Electron Correlation Level Research Articles

Transport properties of methane, ethane, propane, iso-butane and neo-pentane from ab initio potential energy surfaces

In this work, the potential energy surfaces for methane, ethane, propane, iso-butane and neo-pentane, obtained from the ab initio calculations via different levels of electron-correlation, were used in the framework of the kinetic theory to calculate the transport collision integrals and their corresponding low-density transport coefficients. The theoretical results are compared with the available experimental data and the effective scaling potential parameters of methane, ethane, propane, iso-butane and neo-pentane along with the kinetic theory collision integrals and higher order correction factors were obtained. Relation between different potentials and kinetic theory collision integrals are discussed and it was shown that the Mason–Monchick approach is a reliable approximation in the calculation of diffusion coefficients and shear viscosities of chain alkanes, whereas the full predictive Boltzmann weighting method is successful only for lighter alkanes, such as methane and ethane.

Comparative study of pure and Co-dopedBaFe2As2

We present a comparative calculation of the electronic structure of the high critical temperature superconductor Co-doped ${\text{BaFe}}_{2}{\text{As}}_{2}$ and its parent compound at the electron correlation level by the embedded cluster method; the electron correlation is calculated through the second-order M\o{}ller-Plesset perturbation theory. The superconducting doped material is represented by the ${\text{Ba}}_{4}{\text{CoFe}}_{4}{\text{As}}_{8}$ cluster. The analysis of the orbital populations in this cluster reveals the formation of an antiferromagnetic order in the Fe plane with a spin-density increase on the central Co atom with respect to the spin density of the central Fe atom of the undoped case. This increase is associated with an increase of the ${d}_{{z}^{2}}$ orbital population of the central atom. However, the formation mechanism of the local magnetic moment implies also a spin transfer from the nearest-neighbor Fe atoms and from the next-nearest-neighbor As atoms to the central Co atom, and it corresponds to a ${J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnetic Heisenberg model. Some particular features of ${d}_{yz}$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals in the triplet and in the singlet cluster states are interpreted to correspond to a spinless fermion. This result, as well as the result relative to the formation mechanism of the magnetic moments, can be connected with a model of resonating-valence-bond (RVB) superconductors suggested recently by Poilblanc et al. [Phys. Rev. B 89, 241106 (2014)] and based on the Anderson RVB theory.

Combined fragment molecular orbital cluster in molecule approach to massively parallel electron correlation calculations for large systems.

The local correlation "cluster-in-molecule" (CIM) method is combined with the fragment molecular orbital (FMO) method, providing a flexible, massively parallel, and near-linear scaling approach to the calculation of electron correlation energies for large molecular systems. Although the computational scaling of the CIM algorithm is already formally linear, previous knowledge of the Hartree-Fock (HF) reference wave function and subsequent localized orbitals is required; therefore, extending the CIM method to arbitrarily large systems requires the aid of low-scaling/linear-scaling approaches to HF and orbital localization. Through fragmentation, the combined FMO-CIM method linearizes the scaling, with respect to system size, of the HF reference and orbital localization calculations, achieving near-linear scaling at both the reference and electron correlation levels. For the 20-residue alanine α helix, the preliminary implementation of the FMO-CIM method captures 99.6% of the MP2 correlation energy, requiring 21% of the MP2 wall time. The new method is also applied to solvated adamantine to illustrate the multilevel capability of the FMO-CIM method.

Multi-level coupled cluster theory.

We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and present proof of principle applications. The formalism is an essential tool in order to obtain size-intensive complexity in the calculation of local molecular properties.

Dipole polarizability of alkali-metal (Na, K, Rb)-alkaline-earth-metal (Ca, Sr) polar molecules: prospects for alignment.

