Approximations to complete basis set-extrapolated, highly correlated non-covalent interaction energies

The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)∕aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)∕aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent absolute deviation of only 1.7%, relative to the (estimated) complete basis set CCSD(T) results. Use of this composite approach to an additional set of eight dimers gave binding energies to within 1% of previously published high-level data. It is also shown that binding within parallel and parallel-crossed conformations of naphthalene dimer is predicted by the composite approach to be 9% greater than that previously reported in the literature. The ability of some recently developed dispersion-corrected density-functional theory methods to predict the binding energies of the set of ten small dimers was also examined.     

Truncation of the correlation consistent basis sets: extension to third-row (Ga-Kr) molecules

The systematic reduction of the commonly used correlation consistent basis sets [cc-pVnZ where n=D(2), T(3), Q(4), and 5] as a means to reduce computational cost has been extended to hydrogen-containing third-row (Ga-Kr) molecules of the G2 test suite. Coupled cluster with singles, doubles, and quasiperturbative triple excitations [CCSD(T)] calculations were performed using both the full correlation consistent basis sets and a series of truncated basis sets in order to assess the impact of basis set reduction upon the structures and energies of the species. The impact that truncation of the basis sets for hydrogen has upon extrapolation of energies to the complete basis set limit also has been examined, and the cost savings that can be achieved are discussed. Overall, basis set reduction can be accomplished which preserves the systematic convergence behavior of the full correlation consistent basis sets.     

Electronic structure and bonding of the 3d transition metal borides, MB, M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu through all electron ab initio calculations

The electronic structure and bonding of the ground and some low-lying states of all first row transition metal borides (MB), ScB, TiB, VB, CrB, MnB, FeB, CoB, NiB, and CuB have been studied by multireference configuration interaction (MRCI) methods employing a correlation consistent basis set of quintuple cardinality (5Z). It should be stressed that for all the above nine molecules, experimental results are essentially absent, whereas with the exception of ScB and CuB the remaining seven species are studied theoretically for the first time. We have constructed full potential energy curves at the MRCI/5Z level for a total of 27 low-lying states, subsequently used to extract binding energies, spectroscopic parameters, and bonding schemes. In addition, some 20 or more states for every MB species have been examined at the MRCI/4Z level of theory. The ground state symmetries and corresponding binding energies (in kcal/mol) are 5Sigma-(ScB), 76; 6Delta(TiB), 65; 7Sigma+(VB), 55; 6Sigma+(CrB), 31; 5Pi(MnB), 20; 4Sigma-(FeB), 54; 3Delta(CoB), 66; 2Sigma+(NiB), 79; and 1Sigma+(CuB), 49.     

Coupled cluster studies. IV. Analysis of the correlated wavefunction in canonical and localized orbital basis for ethylene,carbon monoxide,and carbon dioxide

An a posteriori analysis of the correlated wavefunctions of three small molecules using canonical and localized orbitals shows that, while more excitations are nearly zero for canonical orbitals than for localized ones, in the latter case a straightforward way exists for a priori selection of negligible excitations. In the case of the larger molecule cytosine the same observation is made. However, in this case 99% of the correlation energy is obtained already with ≈ 10% of the excitations when localized orbitals are used, while ≈ 36% of them are necessary in canonical basis. Furthermore it is shown that, using localized orbitals, the excitations can be split into subsets which can be calculated individually. The results suggest that 80–90% of the correlation energies given by MP2, CCL, or CCD can be obtained from the contributions of individual chemical bonds and their interactions. A simple derivation of the orbital invariant formalism of Pulay and Sæbø for the calculation of MP2 and MP3 correlation energies is given.     

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

The recently introduced method of correlation energy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F(2) molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 A to 8 A, the equilibrium distance being 1.412 A. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail.     

