Dunning's Correlation-consistent Basis Sets Research Articles

Formation Mechanism of the Unsubstituted Chlorophosphazene Cl3P═NH: A Theoretical Study via Quantum Mechanical Calculations.

Although the synthesis of chlorophosphazene polymers has been explored for more than 100 years, the shortest yet most illusive monomer, Cl3P═NH, has never been isolated and fully characterized. Here we investigate the formation of Cl3P═NH from PCl5 and NH3 in chlorobenzene through quantum mechanical calculations. The potential energy surface was mapped using the MP2 Hamiltonian in conjunction with Dunning's correlation-consistent basis sets (aug-cc-pVXZ, where X = D and T). Along with HOMO/LUMO frontier molecular orbitals and natural bond orbital analyses, we found that instead of following the SN1 path proposed in the literature, the reaction proceeds via an addition-elimination mechanism. Our results also indicate that due to the low-lying stable intermediates (IM), most steps are exothermic such that the production of Cl3P═NH·2HCl can be completed once the energy barrier for the formation of [PCl4-NH3]+Cl- is overcome. Therefore, our theoretical work might explain the challenges in isolating any of the IMs in a typical chlorophosphazene reaction in chlorobenzene.

Accurate ab initio potential energy surface, rovibrational energy levels and resonance interactions of triplet ( 3 B1 ) methylene.

In this work, we report rovibrational energy levels for four isotopologues of methylene (CH2 , CHD, CD2 , and 13 CH2 ) in their ground triplet electronic state ( 3 B1 ) from variational calculation up to ~10,000 cm-1 and using a new accurate ab initio potential energy surface (PES). Triplet methylene exhibits a large-amplitude bending vibration and can reach a quasilinear configuration due to its low barrier (~2000 cm-1 ). To construct the ab initio PES, the Dunning's augmented correlation-consistent core-valence orbital basis sets were employed up to the sextuple-ζ quality [aug-cc-pCVXZ, X = T, Q, 5, and 6] combined with the single- and double-excitation unrestricted coupled cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. We have shown that the accuracy of the ab initio energies is further improved by including the corrections due to the scalar relativistic effects, DBOC and high-order electronic correlations. For the first time, all the available experimental rovibrational transitions were reproduced with errors less than 0.12 cm-1 , without any empirical corrections. Unlike more "traditional" nonlinear triatomic molecules, we have shown that even the energies of the ground vibrational state (000) with rather small rotational quantum numbers are strongly affected by the very pronounced rovibrational resonance interactions. Accordingly, the polyad structure of the vibrational levels of CH2 and CD2 was analyzed and discussed. The comparison between the energy levels obtained from the effective Watson A-reduced Hamiltonian, from the generating-function approach and from a variational calculation was given.

Spectroscopic identification of the low-lying electronic states of S2 molecule.

As is well-known, the S2 molecule is a ubiquitous intermediate in the combustion, atmosphere, and interstellar space. The six low-lying bound states of S2 have been characterized via photoelectron velocity map imaging and a high-level multi-reference configuration interaction method with the Davidson correction. Spectroscopic constants have been extracted by fitting the potential energy curves extrapolated to the complete basis set limit with a series of Dunning's correlation-consistent basis sets: aug-cc-pV(Q, 5)Z. The calculated spectroscopic parameters well reproduce the experimental results in this work. On the basis of the theoretical calculations, Franck-Condon simulations are performed to assign six adjacent electronic states, especially for three higher overlapping electronic states (c1Σu -, A'3Δu, and A3Σu +). The dissociation energy De of the S2 - is evaluated to be 4.111 (4) eV in this work, in agreement with the theoretical prediction (4.056 eV).