Electronic open-shell ground-state properties of selected alkali-metal-alkaline-earth-metal polar molecules are investigated. We determine potential energy curves of the (2)Σ(+) ground state at the coupled-cluster singles and doubles with partial triples (CCSD(T)) level of electron correlation. Calculated spectroscopic constants for the isotopes ((23)Na, (39)K, (85)Rb)-((40)Ca, (88)Sr) are compared with available theoretical and experimental results. The variation of the permanent dipole moment (PDM), average dipole polarizability, and polarizability anisotropy with internuclear distance is determined using finite-field perturbation theory at the CCSD(T) level. Owing to moderate PDM (KCa: 1.67 D, RbCa: 1.75 D, KSr: 1.27 D, RbSr: 1.41 D) and large polarizability anisotropy (KCa: 566 a.u., RbCa: 604 a.u., KSr: 574 a.u., RbSr: 615 a.u.), KCa, RbCa, KSr, and RbSr are potential candidates for alignment and orientation in combined intense laser and external static electric fields.

Benchmark theoretical study of the π-π binding energy in the benzene dimer.

We establish a new estimate for the binding energy between two benzene molecules in the parallel-displaced (PD) conformation by systematically converging (i) the intra- and intermolecular geometry at the minimum, (ii) the expansion of the orbital basis set, and (iii) the level of electron correlation. The calculations were performed at the second-order Møller-Plesset perturbation (MP2) and the coupled cluster including singles, doubles, and a perturbative estimate of triples replacement [CCSD(T)] levels of electronic structure theory. At both levels of theory, by including results corrected for basis set superposition error (BSSE), we have estimated the complete basis set (CBS) limit by employing the family of Dunning's correlation-consistent polarized valence basis sets. The largest MP2 calculation was performed with the cc-pV6Z basis set (2772 basis functions), whereas the largest CCSD(T) calculation was with the cc-pV5Z basis set (1752 basis functions). The cluster geometries were optimized with basis sets up to quadruple-ζ quality, observing that both its intra- and intermolecular parts have practically converged with the triple-ζ quality sets. The use of converged geometries was found to play an important role for obtaining accurate estimates for the CBS limits. Our results demonstrate that the binding energies with the families of the plain (cc-pVnZ) and augmented (aug-cc-pVnZ) sets converge [within <0.01 kcal/mol for MP2 and <0.15 kcal/mol for CCSD(T)] to the same CBS limit. In addition, the average of the uncorrected and BSSE-corrected binding energies was found to converge to the same CBS limit much faster than either of the two constituents (uncorrected or BSSE-corrected binding energies). Due to the fact that the family of augmented basis sets (especially for the larger sets) causes serious linear dependency problems, the plain basis sets (for which no linear dependencies were found) are deemed as a more efficient and straightforward path for obtaining an accurate CBS limit. We considered extrapolations of the uncorrected (ΔE) and BSSE-corrected (ΔEcp) binding energies, their average value (ΔEave), as well as the average of the latter over the plain and augmented sets (ΔẼave) with the cardinal number of the basis set n. Our best estimate of the CCSD(T)/CBS limit for the π-π binding energy in the PD benzene dimer is De = -2.65 ± 0.02 kcal/mol. The best CCSD(T)/cc-pV5Z calculated value is -2.62 kcal/mol, just 0.03 kcal/mol away from the CBS limit. For comparison, the MP2/CBS limit estimate is -5.00 ± 0.01 kcal/mol, demonstrating a 90% overbinding with respect to CCSD(T). The spin-component-scaled (SCS) MP2 variant was found to closely reproduce the CCSD(T) results for each basis set, while scaled opposite spin (SOS) MP2 yielded results that are too low when compared to CCSD(T).

The extended CC2 model ECC2

We present a size-extensive extension to the CC2 model that avoids the complications with quasi-degeneracies that are present in the CC2 model and related perturbation theory-based approaches. The formulation also provides a consistent model for treating different parts of a molecular system at different levels of electron correlation. Such a subsystem approach leads to large reductions in the computational requirements without compromising the accuracy. In this initial study, we focus on static molecular properties.

