Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 Å), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.     

Basis sets for molecular interactions. 2. Application to H3N?HF,H3N?HOH,H2O?HF, (NH3)2, and H3CH?OH2

Modifications of the standard 6-31G** basis set as recommended in the accompanying paper are found to markedly lower the basis set superposition error (BSSE) in the title complexes, in contrast to enlargement to a triple-ζ scheme or by addition of a diffuse sp shell or a second set of d-functions without prior optimization, all of which lead to BSSE increase. After appropriate correction for correlation and superposition effects, all basis sets (with the exception of the standard 6-31G** and 6-311G** with their very large BSSE) predict the cyclic geometry of NH₃ dimer to be more stable than the linear arrangement. Correlation and BSSE can shift the equilibrium intermolecular distance in H₃CH-OH₂ by up to 0.4 Å. Failure to correct for superposition error leads to a drastic exaggeration of both the SCF and MP2 components of the interaction energy in this complex. Much better estimates are furnished by our recommended basis sets with their smaller superposition errors.     

Cation-π interactions of curved polycyclic systems: M (M=Li and Na) ion complexation with buckybowls

B3LYP/6-311+G** calculations on alkali metal ion (Li⁺ and Na⁺) complexation with corannulene and sumanene indicate stronger binding compared to [5]-radialene or benzene. The dependence of binding to the convex and concave site is marginal, albeit the preference was consistent for convex binding in the range of 1-4 kcal/mol. The bowl-to-bowl inversion barriers are only marginally affected, below 2 kcal/mol, by metal ion complexation.     

The impact of basis set superposition error on the structure of π?π dimers

The effect of basis set superposition error (BSSE) on the structure and energy of benzene, naphthalene, corannulene, and sumanene dimer has been analyzed. MP2 method was chosen and the effect is estimated using 6‐31G, 6‐31G(d), 6‐311+G(d), cc‐pVDZ, and cc‐pVTZ basis sets. The model calculations on benzene dimer indicate that the impact of BSSE on the equilibrium geometry of π‐stacked dimers appears to be quite significant. Calculations on larger molecular dimers such as the dimers of naphthalene, corannulene, and sumanene are also studied. The practical implication of the current observation on modeling the macromolecular structure is discussed. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Computation of the complexation energies of BH3NH3 and BH3PH3

Extended basis set computations on SCF and CEPA level were performed for BH₃NH₃ and BH₃PH₃ to determine the complexation energy ΔE and the equilibrium distance r(BX) between the “heavy” atoms. Our CEPA results (SCF in parentheses): ΔE(BH₃NH) = ?27(?21.3) kcal/mol, ΔE(BH₃PH₃) = ?17(?11.8) kcal/mol, r(BN) = 1.65(1.68) Å, r(BP) = 1.95(1.99) Å indicate a marked influence of electron correlation on these properties.     

Structure of Mn2(CO)10 and Mn2(CO)9: Insights from ab initio calculations

Optimization of the Mn–Mn distance in Mn₂(CO)₁₀ with various basis sets of at least doublezeta quality results in Mn–Mn bond lengths in the range of 3.07–3.15 Å, 0.2–0.25 Å longer than the experimental value of 2.895 Å. Incrementing the basis set with diffuse p functions (exponent 0.0332) on the carbon atoms improves the calculated bond length to a value of 2.876 Å at the CI level, as a consequence of a charge transfer between each Mn atom and the equatorial carbonyls of the other Mn atom. For Mn₂(CO)₉ four structures have been studied at the SCF and CI levels with assumed geometries. The structure with a symmetric bridging carbonyl turns to be much higher in energy at the SCF level. The two structures which are purely metal–metal bonded [corresponding to the departure of an axial or equatorial carbonyl from Mn₂(CO)₁₀] are nearly degenerate in energy and more stable than the structure with a semibridging carbonyl by 5 kcal/mol at the SCF level and 10–11 kcal/mol at the CI level (seemingly at variance with the conclusions of matrix experiments that favor the semibridging structure).     