Theoretical insight into structural and electronic properties of cationic Scn+ (n=2-13): A benchmark study

Geometric, thermodynamic and electronic properties of cationic scandium clusters are studied. Geometric optimizations and stable spin states of Sc2+ are assessed on high level ab-initio coupled cluster method CCSD(T) with different dunning correlation consistent basis sets (aug-cc-pVDZ, aug-cc-pVTZ and aug-cc-pVQZ). Then, 23 DFT functionals belonging to different classes are evaluated at 6-31G (d), LANL2MB, LANL2DZ and Def2-SVP basis sets, and the results are compared with the benchmarked coupled cluster calculations. Due to excellent correlation, PBEPBE/LANL2DZ was chosen to perform calculation of higher scandium cationic clusters Scn+ (n = 3-13). In addition, we explored relative stability, binding energies, second order energy differences, vertical ionization energies, vertical electron affinities and HOMO-LUMO gaps. Moreover, these results are also compared with the neutral scandium clusters.

Improving "Silver-Standard" Benchmark Interaction Energies with Bond Functions.

We investigate the effect of adding midbond basis functions on the performance of various conventional and explicitly correlated (F12) estimates of complete basis set limit coupled-cluster (CCSD(T)/CBS) noncovalent interaction energies. In particular, we search for an improved "silver standard" of interaction energy calculations for systems where the CCSD(T) computation is feasible in a double-ζ basis but not in a triple-ζ one. We follow a recent study ( Sirianni J. Chem. Theory Comput. 2017 , 13 , 86 ) of different CCSD(T)-F12 variants in midbondless bases over the A24 and S22 benchmark interaction energy databases, and extend Dunning's correlation-consistent basis sets with three different midbond sets. The addition of bond functions is highly beneficial for conventional CCSD(T) and most CCSD(T)-F12 variants, improving both the CCSD part and the unscaled triples contribution. However, the commonly used scaling of triples by the ratio of the MP2-F12 and MP2 correlation energies usually overshoots: as a result, the scaled triples term gets worse upon the addition of bond functions. In contrast, a milder triples scaling by the ratio of the CCSD-F12b and CCSD correlation energies ( Brauer , Phys. Chem. Chem. Phys. 2016 , 18 , 20905 ) leads to the most accurate estimates of this term as long as bond functions are included. The combination of the triples term scaled in this way with the CCSD-F12b interaction energy leads to the CCSD(Tbb)-F12b approach that provides consistent high accuracy when a (3 s3 p2 d2 f) set of midbond functions is added to the aug-cc-pVDZ atom-centered basis set. The combination of midbond functions and the composite MP2/CBS+δ(CCSD(T)) treatment is able to make up for the deficiencies in the atom-centered part of the basis set, in particular, for a partial (or even complete) lack of diffuse functions. Considering both the A24 and S22 accuracy and the computational efficiency, we propose several new "silver standard" approaches improving upon the currently established midbondless levels of theory, ranging from the most consistent CCSD(Tbb)-F12b/aug-cc-pVDZ+(3 s3 p2 d2 f) variant (with mean unsigned errors of 0.010 and 0.042 kcal/mol for the A24 and S22 databases, respectively) to the significantly cheaper MP2/CBS+δ(CCSD(T))/cc-pVDZ+(3 s3 p2 d2 f) approach (mean unsigned errors of 0.039 and 0.096 kcal/mol for A24 and S22, respectively).

Potential energy surfaces of the electronic states of Li2F and Li2F(.).

The potential energy surfaces of the ground and low-lying excited states for the insertion reaction of atomic fluorine (F) and fluoride (F(-)) into the dilithium (Li2) molecule have been investigated. We have carried out explicitly correlated multi-reference configuration interaction (MRCI-F12) calculations using Dunning's augmented correlation-consistent basis sets. For the neutral system, the insertion of F into Li2 proceeds via a harpoon-type mechanism on the ground state surface, involving a covalent state and an ionic state which avoid each other at long distance. A detailed analysis of the changes in the dipole moment along the reaction coordinate reveals multiple avoided crossings among the excited states and shows that the charge-transfer processes play a pivotal role for the stabilization of the low-lying electronic states of Li2F. For the anionic system, which is studied for the first time, the insertion of F(-) is barrierless for many states and there is a gradual charge transfer from F(-) to Li2 along the reaction path. We also report the optimized parameters and the spectroscopic properties of the five lowest states of the neutral and seven lowest states of the anionic systems, which are strongly stabilized with respect to their respective Li2 + F/F(-) asymptotes. The observed barrierless insertion mechanisms for both systems make them good candidates for investigation under the ultracold regime.