A Correlated Electron View of Singlet Fission

Singlet fission occurs when a single exciton splits into multiple electron-hole pairs, and could dramatically increase the efficiency of organic solar cells by converting high energy photons into multiple charge carriers. Scientists might exploit singlet fission to its full potential by first understanding the underlying mechanism of this quantum mechanical process. The pursuit of this fundamental mechanism has recently benefited from the development and application of new correlated wave function methods. These methods-called restricted active space spin flip-can capture the most important electron interactions in molecular materials, such as acene crystals, at low computational cost. It is unrealistic to use previous wave function methods due to the excessive computational cost involved in simulating realistic molecular structures at a meaningful level of electron correlation. In this Account, we describe how we use these techniques to compute single exciton and multiple exciton excited states in tetracene and pentacene crystals in order to understand how a single exciton generated from photon absorption undergoes fission to generate two triplets. Our studies indicate that an adiabatic charge transfer intermediate is unlikely to contribute significantly to the fission process because it lies too high in energy. Instead, we propose a new mechanism that involves the direct coupling of an optically allowed single exciton to an optically dark multiexciton. This coupling is facilitated by intermolecular motion of two acene monomers that drives nonadiabatic population transfer between the two states. This transfer occurs in the limit of near degeneracies between adiabatic states where the Born-Oppenheimer approximation of fixed nuclei is no longer valid. Existing theories for singlet fission have not considered this type of coupling between states and, therefore, cannot describe this mechanism. The direct mechanism through intermolecular motion describes many experimentally observed characteristics of these materials, such as the ultrafast time scale of photobleaching and triplet generation during singlet fission in pentacene. We believe this newly discovered mechanism provides fundamental insight to guide the creation of new solar materials that exhibit high efficiencies through multiple charge generation.

CCSD(T) level interaction energy for halogen bond between pyridine and substituted iodobenzenes: origin and additivity of substituent effects

The CCSD(T) level interaction energies at the basis set limit (E(int)) were calculated for 33 halogen bonded pyridine complexes with substituted iodobenzenes. The CCSD(T) level electron correlation correction substantially decreases the magnitude of attraction in comparison with the MP2. The E(int) for the pyridine complexes with mono substituted iodobenzenes varies from -3.14 to -4.42 kcal mol(-1), depending on the substituent. The electron-withdrawing substituents such as NO2 enhance the attraction, while the effects of electron-donating substituents reduce. The additivity of the substituent effects is observed for the E(int) of the pyridine complexes with multiple substituted iodobenzenes. The electrostatic interactions are mainly responsible for the substituent effects on the magnitude of the attraction in the halogen-bonded complexes. The electrostatic energy depends significantly on the substituent. They have a strong correlation with the E(int). On the other hand the effects of the substituent on the dispersion energy are small, however the dispersion does contribute greatly to the attraction.

Ab initiostudy of permanent electric dipole moment and radiative lifetimes of alkaline-earth-metal--Li molecules

We calculate permanent electric dipole moments (PDMs), as well as spontaneous and black body lifetimes, of alkaline-earth-metal--Li (AEM-Li) ultracold polar molecules to study anisotropic long-range dipole-dipole interactions in a single quantum state. We obtain potential energy curves for the ${}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}$ ground state of MgLi, CaLi, SrLi, and BaLi molecules at the coupled cluster singles and doubles with partial triples [CCSD(T)] level of electron correlation. Calculated spectroscopic constants for the isotopes: ${}^{24}$Mg${}^{7}$Li, ${}^{40}$Ca${}^{7}$Li, ${}^{88}$Sr${}^{7}$Li, and ${}^{138}$Ba${}^{7}$Li, show good agreement with available theoretical and experimental results. We obtain PDM curves using finite field perturbation theory at the CCSD(T) level. We find that AEM-Li molecules have moderate values of PDM at the equilibrium bond distance (MgLi: 0.90 D, CaLi: 1.15 D, SrLi: 0.33 D, and BaLi: --0.42 D) and hence might be suitable candidates for the proposed study in a single quantum state. Radiative lifetime calculations of the $\ensuremath{\nu}$ $=$ 0 state (${}^{24}$Mg${}^{6}$Li: 22 s, ${}^{40}$Ca${}^{6}$Li: 39 s, ${}^{88}$Sr${}^{6}$Li: 380 s, and ${}^{138}$Ba${}^{6}$Li: 988 s) are found to be longer than the typical time scale associated with ultracold experiments with these molecules. The uncertainty in the lifetime calculations are estimated to be less than 10$%$.