Anion⋅⋅⋅Anion Attraction in Complexes of MCl3− (M=Zn,Cd, Hg) with CN−

High-level ab initio calculations show that the MCl₃⁻ anions comprising Group 2B M atoms Zn, Cd, and Hg form a stable complex with the CN⁻ anion, despite the like charge of the two ions. The complexation occurs despite a negative π-hole region above the M atom of MCl₃⁻. The dimerization distorts the planar geometry of MCl₃⁻ into a pyramidal shape which reduces the negative potential above the M atom, facilitating a close approach of the two anions, with R(M⋅⋅⋅C)∼2 Å, and an overall attractive electrostatic attraction within the dimer. In the gas phase, this dimer is less stable than the pair of separated ions by some 30 kcal/mol. However, the dissociation must surmount an energy barrier of roughly 25 kcal/mol which occurs at an intermolecular distance of 4 Å. In aqueous solution, the dimerization process is exothermic and barrier-free, with a binding energy in the 11–18 kcal/mol range.     

Compression effect on structure and proton transfer in crystalline benzoic acid

Geometry optimizations for an isolated dimer and a crystal of benzoic acid were performed in order to evaluate the equilibrium geometries and the energy difference between the dimers in isolated and crystalline states using model potentials. The optimization in the crystal field results in a shortening of the O⋯O distance in comparison with that in an isolated dimer. The magnitude of the shortening agrees well with the difference between the observed values of the O⋯O distance in the gaseous (2.703 Å) and crystalline (2.64 Å) states. The energy increase due to this shortening is estimated to be about 0.24–0.40 kcal mol⁻¹ and is found to be one of the causes of the discrepancy between the barrier height of 1–2 kcal mol⁻¹ measured by NMR for crystalline carboxylic acids and that of 7.1–9.1 kcal mol⁻¹ calculated by the ab initio method for the isolated dimer.     

Dissecting the concave–convex π‐π interaction in corannulene and sumanene dimers: SAPT(DFT) analysis and performance of DFT dispersion‐corrected methods

The characteristics of the concave–convex π‐π interactions are evaluated in 32 buckybowl dimers formed by corannulene, sumanene, and two substituted sumanenes (with S and CO groups), using symmetry‐adapted perturbation theory [SAPT(DFT)] and density functional theory (DFT). According to our results, the main stabilizing contribution is dispersion, followed by electrostatics. Regarding the ability of DFT methods to reproduce the results obtained with the most expensive and rigorous methods, TPSS‐D seems to be the best option overall, although its results slightly tend to underestimate the interaction energies and to overestimate the equilibrium distances. The other two tested DFT‐D methods, B97‐D2 and B3LYP‐D, supply rather reasonable results as well. M06‐2X, although it is a good option from a geometrical point of view, leads to too weak interactions, with differences with respect to the reference values amounting to about 4 kcal/mol (25% of the total interaction energy). © 2017 Wiley Periodicals, Inc.     

Estimates of the structure and dimerization energy of polyacetylene from ab initio calculations on finite polyenes

Ab initio calculations at the Hartree-Fock (HF) and the second-order Møller-Plesset (MP2) levels are performed for finite polyenes C_2nH_2n+2 to estimate the structure and dimerization energy (E_dim) of polyacetylene. The effect of electron correlation on the structure of finite polyenes is analyzed in detail. The MP3/6–31G* C(DOUBLE BOND)C and C(SINGLE BOND)C bond lengths in polyacetylene are estimated by a simple extrapolation method using empirical corrections for the MP2 deficiencies, yielding values [C(DOUBLE BOND)C(MP3) ∼ 1.36 Å and C(SINGLE BOND)C(MP3) ∼ 1.44 Å] that are in a good agreement with experiment (C(DOUBLE BOND)C (DOUBLE BOND) 1.36 Å and C(SINGLE BOND)C (DOUBLE BOND) 1.44–1.45 Å). Comparison is also made with other theoretical estimates of polyacetylene structure. E_dim is approximated by the energy difference between the equilibrium and hypothetical polyenic structures. It is estimated that E_dim is ∼ 1.4–1.5 kcal/mol (0.06–0.07 eV) per carbon-carbon bond at the HF level with 4–21G and 6–31G* basis sets and ∼ 0.3–0.5 kcal/mol (0.013–0.022 eV) at the MP2 level with the 6–31G* basis set. It is concluded that E_dim is very sensitive to the level of approximation employed so that a proper treatment of electron correlation is essential to obtain a reliable estimate of the dimerization energy. © 1997 John Wiley & Sons, Inc.     