Spectroscopic properties of BCl (X1Σ+, a3Π, A1Π) molecule

The X1Σ+, a3Π and A1Π states of BCl molecule are studied using the highly accurate valence internally contracted multireference configuration interaction approach including the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pV6Z and aug-cc-pV5Z, are used in the study. To obtain more reliable results, the potential energy curves (PECs) of three electronic states are extrapolated to the complete basis set limit by the two-point total-energy extrapolation scheme. The effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. By fitting these PECs, the spectroscopic parameters (Te, Re, ωe, ωexe, Be, αe and De) of the X1Σ+, a3Π and A1Π states of BCl are determined. These parameter values coincide with the experimental results. In addition, the whole vibrational states for X1Σ+, a3Π and A1Π states at J =0 (J is the rotational quantum number) are determined by numerically solving the radical Schrödinger equation of the nuclear motion of diatomic molecules. For each vibrational state, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental results. With the potential energy curves obtained at MRCI+Q/56+CV+DK level and the MRCI wave functions, the Franck-Condon factors, radiative lifetime of transition from a3Π and A1Π to the ground state are computed.

High-Level ab Initio Investigations on Structures and Energetics of N2O Clusters

Both experimental and theoretical investigations on weakly bonded small N2O clusters have been a subject of interest for the past decade. The current article presents high-level ab initio calculations for (N2O)n clusters for n = 4-6 employing second-order Møller-Plesset (MP2) theory and coupled cluster singles and doubles with perturbative triple (CCSD(T)) theory using Dunning's correlation-consistent basis sets. The electrostatics-guided cluster building code developed in our laboratory is applied for the generation of initial cluster geometries, followed by geometry optimization at MP2/aug-cc-pVTZ level of theory. Calculations of single point energy at CCSD(T)/aug-cc-pVTZ and vibrational frequency at the MP2/aug-cc-pVTZ level of theory are facilitated by the fragment-based molecular tailoring approach (MTA). A comparison of the results is done with those obtained by employing dispersion-corrected density functional B2PLYPD with aug-cc-pVTZ basis set. The geometrical parameters and vibrational spectra obtained from these ab initio methods are found to be in good agreement with those derived from recent experimental findings of Oliaee et al. [J. Chem. Phys. 2011, 134, 074310] and Rezaei et al. [J. Chem. Phys. 2012, 136, 224308].

Nuclear magnetic resonance shieldings of water clusters: is it possible to reach the complete basis set limit by extrapolation?

We have explored the possibility of using extrapolation techniques to estimate the complete basis set limit of nuclear shieldings of small water clusters. Several density functionals (Becke-Lee-Yang-Parr (BLYP), Perdew-Burke-Ernzerhof (PBE), OPTX-Perdew-Burke-Ernzerhof (OPBE), Swart-Solà-Bickelhaupt functional with Grimme's Dispersion included (SSB-D) and wavefunction methods (Hartree–Fock, Møller-Plesser perturbation theory for electron correlation up to second order (MP2) and coupled cluster) were used in combination with Dunning's (augmented) correlation-consistent and Jensen's polarisation-consistent basis sets. Although density functionals show larger nuclear shieldings than coupled cluster methods for these water clusters, differences in chemical shifts are much smaller. A new extrapolation scheme based on a Gaussian exponential function is shown to achieve better results for reaching the basis set limiting values, but the exponential needed for it cannot be obtained a priori with good confidence. This renders a two-point extrapolation for prediction of the basis set limiting value impossible.