Basis set selection for the calculation of the IR fundamental intensities for 1,1-C2H2F2 and F2CO

The theoretical calculation of the CC, CO and the CF2 asymmetric stretching infrared intensities of the isoelectronic 1,1-C2H2F2 and F2CO molecules has resulted in large errors varying from 41.0 to 60.5 km mol−1 or 13.5% to 28.0% of their experimental intensities when using extended 6-311++G(3d,3p) basis set wave-functions at the Moller–Plesset 2 level. For this reason new theoretical intensity results are reported using wave-functions calculated with a large variety of basis sets at both the MP2 and QCISD levels. Accurate intensities were obtained with wave-functions formed from basis sets with polarization functions but without diffuse functions, 6-31G(d,p), 6-31G(2d,2p), 6-31G(3d,3p), 6-311G(d,p) and 6-311G(3d,3p) at both electron correlation levels. Best results for these bands were obtained with the 6-31G(2d,2p) wave-function at the QCISD level providing errors less than 10 km mol−1 and 3.4% of the experimental values. The rms errors for all the 1,1-C2H2F2 and F2CO intensities at this level are 12.3 and 6.5 km mol−1, respectively. These wave functions at both electron correlation levels also resulted in accurate values for the fundamental intensities of trans-C2H2F2 and cis-C2H2F2 with rms errors of less than 10 km mol−1. Theoretical calculations of the infrared intensities of the 1,1-C2HDF2 isotopomer indicate that the experimental determination of the CH symmetric stretching intensity of 1,1-C2H2F2 is probably over-estimated owing to severe band overlap and/or Fermi resonance with the ν2 + ν3 combination band.

Basis Set Dependence of Coupled Cluster Optical Rotation Computations

Specific rotations for five notoriously difficult molecules, (S)-methyloxirane, (S)-methythiirane, (S)-2-chloropropionitrile, (1S,4S)-norbornenone, and (1R,5R)-β-pinene, have been computed using coupled cluster (CC) and density functional theory (DFT). The performance of the recently developed LPol basis sets compared to the correlation-consistent sets of Dunning and co-workers has been examined at four wavelengths: 355, 436, 589, and 633 nm. We find that the LPol basis sets are an efficient choice, often outperforming the more commonly used correlation-consistent basis sets of comparable size. The smallest of the four, LPol-ds, performs nearly as well as the rest of the series and often yields results closer to the basis set limit than appreciably larger basis sets. While the performance of the LPol bases is admirable, they still do not alleviate the need for high levels of electron correlation, vibrational corrections, and the inclusion of solvent effects to accurately reproduce experimental rotations. In particular in the case of β-pinene we find that they do not produce agreement between DFT and experiment as was previously suggested.

On the relation between basis set convergence and electron correlation: a critical test for modern ab initio quantum chemistry on a “mindless” data set

The correlation of the only two error sources in the solution of the electronic Schrodinger equation is addressed: the basis set convergence (incompleteness) error (BSIE) and the electron correlation effect. The electron correlation effect and basis set incompleteness error are found to be correlated for all of the molecules in Grimme’s “mindless” data set (MB08-165). One can use an extrapolation to the HF or MP2 complete basis set (CBS) limit to see with which type of quantum chemical problem (“simple” and “hard”) the researcher is dealing. The origin of the slow convergence of the partial wave expansion can be the Kato cusp condition for electron–electron coalescence. Such an extrapolation is possible for many large molecular systems and would give the researcher an idea about the expected electron correlation level that would lead to the desired theoretical accuracy. In other words, it is possible to use not only the CBS energy value itself but the speed with which it is reached to get extra information about the molecular system under study.