DFT study on cooperativity in the interactions of hydrazoic acid clusters

Density functional theory at the B3LYP level with the 6‐311G** basis set is performed to calculate the systems consisting of up to four hydrazoic acid molecules. The dimers are found to exhibit cyclic and chain structures with N … H contacts at ca. 2.1–2.7 Å. However, there are only cyclic structures with N … H contacts at ca. 2.0–2.3 Å and 2.0–2.1 Å in the trimer and tetramer, respectively. Hydrogen bond distances in the trimer and tetramer are shorter than those in the cyclic dimer as a result of the stronger interaction between molecules. The contribution of cooperative effect to the interaction energy is significant. After the correction of the basis set superposition error and zero‐point energy, the binding energies are ?10.69, ?29.34, and ?54.26 kJ·mol^?1 for the most stable dimer, trimer, and tetramer, respectively. The calculated IR shifts for N? H stretching mode increase with the size of the cluster growths, reaching more than 200 cm^?1 in the tetramer. For the most stable clusters, the transition from the monomer to dimer, dimer to trimer, and trimer to tetramer involve changes of ?14.40, ?25.68, and ?31.88 kJ·mol^?1 for the enthalpies at 298.15 K and 1atm, respectively. We also perform Mulliken populations analysis and find the Mulliken populations on intermolecular N … H increasing in the sequence of the dimer, trimer, and tetramer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 279–286, 2003     

Charge transfer and dispersion interaction stabilization of the D2h isomer of O4

The results of some minimal basis set valence bond calculations, with an antibonding midbond molecular orbital (π_m*) included, are reported for the D_2h isomer of O₄. The in-plane π_m*←π* excitations describe the charge transfer from each monomer, while the π*←π excitations on each monomer partially describe the intermolecular dispersive attractions. It is found that the charge-transfer interactions by themselves are insufficient to stabilize the S=0 spin D_2h dimer of O₄ relative to two O₂ monomers when a correction is included for basis set superposition error. The inclusion of both the charge transfer and dispersion terms yields an estimate of 14 cm⁻¹ for the binding energy (D_e) at an equilibrium separation (R_e) of 3.29 Å. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 129–134, 1998     

Ab initio studies of isomerization and dissociation reactions of methyl peroxynitrate

Using the CCSD(T)/cc-pVDZ//B3LYP/6-311G(2d,2p) method, we calculated the detailed potential energy surfaces (PESs) for the unimolecular isomerization and decomposition of methyl peroxynitrate (CH₃O₂NO₂). The results show that there are the two most stable isomers, IS1a and IS1b, which are a pair of mirror image isomers. From IS1a and IS1b, different isomerization and unimolecular decomposition reaction channels have been studied and discussed. Among them, the predominant thermal decomposition pathways are those leading to CH₃O₂ + NO₂ and cis-CH₃ONO + O₂. The former is the lowest-energy path through the direct O–N bond rupture in IS1a or IS1b. The PES along the O–N bond in IS1a has been scanned, where the energy of IS1a reaches maximum value of 23.5 kcal/mol when the O–N bond is stretched to about 2.8 Å. This energy is 2.7 kcal/mol larger than the O–N bond dissociation energy (BDE) and 2.8 kcal/mol larger than the experimental active energy. In addition, because the energy barriers of IS1a isomerization to IS2a are 23.8 kcal/mol, close to the 20.8 kcal/mol O–N BDE in IS1a or IS1b, the isomerization reaction may compete with the direct bond rupture dissociation reaction.     