DFT computation and experimental analysis of vibrational and electronic spectra of phenoxy acetic acid herbicides

An absolute vibrational analysis has been attempted on the basis of experimental FTIR and NIR-FT Raman spectra with calculated vibrational wavenumbers and intensities of phenoxy acetic acids. The equilibrium geometry, bonding features and harmonic vibrational wavenumbers have been calculated with the help of B3LYP method with Dunning correlation consistent basis set aug-cc-pVTZ. The electronic structures of molecular fragments were described in terms of natural bond orbital analysis, which shows intermolecular OH⋯O and intramolecular CH⋯O hydrogen bonds. The electronic absorption spectra with different solvents have been investigated in combination with time-dependent density functional theory calculation. The pKa values of phenoxy acetic acids were compared.

Spectroscopic properties of AlC (X4∑-, B4∑-) molecule

The potential energy curves (PECs) of X4∑- and B4∑- states of the AlC molecule have been studied using highly accurate internally contracted multireference configuration interaction approach with the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pVnZ (n=D,T,Q,5,6) are used for the present study. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are considered. Core-valence correlation corrections are calculated with an aug-cc- pCVTZ basis set. Scalar relativistic correction calcualtions are made using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Obvious effect on the PECs by the core-valence correlation and relativistic corrections has been observed. All the PECs are extrapolated to the complete basis set limit. The convergence observations of present calculations are made and the convergent behavior is discussed with respect to the basis set. Using these PECs, the spectroscopic parameters (TeReωeωexeωeyeBe and αe) of the X4∑- and B4∑- states are determined and compared with those reported in the literature. The vibration manifolds are evaluated for each state of non-rotation AlC molecule by numerically solving the radial Schrödinger equation of nuclear motion. For each vibrational state, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental findings.

Coupled-cluster and multireference configuration interaction study of the low-lying excited states of the H2O2-H2O complex

Ab initio molecular orbital methods have been employed to determine the molecular structure, vibrational frequencies, and stability of the H(2)O(2)-H(2)O complex. These parameters were determined using coupled-cluster methods with Dunning correlation consistent basis sets. Vertical excitation energies for the lowest four excited states are calculated with the multireference internally contracted configuration interaction methods and coupled cluster equation of motion methods. No significant difference was observed between the first vertical excited state energies of H(2)O(2) within the H(2)O(2)-H(2)O complex.

Coupled cluster investigation of the axial and equatorial isomers of pyrrolidine

The CCSD(T) methodology coupled with Dunning's correlation-consistent basis sets was employed to study the relative energies of the axial and equatorial pyrrolidine. The enthalpies of formation of both isomers were computed including corrections for relativistic and core-valence effects as well as anharmonic effects. The accurate determination of the lowest energy isomer is a very complex task because of the very small energy gap. At the CCSD(T)/CBS level, equatorial pyrrolidine is 0.10 kcal/mol lower in energy than axial pyrrolidine. When core-valence, scalar relativistic and spin-orbit effects are included, the relative energy is similar, 0.11 kcal/mol. However, when zero-point energies are taken into account, some difficulties are observed. Anharmonic effects on ZPEs were not possible to be accurately estimated as problems were detected in the lowest vibrational modes. Thus, the question of which is the lowest energy isomer of pyrrolidine remains open until accurate ZPEs can be determined for both isomers. The enthalpy of formation of pyrrolidine is predicted to be −2.7 ± 1 kcal/mol at 298 K.