Ab initio investigation of the ground and low-lying states of the diatomic fluorides TiF, VF, CrF, and MnF

The electronic structure of the ground and low-lying states of the diatomic fluorides TiF, VF, CrF, and MnF was examined by multireference and coupled cluster methods in conjunction with extended basis sets. For a total of 34 states we report binding energies, spectroscopic constants, dipole moments, separation energies, and charge distributions. In addition, for all states we have constructed full potential curves. The suggested ground state binding energies of TiF(X (4)Phi), VF(X (5)Pi), CrF(X (6)Sigma(+)), and MnF(X (7)Sigma(+)) are 135, 130, 110, and 108 kcal/mol, respectively, with first excited states A (4)Sigma(-), A (5)Delta, A (6)Pi, and a (5)Sigma(+) about 2, 3, 23, and 19 kcal/mol higher. In essence all our numerical findings are in harmony with experimental results. For all molecules and states studied it is clear that the in situ metal atom (M) shows highly ionic character, therefore the binding is described realistically by M(+)F(-).     

Aqueous microsolvation of mercury halide species

The effects of aqueous solvation on the thermochemistry of reactions between mercury and small halogen molecules has been investigated by the microsolvation approach using ab initio and density functional theory (DFT) calculations. The structures, vibrational frequencies, and binding energies of 1, 2, and 3 water molecules with mercury-halide (HgBr2, HgBrCl, HgCl2, HgBr, and HgCl) and related mercury and halogen species (Br2, BrCl, Cl2, Cl, Hg, and Br) have been computed with second order M?ller-Plesset perturbation theory (MP2) and the B3LYP density functional method. Accurate incremental water binding energies have been obtained at the complete basis set (CBS) limit using sequences of correlation consistent basis sets, including higher order correlation effects estimated from coupled cluster calculations. The resulting energetics were used to calculate the influence of water molecules on the thermochemistry of a number of reactions between mercury and small halogen-containing molecules. In general, the presence of water favors the formation of oxidized mercury halide species.     

Small elemental clusters. I. The structures of Be2, Be3, Be4, and Be5

The geometries and energies of beryllium clusters up to Be₅ are examined using ab initio molecular orbital theory. Allowances are made for electron correlation with Møller—Plesset perturbation theory to fourth order. Correlation is found to have a dramatic effect on the relative energies of the several structures examined for Be₄ and Be₅. Furthermore, the effect of d-type basis functions on the correlation energy results in an increased binding energy for the clusters. Be₂ is only weakly bound. For Be₃, the best estimate of the binding energy is 6 kcal/mole for the singlet equilateral triangle. Be₄ is tetrahedral in its ground state and the estimated binding is 56 kcal/mole. The best structure for Be₅ is a singlet trigonal bipyramid, and the binding energy is 88 kcal/mole at the highest level of theory used.     

Barriers to rotation adjacent to double bonds. 4. Effect of basis set on structures,and of electron correlation on relative energies

The optimized geometries for the rotamers of propanal, 2-butanone, isobutyraldehyde, methyl isopropyl ketone, and isobutyric acid obtained using the 3–21G and 6–31G* basis sets are compared, and systematic changes are noted. The relative 6–31G* energies using the 3–21G and 6–31G* geometries are generally the same within 0.1 kcal/mol. The effect of electron correlation on the relative energies is generally small. These and related data show that 6–31G* relative energies obtained using 3–21G geometries are generally satisfactory when studying rotation about C? C bonds. However, this is not the case for C? O bonds. The calculated relative energies of isomeric compounds are reproduced only with the full MP4 correction for electron correlation.     

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Two related methods to calculate the Kohn-Sham correlation energy within the framework of the adiabatic-connection fluctuation-dissipation theorem are presented. The required coupling-strength-dependent density-density response functions are calculated within exact-exchange time-dependent density-functional theory, i.e., within time-dependent density-functional response theory using the full frequency-dependent exchange kernel in addition to the Coulomb kernel. The resulting resolution-of-identity exact-exchange random-phase approximation (RI-EXXRPA) methods in contrast to previous EXXRPA methods employ an auxiliary basis set (RI basis set) to improve the computational efficiency, in particular, to reduce the formal scaling of the computational effort with respect to the system size N from N(6) to N(5). Moreover, the presented RI-EXXRPA methods, in contrast to previous ones, do not treat products of occupied times unoccupied orbitals as if they were linearly independent. Finally, terms neglected in previous EXXRPA methods can be included, which leads to a method designated RI-EXXRPA+, while the method without these extra terms is simply referred to as RI-EXXRPA. Both EXXRPA methods are shown to yield total energies, reaction energies of small molecules, and binding energies of noncovalently bonded dimers of a quality that is similar and in some cases even better than that obtained with quantum chemistry methods such as Mo?ller-Plesset perturbation theory of second order (MP2) or with the coupled cluster singles doubles method. In contrast to MP2 and to conventional density-functional methods, the presented RI-EXXRPA methods are able to treat static correlation.     

