Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

A theoretical analysis of substituted aromatic compounds

The substituents ? CH₃, ? F, ? NO₂, ? OCH₃, and ? CH₂?CH₂ were placed at the ortho, meta, and para positions on the aromatic molecules aniline, benzaldehdye, nitrobenzene, and phenol. MMFF94, AM1, B3LYP, M06, M06‐2X, ωB97X, ωB97X‐d, and RI‐MP2 using cc‐pVDZ and cc‐pVTZ and CCSD(T) with cc‐pVDZ basis sets were used to calculate the geometries and energies of all regiomers of the molecules. Relative energies of the ortho and meta regiomers relative to the para regiomers were calculated and compared to the CCSD(T) values. A good basis set correlation between cc‐pVDZ and cc‐pVTZ was observed in RI‐MP2. Overall, RI‐MP2 gave the best correlation with the CCSD(T) results. All of the hybrid functionals showed similar accuracy and could effectively describe the intramolecular hydrogen‐bonding interactions of these compounds. The methoxy group at the para position in methoxyaniline, methoxyphenol, methoxynitrobenzene, and methoxybenzaldehyde was rotated around the phenyl‐O bond. HF, along with the cc‐pVDZ basis with the other methods, generated inaccurate energy profiles for p‐methoxyphenol. For the density functional theory methods, it was necessary to use improved grids to get smooth curves. © 2013 Wiley Periodicals, Inc.     

Scaled MP3 Non‐Covalent Interaction Energies Agree Closely with Accurate CCSD(T) Benchmark Data

Scaled MP3 interaction energies calculated as a sum of MP2/CBS (complete basis set limit) interaction energies and scaled third‐order energy contributions obtained in small or medium size basis sets agree very closely with the estimated CCSD(T)/CBS interaction energies for the 22 H‐bonded, dispersion‐controlled and mixed non‐covalent complexes from the S22 data set. Performance of this so‐called MP2.5 (third‐order scaling factor of 0.5) method has also been tested for 33 nucleic acid base pairs and two stacked conformers of porphine dimer. In all the test cases, performance of the MP2.5 method was shown to be superior to the scaled spin‐component MP2 based methods, e.g. SCS–MP2, SCSN–MP2 and SCS(MI)–MP2. In particular, a very balanced treatment of hydrogen‐bonded compared to stacked complexes is achieved with MP2.5. The main advantage of the approach is that it employs only a single empirical parameter and is thus biased by two rigorously defined, asymptotically correct ab‐initio methods, MP2 and MP3. The method is proposed as an accurate but computationally feasible alternative to CCSD(T) for the computation of the properties of various kinds of non‐covalently bound systems.     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

We present density functional theory (DFT) interaction energies for the sandwich and T‐shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree–Fock (HF) and second‐order Møller–Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene–dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The MC‐DFT approach including the SCS‐MP2 energies to the new minnesota‐type functionals

We have applied the multicoefficient density functional theory (MC‐DFT) to four recent Minnesota functionals, including M06‐2X, M08‐HX, M11, and MN12‐SX on the performance of thermochemical kinetics. The results indicated that the accuracy can be improved significantly using more than one basis set. We further included the SCS‐MP2 energies into MC‐DFT, and the resulting mean unsigned errors (MUEs) decreased by approximately 0.3 kcal/mol for the most accurate basis set combinations. The M06‐2X functional with the simple [6–311+G(d,p)/6–311+G(2d,2p)] combination gave the best performance/cost ratios for the MC‐DFT and MC‐SCS‐MP2|MC‐DFT methods with MUE of 1.58 and 1.22 kcal/mol, respectively. © 2014 Wiley Periodicals, Inc.     

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order M?ller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.     

Binding of hydrogen on benzene, coronene, and graphene from quantum Monte Carlo calculations

Quantum Monte Carlo calculations with the diffusion Monte Carlo (DMC) method have been used to compute the binding energy curves of hydrogen on benzene, coronene, and graphene. The DMC results on benzene agree with both M?ller-Plessett second order perturbation theory (MP2) and coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] calculations, giving an adsorption energy of ～25 meV. For coronene, DMC agrees well with MP2, giving an adsorption energy of ～40 meV. For physisorbed hydrogen on graphene, DMC predicts a very small adsorption energy of only 5 ± 5 meV. Density functional theory (DFT) calculations with various exchange-correlation functionals, including van der Waals corrected functionals, predict a wide range of binding energies on all three systems. The present DMC results are a step toward filling the gap in accurate benchmark data on weakly bound systems. These results can help us to understand the performance of current DFT based methods, and may aid in the development of improved approaches.     

