kcal x mol(-1). Additionally, several decomposition schemes have been utilized to partition the ion-molecule complexation energies, namely the Morokuma-Kitaura (MK), reduced variational space (RVS), and symmetry adapted perturbation theory (SAPT) techniques. The reactant complexes fall into two groups, mostly electrostatic complexes (FCH(3).F(-) and ClCH(3).F(-)), and those with substantial covalent character (NCCH(3).F(-), CH(3)OH.F(-), CH(3)SH.F(-), CH(3)NH(2).F(-) and CH(3)PH(2).F(-)). All of the product complexes are of the form FCH(3).X(-) and are primarily electrostatic.     

Model identity SN2 reactions CH3X + X- (X = F, Cl, CN, OH, SH, NH2, PH2): Marcus theory analyzed

The structures of seven gas phase identity S(N)2 reactions of the form CH(3)X + X(-) have been characterized with seven distinct theoretical methods: RHF, B3LYP, BLYP, BP86, MP2, CCSD, and CCSD(T), in conjunction with basis sets of double and triple zeta quality. Additionally, the energetics of said reactions have been definitively computed using focal point analyses utilizing extrapolation to the one-particle limit for the Hartree-Fock and MP2 energies using basis sets of up to aug-cc-pV5Z quality, inclusion of higher order correlation effects [CCSD and CCSD(T)] with basis sets of aug-cc-pVTZ quality, and additional auxiliary terms for core correlation and scalar relativistic effects. Final net activation barriers for the reactions are E(b)(F,F)= -0.8, E(b)(Cl,Cl)= 1.6, E(b)(CN,CN)= 28.7, E(b)(OH,OH)= 14.3, E(b)(SH,SH)= 13.8, E(b)(NH2,NH2)= 28.6, and E(b)(PH2,PH2)= 25.7 kcal mol(-1). General trends in the energetics, specifically the performance of the density functionals, and the component energies of the focal point analyses are discussed. The utility of classic Marcus theory as a technique for barrier predictions has been carefully analyzed. The standard Marcus theory results show disparities of up to 9 kcal mol(-1) with respect to explicitly computed results. However, when alternative approaches to Marcus theory, independent of the well-depths, are considered, excellent performance is achieved, with the largest deviations being under 3 kcal mol(-1).     

The effect of basis set superposition error on the convergence of interaction energies

 For the intermolecular interaction energies of ion-water clusters [OH⁻(H₂O) _n (n=1,2), F⁻(H₂O), Cl⁻(H₂O), H₃O⁺(H₂O) _n (n=1,2), and NH₄ ⁺(H₂O) _n (n=1,2)] calculated with correlation-consistent basis sets at MP2, MP4, QCISD(T), and CCSD(T) levels, the basis set superposition error is nearly zero in the complete basis set (CBS) limit. That is, the counterpoise-uncorrected intermolecular interaction energies are nearly equal to the counterpoise-corrected intermolecular interaction energies in the CBS limit. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are more reliable than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies evaluated using the MP2/aug-cc-pVDZ level is reliable. Received: 14 March 2001 / Accepted: 25 April 2001 / Published online: 9 August 2001     

Proton transfer of NH3-HCl catalyzed by only one molecule

The proton transfer in NH(3)-HCl by only one molecule of catalyst was studied by using the MP2 method with the large 6-311++G(2d,2p) basis set. The 18 structures are obtained for the smallest units, NH(3)-HCl-A trimers, for which the proton transfer maybe occurred. The final results show that the proton transfers have occurred in the 15 cyclic shape structures for A = H(2)SO(4), H(2)SO(3), HCOOH (a), HF, H(2)O(2), HNO(3), HNO(2) (a), CH(3)OH, HCl, HNC, H(2)O, HNO(2) (b), NH(3), HCOOH (b), and HCHO, and not occurred in another 3 trimer structures for A = HCN, H(2)S, and PH(3). These results show that the proton transfer occurs from HCl to NH(3) when catalyst molecule A (acidic, neutral, or basic) not only as a proton donor strongly donates the proton to the Cl atom but as an acceptor strongly accepts the proton from the NH(3) molecule in the cyclic H-bond structure. In this work, a proton circumfluence model is proposed to explain the mechanism of the proton transfer. We find that, for the trimer, when the sum of two hydrogen bond lengths (R = R(1) + R(2)) is shorter than 5.0 A, molecule A has the ability to catalyze the proton transfer. In addition, we also find that the interaction energy E(int) between NH(3)-HCl and A is nearly related to the extent (R(H1)(-)(Cl)) of proton transfer, that is, the interaction energy E(int) increases with the proton transfer.     

