Limiting values for Mo/ller–Plesset second‐order correlation energies of polyatomic systems: A benchmark study on Ne, HF, H2O, N2, and He...He

Symmetric dissociation of the water molecule with truncation energy error. A benchmark study

We use selected configuration interaction with truncation energy error (SCI-TEE) and CI by parts (CIBP) to study the symmetric dissociation of the water molecule with Roos' triple-ζ double polarization basis set and with the Dunning cc-pVTZ basis. The calculations comprise CISDTQ (CI-4x) through CI-8x for H2O at its equilibrium geometry (Req) and up to fifteen times Req. With the Dunning basis our SCI-TEE-8x energies differ from full CI by less than 0.01 mHartree (0.006 kcal mol-1) at all O-H distances, representing the best upper bounds for this system outside Req. We compare our results with those of other relevant ab initio methods finding good agreement with recent DMRG calculations. The non-parallelity error (NPE) for SCI-TEE-6x remains stable below 0.1 mHartree when moving from the Roos to the Dunning orbitals. For the present system, CBS energy errors at the experimental equilibrium geometry and at dissociation can accurately be evaluated as the difference between non-relativistic total electronic energies taken from the literature, and our SCI-TEE-8x energies obtained with Dunning's or Roos' orbitals. In both cases, the difference between CBS energy errors at the equilibrium geometry and dissociation is not smaller than 10 mH, showing that chemically accurate NPE values do not guarantee a chemically accurate potential energy surface.

Micro-solvation of CO in water: infrared spectra and structural calculations for (D2O)2–CO and (D2O)3–CO

The weakly-bound molecular clusters (D₂O)₂–CO and (D₂O)₃–CO are observed in the C–O stretch fundamental region (≈2150 cm⁻¹), and their rotationally-resolved infrared spectra yield precise rotational parameters.

Breaking the bottleneck: Use of molecular tailoring approach for the estimation of binding energies at MP2/CBS limit for large water clusters

A pragmatic method based on the molecular tailoring approach (MTA) for estimating the complete basis set (CBS) limit at Møller-Plesset second order perturbation (MP2) theory accurately for large molecular clusters with limited computational resources is developed. It is applied to water clusters, (H2O)n (n = 7, 8, 10, 16, 17, and 25) optimized employing aug-cc-pVDZ (aVDZ) basis-set. Binding energies (BEs) of these clusters are estimated at the MP2/aug-cc-pVNZ (aVNZ) [N = T, Q, and 5 (whenever possible)] levels of theory employing grafted MTA (GMTA) methodology and are found to lie within 0.2 kcal/mol of the corresponding full calculation MP2 BE, wherever available. The results are extrapolated to CBS limit using a three point formula. The GMTA-MP2 calculations are feasible on off-the-shelf hardware and show around 50%-65% saving of computational time. The methodology has a potential for application to molecular clusters containing ∼100 atoms.

Accurate predictions of water cluster formation, (H₂O)(n=2-10)

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2-10 water molecules. This approach reveals new low energy conformers for (H(2)O)(n=7,9,10). The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.

Photodetachment of Isolated Bicarbonate Anion: Electron Binding Energy of HCO3(.)

We report the first direct photodetachment photoelectron spectroscopy of HCO3(-) in the gas phase under low-temperature conditions. The observed photoelectron spectra are complicated due to excitations of manifolds in both vibrational and electronic states. A long and single vibrational progression with a frequency of 530 ± 20 cm(-1) is partially resolved in the threshold of the T = 20 K, 266 nm spectrum. The adiabatic electron detachment energy (ADE) of HCO3(-), or, in other words, the electron affinity (EA) of neutral HCO3, is experimentally determined from the (0,0) transition to be 3.680 ± 0.015 eV. The computed values of the Franck-Condon integral and intensity are favorable for observing the (0,0) transition. High-level ab initio calculations at the CCSD(T) level of theory produce an estimated anharmonic frequency of 546 cm(-1) for HCO3 and a value of 3.79 eV for the (0,0) transition, both in good agreement with the experimentally determined values.

Probing phenylalanine/adenine pi-stacking interactions in protein complexes with explicitly correlated and CCSD(T) computations

To examine the effects of pi-stacking interactions between aromatic amino acid side chains and adenine bearing ligands in crystalline protein structures, 26 toluene/(N9-methyl)adenine model configurations have been constructed from protein/ligand crystal structures. Full geometry optimizations with the MP2 method cause the 26 crystal structures to collapse to six unique structures. The complete basis set (CBS) limit of the CCSD(T) interaction energies has been determined for all 32 structures by combining explicitly correlated MP2-R12 computations with a correction for higher-order correlation effects from CCSD(T) calculations. The CCSD(T) CBS limit interaction energies of the 26 crystal structures range from -3.19 to -6.77 kcal mol (-1) and average -5.01 kcal mol (-1). The CCSD(T) CBS limit interaction energies of the optimized complexes increase by roughly 1.5 kcal mol (-1) on average to -6.54 kcal mol (-1) (ranging from -5.93 to -7.05 kcal mol (-1)). Corrections for higher-order correlation effects are extremely important for both sets of structures and are responsible for the modest increase in the interaction energy after optimization. The MP2 method overbinds the crystal structures by 2.31 kcal mol (-1) on average compared to 4.50 kcal mol (-1) for the optimized structures.