Theoretical study of Pt(PR3)(2)(AlCl3) (R = H, Me, Ph, or Cy) including an unsupported bond between transition metal and non-transition metal elements: geometry, bond strength, and prediction

The molecular structure and the binding energy of Pt(PR(3))(2)(AlCl(3)) (R = H, Me, Ph, or Cy) were investigated by DFT, MP2 to MP4(SDTQ), and CCSD(T) methods. The optimized structure of Pt(PCy(3))(2)(AlCl(3)) (Cy = cyclohexyl) by the DFT method with M06-2X and LC-BLYP functionals agrees well with the experimental one. The MP4(SDTQ) and CCSD(T) methods present similar binding energies (BE) of Pt(PH(3))(2)(AlCl(3)), indicating that these methods provide reliable BE value. The DFT(M06-2X)-calculated BE value is close to the MP4(SDTQ) and CCSD(T)-calculated values, while the other functionals present BE values considerably different from the MP4(SDTQ) and CCSD(T)-calculated values. All computational methods employed here indicate that the BE values of Pt(PMe(3))(2)(AlCl(3)) and Pt(PPh(3))(2)(AlCl(3)) are considerably larger than those of the ethylene analogues. The coordinate bond of AlCl(3) with Pt(PR(3))(2) is characterized to be the σ charge transfer (CT) from Pt to AlCl(3). This complex has a T-shaped structure unlike the well-known Y-shaped structure of Pt(PMe(3))(2)(C(2)H(4)), although both are three-coordinate Pt(0) complex. This T-shaped structure results from important participation of the Pt d(σ) orbital in the σ-CT; because the Pt d(σ) orbital energy becomes lower as the P-Pt-P angle decreases, the T-shaped structure is more favorable for the σ-CT than is the Y-shaped structure. [Co(alcn)(2)(AlCl(3))](-) (alcn = acetylacetoneiminate) is theoretically predicted here as a good candidate for the metal complex, which has an unsupported M-Al bond because its binding energy is calculated to be much larger than that of Pt(PCy(3))(2)(AlCl(3)).     

Conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete

The conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero-point vibrational energies are computed for all pertinent molecular systems using SCF theory, second-order perturbation theory, and density functional theory and employing the correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ. Single-point fourth-order perturbation theory, CCSD, and CCSD(T) calculations employing the cc-pVTZ and the cc-pVQZ basis sets are computed using the MP2/cc-pVTZ and MP2/cc-pVQZ optimized geometries, respectfully, to ascertain the contribution of higher order correlation. Three DFT functionals, B3LYP, wB97XD, and M06-2X, are employed to determine whether they can yield results similar to those obtained at the CCSD(T) level.     

Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Density functional theory and post-Hartree-Fock studies on molecular structure and harmonic vibrational spectrum of formaldehyde

Density functional theory (DFT) with the Becke's three-parameter exchange correlation functional and the functional of Lee, Yang and Parr, gradient-corrected functionals of Perdew, and Perdew and Wang [the DFT(B3LYP), DFT(B3P86) and DFT(B3PW91) methods, respectively], and several levels of conventional ab initio post-Hartree-Fock theory (second- and fourth-order perturbation theory M?ller-Plesset MP2 and MP4(SDTQ), coupled cluster with the single and double excitations (CCSD), and CCSD with perturbative triple excitation [CCSD(T)], configuration interaction with the single and double excitations [CISD], and quadratic configuration interaction method [QCISD(T)], using several basis sets [ranging from a simple 6-31G(d,p) basis set to a 6-311+ +G(3df, 2pd) one], were applied to study of the molecular structure (geometrical parameters, rotational constants, dipole moment) and harmonized infrared (IR) spectrum of formaldehyde (CH₂O). High-level ab initio methods CCSD(T) and QCISD(T) with the 6-311+ +G(3df, 2pd) predict correctly molecular parameters, vibrational harmonic wavenumbers and the shifts of the harmonic IR spectrum of ¹²CH₂ ¹⁶O upon isotopic substitution. Received: 30 January 1997 / Accepted: 7 May 1997     