Interaction of dihydrogen with small and light molecules

Second-order M?ller-Plesset (MP2) calculations (using the approximate resolution of the identity, RI-MP2), explicitly correlated MP2 (MP2-R12) calculations, and coupled-cluster calculations including all single and double excitations with a perturbative estimate of triple excitations [CCSD(T)] are performed to study the interaction of molecular hydrogen with the small molecules HF, H2O, NH3, and LiOH. Different adsorption positions are studied. In the cases of H2O and NH3, the most favorable configuration places H2 in an end-on fashion on the O or N atom, respectively. In the cases of HF and LiOH, the H2 molecule takes a side-on position on the H atom of HF or the Li atom. With respect to MP2 calculations in a triple-zeta basis, both the enlargement of the basis set and the extension of the correlation treatment (CCSD(T) vs MP2) increase the interaction energy. The basis set limit CCSD(T) estimates of the interaction energy of H2 with the HF, H2O, NH3, and LiOH molecules amount to 4.40, 2.67, 3.02, and 10.74 kJ mol-1, respectively. The interaction energy for the simultaneous interaction of H2 with two LiOH molecules does not significantly exceed the value obtained for the interaction with a single LiOH molecule. Furthermore, the interaction energies (by MP2) of H2 with glycine, the glycine dimer, and imidazolium chloride amount to 2.78, 5.00, and 6.30 kJ mol-1, respectively.     

Methyl and phenyl substitution effects on the proton affinities of hydrides of first and second row elements and substituent effects on the proton affinities of ring carbons in benzene: a DFT study

Theoretical calculations using B3LYP density functional theory (DFT) with the 6-311++G(d,p) basis set have been performed to determine proton affinities (PAs) of a series of H-X compounds and the corresponding methyl- (H(3)C-X) and phenyl- (Ph-X) substituted derivatives with a variety of proton acceptor atoms, such as C, O, N, F, Si, P, S, Cl, etc. Our results illustrate an interesting substituent effect on PAs. The PAs of ring carbon atoms for a series of monosubstituted benzene molecules (Y-C(6)H(5); Y = F, Cl, CH(3), OCH(3), NH(2), PH(2), OH, SH, SiH(3), CN, CF(3), and NO(2)) have also been estimated. Correlations between proton affinities of H-X, H(3)C-X, and Ph-X and substituent effects on the PAs of the ring carbon atoms for a series of monosubstituted benzene molecules have been studied. It has been observed that substituent effects on the PAs of the ring carbon atoms follow a good Hammett-type correlation.     

Ab initio molecular orbital investigation of the amine-alanes (CH(3))(n)H(3)(-)(n)AlNX(3) and phosphane-alanes (CH(3))(n)H(3)(-)(n)AlPX(3) (X = H, F, and Cl; n = 0-3) complexes

We report on ab initio calculations at the G2(MP2) level of the structures and Al-N(P) bond complexation energies of the (CH(3))(n)H(3)(-)(n)AlNX(3) and (CH(3))(n)H(3)(-)(n)()AlPX(3) (X = H, F, and Cl; n = 0-3) donor-acceptor complexes. For the (CH(3))(3)AlNX(3) and (CH(3))(3)AlPX(3) complexes, the C(3)(v) symmetry is found to be favored, and for the other complexes the C(s) symmetry is found to be favored. The G2(MP2) calculated complexation energies show for the amine ligands the trend NH(3) > NCl(3) > NF(3). A similar trend PH(3) approximately PCl(3) > PF(3) is predicted for the phosphane ligands. The NBO partitioning scheme shows that there is no correlation between the stability and the charge transfer.     