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.

Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets: applications to atoms and diatomics

We have implemented the use of mixed basis sets of Gaussian one- and two-electron (geminal) functions for the calculation of second-order Møller-Plesset (MP2) correlation energies. In this paper, we describe some aspects of this implementation, including different forms chosen for the pair functions. Computational results are presented for some closed-shell atoms and diatomics. Our calculations indicate that the method presented is capable of yielding highly accurate second-order correlation energies with rather modest Gaussian orbital basis sets, providing an alternative route to highly accurate wave functions. For the neon atom, the hydrogen molecule, and the hydrogen fluoride molecule, our calculations yield the most accurate MP2 energies published so far. A critical comparison is made with established MP2-R12 methods, revealing an erratic behaviour of some of these methods, even in large basis sets.

Combining explicitly correlated R12 and Gaussian geminal electronic structure theories

Explicitly correlated R12 methods using a single short-range correlation factor (also known as F12 methods) have dramatically smaller basis set errors compared to the standard wave function counterparts, even when used with small basis sets. Correlations on several length scales, however, may not be described efficiently with one correlation factor. Here the authors explore a more general MP2-R12 method in which each electron pair uses a set of (contracted) Gaussian-type geminals (GTGs) with fixed exponents, whose coefficients are optimized linearly. The following features distinguish the current method from related explicitly correlated approaches published in the literature: (1) only two-electron integrals are needed, (2) the only approximations are the resolution of the identity and the generalized Brillouin condition, (3) only linear parameters are optimized, and (4) an arbitrary number of (non-)contracted GTGs can appear. The present method using only three GTGs and a double-zeta quality basis computed valence correlation energies for a set of 20 small molecules only 2.2% removed from the basis set limit. The average basis set error reduces to 1.2% using a near-complete set of seven GTGs with the double-zeta basis set. The conventional MP2 energies computed with much larger quadruple, quintuple, and sextuple basis sets all had larger average errors: 4.6%, 2.4%, and 1.5%, respectively. The new method compares well to the published MP2-R12 method using a single Slater-type geminal (STG) correlation factor. For example, the average basis set error in the absolute MP2-R12 energy obtained with the exp(-r12) correlation factor is 1.7%. Correlation contribution to atomization energies evaluated with the present method and with the STG-based method only required a double-zeta basis set to exceed the precision of the conventional sextuple-zeta result. The new method is shown to always be numerically stable if linear dependencies are removed from the two-particle basis and the zeroth-order Hamiltonian matrix is made positive definite.

An ab Initio Benchmark Study of Hydrogen Bonded Formamide Dimers

The five singly and doubly hydrogen bonded dimers of formamide are calculated at the correlated level by using resolution of identity Møller-Plesset second-order perturbation theory (RIMP2) and the coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] method. All structures are optimized with the Dunning aug-cc-pVTZ and aug-cc-pVQZ basis sets. The binding energies are extrapolated to the complete basis set (CBS) limit by using the aug-cc-pVXZ (X = D, T, Q) basis set series. The effect of extending the basis set to aug-cc-pV5Z on the geometries and binding energies is studied for the centrosymmetric doubly N-H...O bonded dimer FA1 and the doubly C-H...O bonded dimer FA5. The MP2 CBS limits range from -5.19 kcal/mol for FA5 to -14.80 kcal/mol for the FA1 dimer. The DeltaCCSD(T) corrections to the MP2 CBS limit binding energies calculated with the 6-31+G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are mutually consistent to within < or =0.03 kcal/mol. The DeltaCCSD(T) correction increases the binding energy of the C-H...O bonded FA5 dimer by 0.4 kcal/mol or approximately 9% over the distance range +/-0.5 Angstrom relative to the potential minimum. This implies that the ubiquitous long-range C-H...O interactions in proteins are stronger than hitherto calculated.

A comparison of linear and nonlinear correlation factors for basis set limit Møller-Plesset second order binding energies and structures of He2, Be2, and Ne2

The basis set limit Møller-Plesset second-order equilibrium bond lengths of He2, Be2, and Ne2, accurate to 0.01a0, are computed to be 5.785a0, 5.11a0, and 6.05a0. The corresponding binding energies are 22.4+/-0.1, 2180+/-20, and 86+/-2 muE(h), respectively. An accuracy of 95% in the binding energy requires an aug-cc-pV6Z basis or larger for conventional Møller-Plesset theory. This accuracy is obtained using an aug-cc-pV5Z basis if geminal basis functions with a linear correlation factor are included and with an aug-cc-pVQZ basis if the linear correlation factor is replaced by exp(-gammar(12)) with gamma=1. The correlation factor r(12) exp(-gammar(12)) does not perform as well, describing the atom more efficiently than the dimer. The geminal functions supplement the orbital basis in the description of both the short-range correlation, at electron coalescence, and the long-range dispersion correlation and the values of gamma that give the best binding energies are smaller than those that are optimum for the atom or the dimer. It is important to sufficiently reduce the error due to the resolution of the identity approximation for the three- and four-electron integrals and we recommend the complementary auxiliary basis set method. The effect of both orbital and geminal basis set superposition error must be considered to obtain accurate binding energies with small orbital basis sets. In this respect, we recommend using exp(-gammar(12)) with localized orbitals and the original orbital-variant formalism.