Structures, energetics and vibrational frequency shifts of hydrated pyrimidine

More than 70 unique micro-hydrated structures of pyrimidine, ranging in size from 1 to 7 water molecules, have been characterized with the B3LYP density functional and the 6-311++G(2df,2pd) triple-ζ split-valence basis set. Explicitly correlated MP2-F12 single-point computations were performed on each structure with a correlation consistent triple-ζ basis set to estimate the relative and dissociation energies at the MP2 complete basis set (CBS) limit. Many of these new structures have significantly lower energies than those previously reported (by as much as 12.66 kcal?mol(-1)). For clusters with 1 and 2 water molecules, the MP2-F12 relative and dissociation energies are virtually identical to the corresponding CCSD(T)-F12 values. As the number of hydrating waters increases, the structures in which the water molecules are clustered together at one of the N atoms have lower energies than those where the water molecules are more distributed around the pyrimidine ring. Micro-hydrated structures that effectively extend the low-energy hydrogen-bonding motifs to both sides of the ring, as would be expected in the bulk phase, reproduce the experimentally observed vibrational frequency shifts of ν(1) and ν(8b) in very dilute aqueous pyrimidine solutions to within 1 cm(-1) . Micro-hydrated structures of pyrimidine in which water molecules are clustered together have lower energies than structures in which the water molecules are more evenly spread around the pyrimidine ring.     

Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor

The recently introduced MP2-R122*A(loc) and LMP2-R122*A(loc) methods are modified to use a short-range correlation factor expanded as a fixed linear combination of Gaussian geminals. Density fitting is used to reduce the effort for integral evaluation, and local approximations are introduced to improve the scaling of the computational resources with molecular size. The MP2-F122*A(loc) correlation energies converge very rapidly with respect to the atomic orbital basis set size. Already with the aug-cc-pVTZ basis the correlation energies computed for a set of 21 small molecules are found to be within 0.5% of the MP2 basis set limit. Furthermore the short-range correlation factor leads to an improved convergence of the resolution of the identity, and eliminates problems with long-range errors in density fitting caused by the linear r12 factor. The DF-LMP2-F122*A(loc) method is applied to compute second-order correlation energies for molecules with up to 49 atoms and more than 1600 basis functions.     

A natural linear scaling coupled-cluster method

It is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupled-cluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupled-cluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation. (c) 2004 American Institute of Physics.     

Metal cation dependence of interactions with amino acids: bond energies of Cs+ to Gly, Pro, Ser, Thr, and Cys

The interactions of cesium cations with five amino acids (AA) including glycine (Gly), proline (Pro), serine (Ser), threonine (Thr), and cysteine (Cys) are examined in detail. Experimentally, the bond dissociation energies (BDEs) are determined using threshold collision-induced dissociation of the Cs(+)(AA) complexes with xenon in a guided ion beam tandem mass spectrometer. Analyses of the energy-dependent cross sections include consideration of unimolecular decay rates, internal energy of the reactant ions, and multiple ion-neutral collisions. Bond dissociation energies (0 K) of 93.3 ± 2.5, 107.9 ± 4.6, 102.3 ± 4.1, 105.4 ± 4.3, and 96.8 ± 4.2 kJ/mol are determined for complexes of Cs(+) with Gly, Pro, Ser, Thr, and Cys, respectively. Quantum chemical calculations are conducted at the B3LYP, B3P86, MP2(full), and M06 levels of theory with geometries and zero-point energies calculated at the B3LYP level using both HW*/6-311+G(2d,2p) and def2-TZVPPD basis sets. Results obtained using the former basis sets are systematically low compared to the experimental bond energies, whereas the latter basis sets show good agreement. For Cs(+)(Gly), theory predicts the ground-state conformer has the cesium cation binding to the carbonyl group of the carboxylic acid. For Cs(+)(Pro), the secondary nitrogen accepts the carboxylic acid hydrogen to form the zwitterionic structure, and the metal cation binds to both oxygens. Cs(+)(Ser), Cs(+)(Thr), and Cs(+)(Cys) are found to have tridentate binding at the MP2(full) level, whereas the density functional approaches slightly prefer bidentate binding of Cs(+) at the carboxylic acid moiety. Comparison of these results to those for the smaller alkali cations provides insight into the trends in binding affinities and structures associated with metal cation variations.     

Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10 microE(h) precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.     

Are AM1 ligand‐protein binding enthalpies good enough for use in the rational design of new drugs?

We have examined the performance of semiempirical quantum mechanical methods in solving the problem of accurately predicting protein-ligand binding energies and geometries. Firstly, AM1 and PM3 geometries and binding enthalpies between small molecules that simulate typical ligand-protein interactions were compared with high level quantum mechanical techniques that include electronic correlation (e.g., MP2 or B3LYP). Species studied include alkanes, aromatic systems, molecules including groups with hypervalent sulfur or with donor or acceptor hydrogen bonding capability, as well as ammonium or carboxylate ions. B3LYP/6-311+G(2d,p) binding energies correlated very well with the BSSE corrected MP2/6-31G(d) values. AM1 binding enthalpies also showed good correlation with MP2 values, and their systematic deviation is acceptable when enthalpies are used for the comparison of interaction energies between ligands and a target. PM3 otherwise gave erratic energy differences in comparison to the B3LYP or MP2 approaches. As one would expect, the geometries of the binding complexes showed the known limitations of the semiempirical and DFT methods. AM1 calculations were subsequently applied to a test set consisting of "real" protein active site-ligand complexes. Preliminary results indicate that AM1 could be a valuable tool for the design of new drugs using proteins as templates. This approach also has a reasonable computational cost. The ligand-protein X-ray structures were reasonably reproduced by AM1 calculations and the corresponding AM1 binding enthalpies are in agreement with the results from the "small molecules" test set.     

Multiple bonds and excited states from the Hartree-Fock-Heitler-London method

The recently proposed Hartree-Fock-Heitler-London, HF-HL, method (Corongiu, G. J. Phys. Chem. A 2006, 110, 11584) previously tested for single bond molecules is validated by potential energy computations for open and closed shells, single and multiple bonds, in ground and excited states of homopolar diatomic molecules of the first and second period. The simple HF-HL function, including the configurations for 2s/2p near degeneracy and avoiding state crossing, yields correct dissociation products, qualitatively correct binding, and accounts for non-dynamical correlation. Addition of ionic structures improves the ab initio HF-HL function and yields about 95% of the experimental binding energies on average. Computed excitation energies are also in agreement with laboratory values as verified for the 3 Pi u and 3 Zeta g- excited states of the C2 molecule. Computation of the remaining dynamical correlation using a semiempirical functional yields binding energies with an average deviation of 1.5 kcal/mol from laboratory values, and total energies with an average deviation of 0.7 kcal/mol from exact nonrelativistic dissociation energies.     

The H and H2 interaction with Pd3Cu,Pd4, and Cu4 fcc (111) clusters: A DFT comparative study

A comparative study of adsorption of H atoms and H₂ molecules on Pd₃Cu, Cu₄, and Pd₄ clusters has been performed through density functional calculations, using the hybrid B3LYP exchange‐correlation functional as implemented in the Gaussian98 program. For Pd atoms the relativistic small‐core effective core potential LANL and LANL2DZ basis set was used and for hydrogen a 6‐31G** basis set was used. The main emphasis is set in the reaction behavior of the different clusters with hydrogen atoms and molecules. We find that full geometry optimization does not appreciably change the metal cluster geometry either for certain reaction modes or the H and H₂ capture parameters, but increases the number of reactive sites of the metal clusters. Also, we found that there is charge transfer competition between H and Cu atoms, which drastically diminishes H₂ adsorption energy, related to the Pd cluster observed value. Edges and threefold sites are the principal hydrogen adsorption sites. Hydrogen has a great mobility over the metal clusters for different minima, especially when Cu is present; many initial pathways end in the same adsorption site. The observed hydrogen adsorption and binding energies are well reproduced by the calculations. Also, the adsorption mechanisms were determined. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005