Comprehensive theoretical studies on the gas phase SN2 reactions of anionic nucleophiles toward chloroamine and N-chlorodimethylamine with inversion and retention mechanisms

The anionic S(N)2 reactions at neutral nitrogen, Nu(-) + NR(2)Cl → NR(2)Nu + Cl(-) (R = H, Me; Nu = F, Cl, Br, OH, SH, SeH, NH(2), PH(2), AsH(2)) have been systematically studied computationally at the modified G2(+) level. Two reaction mechanisms, inversion and retention of configuration, have been investigated. The main purposes of this work are to explore the reactivity trend of anions toward NR(2)Cl (R = H, Me), the steric effect on the potential energy surfaces, and the leaving ability of the anion in S(N)2@N reactions. Our calculations indicate that the complexation energies are determined by the gas basicity (GB) of the nucleophile and the electronegativity (EN) of the attacking atom, and the overall reaction barrier in the inversion pathway is basically controlled by the GB value of the nucleophile. The retention pathway in the reactions of NR(2)Cl with Nu(-) (Nu = F, Cl, Br, OH, SH, SeH) is energetically unfavorable due to the barriers being larger than those in the inversion pathway by more than 120 kJ mol(-1). Activation strain model analyses show that a higher deformation energy and a weaker interaction between deformed reactants lead to higher overall barriers in the reactions of NMe(2)Cl than those in the reactions of NH(2)Cl. Our studies on the reverse process of the title reactions suggest that the leaving ability of the anion in the gas phase anionic S(N)2@N reactions is mainly determined by the strength of the N-LG bond, which is related to the negative hyperconjugation inherent in NR(2)Nu (R = H, Me; Nu = HO, HS, HSe, NH(2), PH(2), AsH(2)).     

Dissociation chemistry of hydrogen halides in water

To understand the mechanism of aqueous acid dissociation, which plays a fundamental role in aqueous chemistry, the ionic dissociation of HX acids (X=F, Cl, Br, and I) in water clusters up to hexamer is examined using density functional theory and M?ller-Plesset second-order perturbation methods (MP2). Further accurate analysis based on the coupled clusters theory with singles and doubles excitations agrees with the MP2 results. The equilibrium structures, binding energies, electronic properties, stretching frequencies, and rotational constants of HX(H(2)O)(n) and X(-)(H(3)O)(+)(H(2)O)(n-1) are calculated. The dissociated structures of HF and HCl can be formed for n>/=4, while those of HBr and HI can be formed for n>/=3. Among these, the dissociated structures of HX (X=Cl, Br, and I) are more stable than the undissociated ones for n>/=4, while such cases for HF would require much more than six water molecules, in agreement with previous reports. The IR spectra of stable clusters including anharmonic frequencies are predicted to facilitate IR experimental studies. Undissociated systems have X-H stretching modes which are highly redshifted by hydration. Dissociated hydrogen halides show three characteristic OH stretching modes of hydronium moiety, which are redshifted from the OH stretching modes of water molecules.     

How short can the H...H intermolecular contact be? New findings that reveal the covalent nature of extremely strong interactions

Ab initio calculations at the MP2/6-311++G(d,p) and MP2/aug-cc-pVDZ//MP2/aug-cc-pVTZ levels have been performed for the following complexes: H2OH+...HBeH, H2OH+...HBeBeH, H2OH+...HBeF, HClOH+...HBeH, Cl2OH+...HBeH, and Cl2OH+...HBeF. For all dimers considered, extremely short H...H intermolecular contacts (1.0-1.3 A) were obtained. These are the shortest intermolecular distances which have ever been reported, with binding energies within the range of 13.7-24.3 kcal/mol (MP2/aug-cc-pVDZ//MP2/aug-cc-pVTZ level). The interaction energies of the complexes analyzed were also extrapolated to the complete basis set (CBS) limit. To explain the nature of such strong interactions, the Bader theory was applied, and the characteristics of the bond critical points (BCPs) were analyzed. It was pointed out that for the major part of the H...H contacts considered here the Laplacian of the electron density at H...H BCP is negative indicating the partly covalent nature of such a connection. The term "covalent character of the hydrogen bond" used sometimes in recent studies is discussed. An analysis of the interaction energy components for dihydrogen bonded systems considered indicates that in contrast to conventional hydrogen bonded systems the attractive electrostatic term is outweighed by the repulsive exchange energy term and that the higher order delocalization energy term is the most important attractive term.     