Large Amplitude Motions in Cyclopentene and 1-Butene: Quantum Chemical Insights into the Ground- and Excited State Potential Energy Surfaces

Abstract The ring-puckering motion in cyclopentene as well as the hindered internal rotation around the central C–C bond in 1-butene have been studied by high-level quantum chemical calculations. Relevant potential energy surfaces of these molecules along these large-amplitude motions are provided as well as rotational constants are given allowing for thorough comparison with recent results from time-resolved femtosecond degenerate four-wave mixing (fs DFWM) spectroscopy. Emphasis is put on the performance of various post-Hartree Fock methods, the required level of electron correlation as well as the basis set quality.

A theoretical survey on the structures, energetics, and isomerization pathways of the B5O radical

Boron-centered radicals have received growing interest. Recently, two groups reported density functional theory investigations (GGA-PW91 and B3LYP) on a hexa-atomic boron-oxide radical, B(5)O, which has led to great discrepancies on the type of low-lying structures. In this article, we not only explore the energetics of doublet and quartet B(5)O isomers at high electron-correlated levels (CCSD(T)/6-311+G(2df), CCSD(T)/aug-cc-pVTZ, and G3B3) but also investigate the isomerization and fragmentation stability of the low-lying B(5)O isomers. All the high-level studies consistently show that the B(5)O radical possesses a belt-like ground structure (2)01 in doublet electronic state followed by isomer (2)02 with an exocyclic - BO moiety at around 3.0 kcal/mol. Kinetically, (2)01 and (2)02 are separated by a considerable barrier of about 20 kcal/mol. Thus, the two isomeric forms of B(5)O radical should be very promising for isolation in laboratory. However, the other four isomers reported recently are all kinetically unstable toward conversion to (2)01 and (2)02. The high thermodynamic and kinetic stability of (2)01 and (2)02 might make them as important building cores in the growth of boron-oxide clusters. This results would also help deeply understand the oxidation and doping mechanism of pure boron clusters.

Accelerated ab initio molecular dynamics with response equation extrapolation

Polynomial extrapolation of response (‘ z-vector’) elements is shown to reduce the cost of correlated-wavefunction, classical ab initio molecular dynamics. Demonstrations with resolution-of-the-identity Møller–Plesset perturbation theory (RI-MP2) show that the number of response equation iterations is reduced by a factor of 2–3, thereby enabling accelerated MP2 dynamics. Coupled with previously demonstrated Fock matrix extrapolation, the combined iterative SCF and z-vector calculations are reduced to a minority share of the total calculation. Though demonstrated for MP2, these methods can also be generalized to higher levels of electron correlation or excited state methods.

Ab initio molecular geometry and anharmonic vibrational spectra of thiourea and thiourea‐d4