Correlation energy extrapolation by intrinsic scaling. V. Electronic energy, atomization energy, and enthalpy of formation of water

The method of correlation energy extrapolation by intrinsic scaling, recently introduced to obtain accurate molecular electronic energies, is used to calculate the total nonrelativistic electronic ground state energy of the water molecule. Accurate approximations to the full configuration interaction energies are determined for Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation-consistent double-, triple- and quadruple-zeta basis sets and then extrapolated to the complete basis set limit. The approach yields the total nonrelativistic energy -76.4390+/-0.0004 hartree, which compares very well with the value of -76.4389 hartree derived from experiment. The energy of atomization is recovered within 0.1 mh. The enthalpy of formation, which is obtained in conjunction with our previous calculation of the dissociation energy of the oxygen molecule, is recovered within 0.05 mh.

Convergence of third order correlation energy in atoms and molecules

We have investigated the convergence of third order correlation energy within the hierarchies of correlation consistent basis sets for helium, neon, and water, and for three stationary points of hydrogen peroxide. This analysis confirms that singlet pair energies converge much slower than triplet pair energies. In addition, singlet pair energies with (aug)-cc-pVDZ and (aug)-cc-pVTZ basis sets do not follow a converging trend and energies with three basis sets larger than aug-cc-pVTZ are generally required for reliable extrapolations of third order correlation energies, making so the explicitly correlated R12 calculations preferable.

Competition between van der Waals and hydrogen bonding interactions: structure of the trans-1-naphthol/N(2) cluster

The excitation energy in the multiphoton ionization spectrum of the trans-1-naphthol/N(2) cluster shows only a small red shift with respect to isolated naphthol, indicating a van der Waals pi-bound structure rather than a hydrogen-bonded one. To confirm this interpretation, high-level electronic structure calculations were performed for several pi- and hydrogen-bonded isomers of this cluster. The calculations were carried out at the second order Møller-Plesset (MP2) level of perturbation theory with the family of correlation consistent basis sets up to quintuple-zeta quality including corrections for the basis set superposition error and extrapolation to the MP2 complete basis set (CBS) limit. We report the optimal geometries, vibrational frequencies, and binding energies (D(e)), also corrected for harmonic zero-point energies (D(0)), for three energetically low-lying isomers. In all calculations the lowest energy structure was found to be an isomer with the N(2) molecule bound to the pi-system of the naphthol ring carrying the OH group. In the CBS limit its dissociation energy was computed to be D(0) = 2.67 kcal/mol (934 cm(-1)) as compared to D(0) = 1.28 kcal/mol (448 cm(-1)) for the H-bound structure. The electronic structure calculations therefore confirm the assignment of the experimental electronic spectrum corresponding to a van der Waals pi-bound structure. The energetic stabilization of the pi-bound isomer with respect to the hydrogen-bonded one is rather unexpected when compared with previous findings in related systems, in particular phenol/N(2).

High-level ab initio calculations for the four low-lying families of minima of(H2O)20. II. Spectroscopic signatures of the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms hydrogen bonding networks

We report the first harmonic vibrational spectra for each of the lowest lying isomers within the four major families of minima of (H2O)20, namely, the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms. These were obtained at the second-order Moller-Plesset perturbation level of theory (MP2) with the augmented correlation consistent basis set of double zeta quality (aug-cc-pVDZ) at the corresponding minimum energy geometries. The computed infrared (IR) spectra are the first ones obtained from first principles for these clusters. They were found to contain spectral features, which can be directly mapped onto the distinctive spectroscopic signatures of their constituent tetramer, pentamer, and octamer fragments. The dodecahedron spectra show the richest structure in the OH stretching region and are associated with the most redshifted OH vibrations with respect to the monomer. The lowest lying edge-sharing pentagonal prism isomer displays intense IR active vibrations that are redshifted by approximately 600 cm(-1) with respect to the water monomer. Furthermore the most redshifted, IR-active OH stretching vibrations for all four networks correspond to hydrogen bonded OH groups, which exhibit the following two common characteristics: (i) they belong to fragments which have a "free" OH stretch and (ii) they act as donors to a neighboring water molecule along a "dimerlike" (strong) hydrogen bond. The zero-point energy corrected MP2/CBS (complete basis set) limit binding energies D(0) for the four isomers are -163.1 kcal/mol (edge-sharing pentagonal prism), -160.1 kcal/mol (face-sharing pentagonal prism), -157.5 kcal/mol (fused cubes), and -148.1 kcal/mol (dodecahedron).