Theoretical study on the reaction mechanism of NH2(-) with O2 (a1Δg)

A detailed theoretical study of the potential energy surface of poorly understood ion-molecule reaction of NH(2)(-) and O(2) (a(1)Δ(g)) is explored at the density functional theory B3LYP/6-311++G(d,p), ab initio of QCISD/6-311++G(d,p) and CCSD(T)/6-311++G(3df, 2pd) (single-point) theoretical levels for the first time. It is shown that there are six total possible products from P(1) to P(6) on the singlet potential energy surface. Among these, the charge-transfer product P(1) (NH(2) + O(2)(-)) is the most favorable product with predominant abundances, whereas P(4) (NO(-) + H(2)O) and P(2) (HNO + OH(-)) may be the second and third feasible products followed by the almost neglectable P(3) (NO(2)(-) + H(2)), while P(5) (c-NO(2)(-) + H(2)) and P(6) (ONO(-) + H(2)) will not be observed due to their either high barriers or being secondary products. The present theoretical study points out that besides P(1) (NH(2) + O(2)(-)) and P(2) (HNO + OH(-)), P(4) (NO(-) + H(2)O) should be also observed, which is different from the previous experiment study by Anthony Midey et al. in 2008. In addition, almost all of the reaction pathways to products are exothermic and the reaction rate should be very fast since the reaction barriers are very low except for P(5) (c-NO(2)(-) + H(2)) which is in agreement with the measured total reaction rate constant k = 9.0 × 10(-10) cm(3)s(-1) at 300 K in the experiment study. It is expected that the present theoretical study may be helpful for the understanding of the reaction mechanism related to NHX(-), NX(2)(-), PHX(-), and PX(2)(-) (X = H, F, and Cl).     

Primary and secondary phosphane complexes of metalloporphyrins: isolation, spectroscopy, and X-ray crystal structures of ruthenium and osmium porphyrins binding phenyl- or diphenylphosphane

[Ru(II)(por)(PH(n)Ph(3-n))2], [Os(II)(por)(CO)(PH(n)Ph(3-n))] (n=1, 2), and [Os(II)(F20-tpp){P(OH)Ph2}(PHPh2)] (F20-tpp=5,10,15,20-tetrakis(pentafluorophenyl)porphyrinato dianion) were prepared from the reaction of [M(II)(por)(CO)] (M=Ru, Os) or [Os(VI)(por)O2] with the respective primary/secondary phosphane and characterized by 1H NMR, 31P NMR, UV/Vis, and IR spectroscopy, mass spectrometry, and elemental analysis. The reaction of [Os(VI)(por)O2] with PHPh2 also gave minor amounts of [Os(II)(por){P(OH)Ph2}2]. [Ru(II)(F20-tpp)(PH2Ph)2] exhibits a remarkable stability toward air and shows a reversible metal-centered oxidation couple at E(1/2)=0.39 V versus [Cp2Fe](+/0) in the cyclic voltammogram. The structures of [Ru(II)(F20-tpp)(PH2Ph)2] x 2CH2Cl2, [Ru(II)(4-Cl-tpp)(PHPh2)2] x 2CH2Cl2 (4-Cl-tpp=5,10,15,20-tetrakis(p-chlorophenyl)porphyrinato dianion), [Ru(II)(F20-tpp)(PHPh2)2], and [Os(II)(F20-tpp){P(OH)Ph2}2] were determined by X-ray crystallography and feature Ru-P distances of 2.3397(11)-2.3609(9) A and an Os-P distance of 2.369(2) A.     