The entrance complex, transition state, and exit complex for the F + H2O → HF + OH reaction. Definitive predictions. Comparison with popular density functional methods

Following the H + H(2) and F + H(2) reactions, the fluorine atom - water system has the potential to become one of the best understood chemical reactions. Stationary points for the F + H(2)O potential energy surface have been located with the "Gold Standard" CCSD(T) method using the Dunning correlation consistent basis sets through quintuple zeta. The CCSD(T)/cc-pV5Z barrier height is prediced to be 2.5 kcal mol(-1), less than previous estimates of 4-7 kcal mol(-1). From higher level theoretical studies of the prototypical F + H(2) reaction, this barrier should be less than 0.5 kcal mol(-1) above the exact, nonrelativistic classical barrier height. 41 of the 49 DFT methods applied to F + H(2)O predict no barrier at all. The eight DFT methods that do predict a barrier show exothermicities that are somewhat too small. The CCSD(T)/cc-pV5Z entrance complex is bound by 3.4 kcal mol(-1) relative to separated F + H(2)O. The analogous exit complex is bound by 5.9 kcal mol(-1) relative to separated HF + OH.

Study on spectroscopic properties of B2 (X3g-, A3u) molecule

The X3g- and A3u states of B2 molecule are studied using highly accurate valence internally contracted multireference configuration interaction approach including the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pV6Z and aug-cc-pV5Z, are used in the study. To obtain more reliable results, the potential energy curves (PECs) of two electronic states are extrapolated to the complete basis set limit by the two-point total-energy extrapolation scheme. The effects of the core-valence correlation and relativistic correction on PEC are taken into account. Employing these PECs, the spectroscopic parameters (Te, Re, e, exe, eye, Be, e, e and e) of the X3g- and A3u states of two main isotopes (11B2, 10B11B) are determined and compared with those reported in the literature. Comparison with the experimental data demonstrates that the present results are accurate. With the PECs determined here, the whole vibrational states for 11B2 (X3g-, A3u) and 10B11B (X3g-, A3u) are determined when the rotational quantum number J equals zero (J=0) by numerically solving the radical Schrdinger equation of nuclear motion. For each vibrational state of every isotope species, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental findings.

A systematical comparison of DFT methods in reproducing the interaction energies of halide series with protein moieties

A systematic theoretical investigation on the interaction energies of halogen-ionic bridges formed between halide ions and the polar H atoms bonded to N of protein moieties has been carried out by employing a variety of density functional methods. In this procedure, full geometry optimizations are performed at the Møller-Plesset second-order perturbation (MP2) level of theory in conjunction with the Dunning's augmented correlation-consistent basis set, aug-cc-pVDZ. Subsequently, two distinct basis sets, i.e. 6-311++G(df,pd) and aug-cc-pVTZ, are employed in the following single-point calculations so as to check the stability of the results obtained at the different levels of DFT. The performance of DFT methods has been evaluated by comparing the results with those obtained from the rigorous MP2 theory. It is shown that the B98, B97-1, and M05 give the lowest root-mean-square error (RMSE) for predicting fluoride-binding energies, M05-2X, MPW1B95, and MPW1PW91 have the best performance in reproducing chloride-binding energies, B97-1, PBEKCIS, and PBE1KCIS present the optimal result for bromide-binding energies, while B97-1, MPW1PW91, and TPSS perform most well on iodide-binding energies. The popular B3LYP functional seems to be quite modest for studying halide-protein moiety interactions. In addition, the PBE1KCIS functional provide accuracies close to the computationally expensive MP2 method for the calculation of interaction energies of all halide-binding systems.