A comparative relativistic DFT and ab initio study on the structure and thermodynamics of the oxofluorides of uranium(IV), (V) and (VI)

All the possible uranium(VI, V, IV) oxides, fluorides and oxofluorides were studied theoretically by using density functional theory (DFT) in the generalised gradient approximation (GGA), and three different relativistic methods (all-electron scalar four component Dyall RESC method (AE), relativistic small-core ECPs, and zeroth order regular approximation ZORA). In order to test different correlation methods, for the two former relativistic methods hybrid DFT, and, for the AE method, MP2 molecular orbital calculations were performed as well. Single-point AE-CCSD(T) energies were calculated on MP2 geometries as well. Energies of the uranium(VI) and (V) oxofluorides dissociation, uranium(VI) fluoride hydrolysis and oxofluoride disproportionation were calculated and compared against the available experimental thermochemical data. AE-CCSD(T) energies were the closest to the experiment. For GGA DFT methods, all the relativistic methods used yield similar results. For thermochemistry, the best quantitative agreement with the experimental and CCSD(T) values for both U=O and U-F bond strengths was obtained with hybrid DFT methods, provided that a reliable basis set was used. Both the GGA DFT and MP2 MO methods show overbinding of these bonds; moreover, this overbinding was found to be not uniform but strongly dependent on the coordination environment of the uranium atom in each case. U=O vibrational frequencies given by hybrid DFT, however, are systematically overestimated, and are better reproduced by GGA DFT; MP2 values usually fall in-between. Reaction enthalpies, U=O frequencies and complex geometries given by the PBE, MPBE, BPBE, BLYP and OLYP GGA functionals are quite similar, with OLYP performing slightly better than the others but still not as good as hybrid DFT. The geometries of the molecules are found to be influenced by the following factors: the inverse transinfluence (ITI) of the oxygen ligand and, for U(V), and U(IV), the Jahn-Teller distortion.     

Static dipole polarizability and binding energy of sodium clusters Nan (n=1-10): A critical assessment of all-electron based post Hartree-Fock and density functional methods

A systematic all electron post Hartree-Fock as well as density functional theory (DFT) based calculations for the polarizability and binding energy of sodium metal clusters have been performed and an in-depth analysis of the discrepancy between the experimental and theoretical results is presented. A systematic investigation for the assessment of different DFT exchange-correlation functionals in predicting the polarizability values has also been reported. All the pure DFT functionals have been found to considerably underestimate the calculated polarizability values as compared to the MP2 results. DFT calculations using the full Hartree-Fock exchange along with one-parameter progressive correlation functional have, however, been shown to yield results in good agreement with the MP2 and experimental results. The possible sources of error present in the experimental measurements as well as in the different theoretical methods have also been analyzed. One of the most important conclusions of the present study is that the effect of electron correlation plays a significant role in determining the polarizability of the clusters and the MP2 method can be considered to be one of the most reliable methods for their prediction. It has also been noted that the polarizability value of the lower member clusters (Na2 and Na4) calculated by highly sophisticated methods such as, CCSD and CCSD(T) are found to be very close to the corresponding MP2 values. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. A good linear correlation between the polarizability and volume of the cluster has also been found to exist.     

Ab initio calculations on halogen-bonded complexes and comparison with density functional methods

A systematic theoretical investigation on a series of dimeric complexes formed between some halocarbon molecules and electron donors has been carried out by employing both ab initio and density functional methods. Full geometry optimizations are performed at the Moller-Plesset second-order perturbation (MP2) level of theory with the Dunning's correlation-consistent basis set, aug-cc-pVDZ. Binding energies are extrapolated to the complete basis set (CBS) limit by means of two most commonly used extrapolation methods and the aug-cc-pVXZ (X = D, T, Q) basis sets series. The coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] correction term, determined as a difference between CCSD(T) and MP2 binding energies, is estimated with the aug-cc-pVDZ basis set. In general, the inclusion of higher-order electron correlation effects leads to a repulsive correction with respect to those predicted at the MP2 level. The calculations described herein have shown that the CCSD(T) CBS limits yield binding energies with a range of -0.89 to -4.38 kcal/mol for the halogen-bonded complexes under study. The performance of several density functional theory (DFT) methods has been evaluated comparing the results with those obtained from MP2 and CCSD(T). It is shown that PBEKCIS, B97-1, and MPWLYP functionals provide accuracies close to the computationally very expensive ab initio methods.