A systematic ab initio study of the water dimer in hierarchies of basis sets and correlation models

A systematic, high-level ab initio investigation of the water dimer has been performed. The oxygen-oxygen bond distance has been estimated to be around 2.90 ?, about 0.05 ? shorter than the experimentally estimated distance, challenging the accuracy of the latter. The interaction energy has been obtained at −5.0±0.1 kcal/mol, which compares favourably with the experimentally estimated value of −5.4±0.7 kcal/mol. The importance of employing basis sets that include diffuse functions in correlated calculations on hydrogen-bonded systems is confirmed. In correlated calculations on the water dimer and the hydrogen fluoride dimer, the counterpoise-corrected interaction energies converge considerably slower towards the basis set limit than do the uncorrected energies, provided that the correlation-consistent basis sets are augmented with diffuse functions. Received: 12 February 1997 / Accepted: 5 June 1997     

Internal rotation and equilibrium structure of the 2-methyl-2-nitropropane molecule from joint processing of gas phase electron diffraction data,vibrational and microwave spectroscopy data,and quantum chemical calculation results

The structure and internal rotation of the 2-methyl-2-nitropropane molecule is studied by electron diffraction and quantum chemical calculations with the use of microwave and vibrational spectroscopy data. The electron diffraction data are analyzed within the general intramolecular anharmonic force field model and the quantum chemical pseudoconformer model, considering the adiabatic separation of the degree of freedom of large amplitude motion, i.e., the internal rotation of the NO₂ group. The equilibrium eclipsed configuration of the C _s symmetry molecule has the following experimental bond lengths and valence angles: r _e(N=O) = 1.226//1.226(8) Å, r _e(C–N)//r _e(C–C) = 1.520//1.515/1,521(4) Å, ∠_еC–C–N = = 109.1/106,1(8)°, ∠_еO=N=O = 124.2(6)°, ∠_eC–C–H_avg = 110(3)°. The equilibrium geometry parameters are well consistent with MP2/cc-pVTZ quantum chemical calculations and microwave spectroscopy data. The thermally average parameters previously obtained within the small vibration model show a satisfactory agreement with the new results. The electron diffraction data used in this work do not allow a reliable determination of the barrier to internal rotation. However, at a barrier of 203(2) cal/mol, which is derived from the microwave study, it follows from the electron diffraction data that the equilibrium configuration must correspond to an eclipsed arrangement of C–C and N=O bonds, which is also consistent with the results of quantum chemical calculations of various levels.     

The structure of μ-oxo dimer of aluminium(III) porphyrin: a theoretical study

The gas-phase molecular structure of μ-oxo dimer of aluminium(III) porphyrin, (AlP)₂O, has been studied for the first time by density functional theory calculations using the B3LYP and M06 functionals and triple-ζ valence basis sets. The molecule has two conformers with equilibrium structures of D _4d and D _4h symmetries with parallel macrocycles and aluminium-oxygen distances of 1.680–1.684 Å (M06/cc-pVTZ). The aluminium atom lies out of the plane of the four central nitrogen atoms and forms a square-based pyramid with them, with the following parameters (M06/cc-pVTZ): r(Al–N) = 2.030–2.031 Å, r(N···N) = 2.803–2.804 Å (the side of the pyramid base), z(Al)–z(N) = 0.434–0.446 Å (the height of the pyramid).     