Gas-phase chemistry of ionized and protonated GeF4: a joint experimental and theoretical study

The gas-phase ion chemistry of GeF(4) and of its mixtures with water, ammonia and hydrocarbons was investigated by ion trap mass spectrometry (ITMS) and ab initio calculations. Under ITMS conditions, the only fragment detected from ionized GeF(4) is GeF(3)(+). This cation is a strong Lewis acid, able to react with H(2)O, NH(3) and the unsaturated C(2)H(2), C(2)H(4) and C(6)H(6) by addition-HF elimination reactions to form F(2)Ge(XH)(+), FGe(XH)(2)(+), Ge(XH)(3)(+) (X = OH or NH(2)), F(2)GeC(2)H(+), F(2)GeC(2)H(3)(+) and F(2)GeC(6)H(5)(+). The structure, stability and thermochemistry of these products and the mechanistic aspects of the exemplary reactions of GeF(3)(+) with H(2)O, NH(3) and C(6)H(6) were investigated by MP2 and coupled cluster calculations. The experimental proton affinity (PA) and gas basicity (GB) of GeF(4) were estimated as 121.5 ± 6.0 and 117.1 ± 6.0 kcal mol(-1), respectively, and GeF(4)H(+) was theoretically characterized as an ion-dipole complex between GeF(3)(+) and HF. Consistently, it reacts with simple inorganic and organic molecules to form GeF(3)(+)-L complexes (L = H(2)O, NH(3), C(2)H(2), C(2)H(4), C(6)H(6), CO(2), SO(2) and GeF(4)). The theoretical investigation of the stability of these ions with respect to GeF(3)(+) and L disclosed nearly linear correlations between their dissociation enthalpies and free energies and the PA and GB of L. Comparing the behavior of GeF(3)(+) with the previously investigated CF(3)(+) and SiF(3)(+) revealed a periodically reversed order of reactivity CF(3)(+) < GeF(3)(+) < SiF(3)(+). This parallels the order of the Lewis acidities of the three cations.     

Two new "onium" fluorosilicates, the products of interaction of fluorosilicic acid with 12-membered macrocycles: structures and spectroscopic properties

Two novel compounds, (L(1)H)(2)[SiF(6)] x 2H(2)O (1) and (L(2)H)(2)[SiF(5)(H(2)O)](2) x 3H(2)O (2), resulting from the reactions of H(2)SiF(6) with 4'-aminobenzo-12-crown-4 (L(1)) and monoaza-12-crown-4 (L(2)), respectively, were studied by X-ray diffraction and characterised by IR and (19)F NMR spectroscopic methods. Both complexes have ionic structures due to the proton transfer from the fluorosilicic acid to the primary amine group in L(1) and secondary amine group incorporated into the macrocycle L(2). The structure of 1 is composed of [SiF(6)](2-) centrosymmetric anions, N-protonated cations (L(1)H)(+), and two water molecules, all components being bound in the layer through a system of NH[...]F, NH[...]O and OH[...]F hydrogen bonds. The [SiF(6)](2-) anions and water molecules are assembled into inorganic negatively-charged layers via OH[dot dot dot]F hydrogen bonds. The structure of 2 is a rare example of stabilisation of the complex anion [SiF(5)(H(2)O)](-), the labile product of hydrolytic transformations of the [SiF(6)](2-) anion in an aqueous solution. The components of 2, i.e., [SiF(5)(H(2)O)](-), (L(2)H)(+), and water molecules, are linked by a system of NH[...]F, NH[...]O, OH[...]F, OH[dot dot dot]O hydrogen bonds. In a way similar to 1, the [SiF(5)(H(2)O)](-) anions and water molecules in 2 are combined into an inorganic negatively-charged layer through OH[...]F and OH[...]O interactions.     