Effect of substituents and hydrogen bonding on barrier heights in dehydration reactions of carbon and silicon geminal diols

Activation barrier heights for the dehydration reaction of geminal carbinols and silanediols R'R″X(OH)(2) (X = C, Si) were estimated at the B3LYP and MP2 levels of theory employing Dunning's correlation-consistent triple-zeta basis sets. It was shown that the barrier height for carbon derivatives steadily decreases upon substitution by R groups, usually termed as electron-donating, such as alkyl and amino groups. Substitution by electron-withdrawing groups leads, however, only to small changes in barrier heights compared to that of methanediol. A similar tendency was also found for silicon derivatives, but high activation barriers of this reaction remain even for amino group substituted silanediols. Introduction of additional water molecules into the reactive space of carbinol dehydration drastically reduces barrier heights and brings the transition state energy for methanediol close to the experimental value. The difference between dehydration barrier heights for both methanediol and carbinols with electron-rich substituents becomes well-defined for dimeric species. The higher acidity of the hydroxyl group protons in molecules containing halogens and C==O groups brings about a noticeable growth in the dehydration barrier heights of these compounds. This difference in barrier heights for oligomeric species may be the reason for the stability of carbinols with electron-rich substituents.

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.

Importance of the Basis Set for the Spin-State Energetics of Iron Complexes

We have performed a systematic investigation of the influence of the basis set on relative spin-state energies for a number of iron compounds. In principle, with an infinitely large basis set, both Slater-type orbital (STO) and Gaussian-type orbital (GTO) series should converge to the same final answer, which is indeed what we observe for both vertical and relaxed spin-state splittings. However, we see throughout the paper that the STO basis sets give consistent and rapidly converging results, while the convergence with respect to the basis set size is much slower for the GTO basis sets. For example, the large GTO basis sets that give good results for the vertical spin-state splittings of compounds 1-3 (6-311+G**, Ahlrichs VTZ2D2P) fail for the relaxed spin-state splittings of compound 4 (where 1 is Fe-(PyPepS)2 (PyPepSH 2 = N-(2-mercaptophenyl)-2-pyridinecarboxamide), 2 is Fe(tsalen)Cl (tsalen = N, N'-ethylenebis-(thiosalicylideneiminato)), 3 is Fe(N(CH2-o-C6H4S) 3)(1-Me-imidazole), and 4 is FeFHOH). Very demanding GTO basis sets like Dunning's correlation-consistent (cc-pVTZ, cc-pVQZ) basis sets are needed to achieve good results for these relaxed spin states. The use of popular (Pople-type) GTO, effective core potentials basis set (ECPB), or mixed ECPB(Fe):GTO(rest) basis sets is shown to lead to substantial deviations (2-10 kcal/mol, 14-24 kcal/mol for 3-21G), in particular for the high spin states that are typically placed at too low energy. Moreover, the use of an effective core potential in the ECPB basis sets results in spin-state splittings that are systematically different from the STO-GTO results.

Conformations of Allyl Amine: Theory vs Experiment

The relative stabilities of the five conformers of allyl amine, a medium-size aliphatic molecule, were estimated by applying ab initio quantum mechanical methods at several levels of theory. The second-order Møller-Plesset perturbation method (MP2), quadratic configuration interaction including single and double excitations (QCISD), coupled-cluster with single and double excitations (CCSD) and CCSD plus perturbative triple excitations [CCSD(T)] were applied. The Dunning correlation consistent basis sets (through aug-cc-pVQZ and cc-pV5Z) were employed. The MP2 energies relative to the energy of the cis-trans conformer reported here appear to approach the basis set limit. The predicted allyl amine conformer energies approaching the Hartree-Fock basis set limit are 158 cm-1 (cis-gauche), -5 cm-1 (gauche-trans), and -146 cm-1 (gauche-gauche). The same three relative energies near the MP2 basis set limit are 135, 103, and 50 cm-1, respectively. The analogous energies deduced from experiment are 173 +/- 12, 92 +/- 8, and 122 +/- 5 cm-1. The theoretical results obtained in the present study suggest that satisfactory predictions of the conformer energetics of allyl amine may be achieved only by theoretical methods that incorporate consideration of correlation effects in conjunction with large basis sets. Evaluation of the zero-point vibrational energy corrections is critical, due to the very small classical energy differences between the five conformers of allyl amine. Agreement between theory and experiment for the gauche-gauche conformational energy remains problematical.