Rapid evaluation of the binding energies between peptide amide and DNA base

The binding energies and the equilibrium hydrogen bond distances as well as the potential energy curves of 20 hydrogen‐bonded amide–base dimers are evaluated from the analytic potential energy function established in our laboratory recently. The analytic potential energy function is used to calculate the N? H···N, N? H···O?C, C? H···N, and C? H···O?C dipole–dipole attractive interaction energies and C?O···O?C, N? H···H? N, and N? H···H? C dipole–dipole repulsive interaction energies in the 20 dimers composed of DNA bases adenine, guanine, cytosine, or thymine and peptide amide. The calculation results show that the potential energy curves obtained from the analytic potential energy function are in good agreement with those obtained from MP2/6‐311+G** calculations by including the basis set superposition error (BSSE) correction. For all the 20 dimers, the analytic potential energy function yields the binding energies of the MP2/6‐311+G** with BSSE correction within the error limits of 0.50 kcal/mol for 19 dimers, only one difference is larger than 0.50 kcal/mol and the difference is only 0.61 kcal/mol. The analytic potential energy function produces the equilibrium hydrogen bond distances of the MP2/6‐311+G** with BSSE correction within the error limits of 0.030 Å for all the 20 dimers. The analytic potential energy function is further applied to four more complicated DNA base‐peptide amide systems involving amino acid side chain and β‐sheet. The values of the binding energies and equilibrium hydrogen bond distances obtained from the analytic potential energy function are also in good agreement with those obtained from MP2 calculations with the BSSE correction. These results demonstrate that the analytic potential energy function can be used to evaluate the binding energies in hydrogen‐bonded peptide amide–DNA base dimers quickly and accurately. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Revealing the importance of linkers in K-series oxime reactivators for tabun-inhibited AChE using quantum chemical,docking and SMD studies

Inhibition of acetylcholinesterase (AChE) with organophosphorus compounds has a detrimental effect on human life. Oxime K203 seems to be one of the promising reactivators for tabun-inhibited AChE than (K027, K127, and K628). These reactivators differ only in the linker units between the two pyridinium rings. The conformational analyses performed with quantum chemical RHF/6-31G* level for K027, K127, K203 and K628 showed that the minimum energy conformers have different orientations of the active and peripheral pyridinium rings for these reactivator molecules. K203 with (–CH₂–CH=CH–CH₂–) linker unit possesses more open conformation compared to the other reactivators. Such orientation of K203 experiences favorable interaction with the surrounding residues of catalytic anionic site (CAS) and peripheral anionic site (PAS) of tabun-inhibited AChE. From the steered molecular dynamics simulations, it has been observed that the oxygen atom of the oxime group of K203 reactivator approaches nearest to the P-atom of the SUN203 (3.75 Å) at lower time scales (less than ~1000 ps) as compared to the other reactivators. K203 experiences less number of hydrophobic interaction with the PAS residues which is suggested to be an important factor for the efficient reactivation process. In addition, K203 crates large number of H-bonding with CAS residues SUN203, Phe295, Tyr337, Phe338 and His447. K203 barely changes its conformation during the SMD simulation process and hence the energy penalty to adopt any other conformation is minimal in this case as compared to the other reactivators. The molecular mechanics and Poisson–Boltzmann surface area binding energies obtained for the interaction of K203 inside the gorge of tabun inhibited AChE is substantially higher (?290.2 kcal/mol) than the corresponding K628 reactivator (?260.4 kcal/mol), which also possess unsaturated aromatic linker unit.     

Geometries and stabilities of various configurations of benzene dimer: details of novel V-shaped structure revealed

Benzene dimer configurations namely T-shaped, parallel-displaced, sandwich, and V-shaped that were proposed by experimental studies are investigated using second- and fourth-order Møller–Plesset perturbation theory. The MP2 method with aug-cc-pVDZ and aug-cc-pVTZ basis sets unequivocally shows that the parallel-displaced configuration is considerably more stable than T-shaped structure. On the other hand, the MP4(SDTQ)/aug-cc-pVDZ level predicts that the T-shaped and parallel-displaced configurations are nearly isoenergetic, which is parallel to the previous results of estimated CCSD(T)/CBS level reported recently. The lowest energy T-shaped configuration is stabilized by 0.17 kcal/mol over the parallel-displaced configuration at the MP4(SDTQ)/aug-cc-pVDZ level. Although the structures of all the four different types of configurations are found to be stable at both MP2 and full MP4 methods, the V-shaped configuration is the least stable among them. The calculated interaction energy of ?2.3 kcal/mol for the lowest energy T-shaped structure at the MP4(SDTQ)/aug-cc-pVDZ level is in good agreement with the experimental value of ?2.4 ± 0.4 kcal/mol. We conclude that the MP4(SDTQ) with a reasonably good basis set can be used for systems involving π–π interactions to obtain qualitative and quantitative results.