高能体系分子间相互作用研究: 含NNO~2和NH~2混合物

以abinitioHF/6-31G^*计算求得NH~3+NH~2NO~2的两种优化构型,经MP4电子相关能校正和Boys-Bernardi方案校正基组叠加误差求得精确的分子间相互作用能。还用PM3方法计算研究TATB(均三氨基三硝基苯)分别与HMX(奥克托金)和RDX(黑索金)的混合体系,经色散能校正电子相关近似地求得分子间相互作用能。结果表明,NH~3与NH~2NO~2之间的最大结合能为-38.32kJ/mol;分子间相互作用增强了N-NO~2键强度;TATB与HMX,RDX的结合能远大于石墨与HMX或RDX的结合能,表明TATB对HMX和RDX的润湿和钝感作用较石墨更强。     

Nitrosyl induces phosphorous-acid dissociation in ruthenium(II)

The trans-[Ru(NO)(NH(3))(4)(P(OH)(3))]Cl(3) complex was synthesized by reacting [Ru(H(2)O)(NH(3))(5)](2+) with H(3)PO(3) and characterized by spectroscopic ((31)P-NMR, δ = 68 ppm) and spectrophotometric techniques (λ = 525 nm, ε = 20 L mol(-1) cm(-1); λ = 319 nm, ε = 773 L mol(-1) cm(-1); λ = 241 nm, ε = 1385 L mol(-1) cm(-1); ν(NO(+)) = 1879 cm(-1)). A pK(a) of 0.74 was determined from infrared measurements as a function of pH for the reaction: trans-[Ru(NO)(NH(3))(4)(P(OH)(3))](3+) + H(2)O ? trans-[Ru(NO)(NH(3))(4)(P(O(-))(OH)(2))](2+) + H(3)O(+). According to (31)P-NMR, IR, UV-vis, cyclic voltammetry and ab initio calculation data, upon deprotonation, trans-[Ru(NO)(NH(3))(4)(P(OH)(3))](3+) yields the O-bonded linkage isomer trans- [Ru(NO)(NH(3))(4)(OP(OH)(2))](2+), then the trans-[Ru(NO)(NH(3))(4)(OP(H)(OH)(2))](3+) decays to give the final products H(3)PO(3) and trans-[Ru(NO)(NH(3))(4)(H(2)O)](3+). The dissociation of phosphorous acid from the [Ru(NO)(NH(3))(4)](3+) moiety is pH dependent (k(obs) = 2.1 × 10(-4) s(-1) at pH 3.0, 25 °C).     

Origin of the SN2 benzylic effect

The S N2 identity exchange reactions of the fluoride ion with benzyl fluoride and 10 para-substituted derivatives (RC6H 4CH 2F, R = CH3, OH, OCH 3, NH2, F, Cl, CCH, CN, COF, and NO2) have been investigated by both rigorous ab initio methods and carefully calibrated density functional theory. Groundbreaking focal-point computations were executed for the C6H5CH 2F + F (-) and C 6H 5CH2Cl + Cl (-) SN2 reactions at the highest possible levels of electronic structure theory, employing complete basis set (CBS) extrapolations of aug-cc-pV XZ (X = 2-5) Hartree-Fock and MP2 energies, and including higher-order electron correlation via CCSD/aug-cc-pVQZ and CCSD(T)/aug-cc-pVTZ coupled cluster wave functions. Strong linear dependences are found between the computed electrostatic potential at the reaction-center carbon atom and the effective SN2 activation energies within the series of para-substituted benzyl fluorides. An activation strain energy decomposition indicates that the SN2 reactivity of these benzylic compounds is governed by the intrinsic electrostatic interaction between the reacting fragments. The delocalization of nucleophilic charge into the aromatic ring in the SN2 transition states is quite limited and should not be considered the origin of benzylic acceleration of SN2 reactions. Our rigorous focal-point computations validate the benzylic effect by establishing SN2 barriers for (F (-), Cl (-)) identity exchange in (C6H5CH2F, C6H 5CH2Cl) that are lower than those of (CH3F, CH3Cl) by (3.8, 1.6) kcal mol (-1), in order.     

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.