Potential energy surface (PES) of thiourea, SC(NH(2))(2), has been searched for stable conformers under C(1), C(s), C(2), and C(2v) symmetry constraints by post-Hartree-Fock ab initio methods with electron correlation level varying from second-order Moeller-Plesset perturbation theory (MP2) to quadratic configuration interaction with single and double excitations (QCISD) and basis sets of double- and triple-zeta quality within 6-31+G(d,p) to aug-cc-pVTZ range. Thiourea conformers of C(2) and C(s) symmetry have been found as stationary points on the PES with no imaginary frequencies at MP2/6-31+G(d,p) level, whereas only the C(2) conformer seems as true minimum when basis sets containing more polarization and/or diffuse functions were used. At QCISD/cc-pVTZ level, only the C(2) thiourea conformer has been found as true minimum on the PES. Anharmonic vibrational spectra of C(2) conformers of thiourea and thiourea-d(4) have been computed by vibrational self-consistent field (VSCF) and correlation-corrected VSCF methods using quartic force field approximation at MP2/TZV+(2d,2p), and MP2/6-311+G(3df,2p) level and direct approach at MP2/6-31+G(2d,p) level. Both quartic force field and direct VSCF methods used PES expansion in curvilinear (internal) coordinates. Wavenumbers of fundamental, first overtone, and combination transitions of C(2) symmetry conformer have been calculated for natural abundance thiourea and thiourea-d(4) isotopomer. Anharmonic corrections originating from mean field and mode coupling effects vary from 5 to 60 cm(-1), whereas mode-mode correlation contribution seems significant in the case of ν(N-H) stretching and δ(NH(2)) deformation modes (15-5 cm(-1)). Application of internal coordinates in the VSCF calculation results in slight underestimation of δ(NH(2)) deformation mode fundamentals and correct description of out-of-plane large-amplitude τ(SCNH) modes.

Direct Dynamics Implementation of the Least-Action Tunneling Transmission Coefficient. Application to the CH4/CD3H/CD4 + CF3 Abstraction Reactions.

We present two new direct dynamics algorithms for calculating transmission coefficients of polyatomic chemical reactions by the multidimensional least-action tunneling approximation. The new algorithms are called the interpolated least-action tunneling method based on one-dimensional interpolation (ILAT1D) and the double interpolated least-action tunneling (DILAT) method. The DILAT algorithm, which uses a one-dimensional spline under tension to interpolate both of the effective potentials along the nonadiabatic portions of tunneling paths and the imaginary action integrals as functions of tunneling energies, was designed for the calculation of multidimensional LAT transmission coefficients for very large polyatomic systems. The performance of this algorithm has been tested for the CH4/CD3H/CD4 + CF3 hydrogen abstraction reactions with encouraging results, i.e., when the fitting is performed using 13 points, the algorithm is about 30 times faster than the full calculation with deviations that are smaller than 5%. This makes direct dynamics least-action tunneling calculations practical for larger systems, higher levels of electron correlation, and/or larger basis sets.

Structure and Conformational Stability of Protonated Dialanine

A systematic investigation on the structure and stability of the four conformers of the protonated dialanine cation (transA1, transA2, transO1, cisA3) was performed employing the HF, MP2, and hybrid DFT methods with various basis sets which ranged from the 6-31G* to the basis set larger than the correlation consistent aug-cc-pVTZ basis set. It is found that the backbone dihedral angles and energies of the conformers are sensitive to the electron correlation level and basis set, especially manifesting slow convergence of conformer structure and energetics with basis set at the MP2 level. At the MP2 basis set limit corrected by CCSD(T) correlation effect, the lowest transA1 conformer is almost isoenergetic with the cisA3 conformer, followed by the transA2 conformer ( approximately 0.5 kcal/mol above transA1), and, last, the transO1 conformer ( approximately 1.2 kcal/mol above transA1). Vibrational and thermal (entropic) factors appear to have an important effect on the relative stability between conformers at room temperature, reducing the energy difference between transA1 and transA2 conformers and making cisA3 higher in energy than transA1 or transA2, which is in accord with the recent infrared multiphoton dissociation experimental data on this cation. According to the polarizable continuum model calculations, solvation of protonated dialanine in water would significantly enhance the stability of the transA2 conformer, making it most populated in aqueous solution at room temperature. Among the tested hybrid DFT methods in this study, B3LYP/6-31G* was found to be the most effective for predicting the conformational structures and relevant stability of protonated dialanine cation in the gas phase.

Quantum Chemical Modeling of Ground States of CO 2 Chemisorbed on Anatase (001), (101), and (010) TiO 2 Surfaces

To design efficient CO 2 photoreduction catalysts, we need to understand the intermediates and energetics of various reactions involved in the photoreduction of CO 2 in greater detail. As a first step in this process, the ground states of CO 2 chemisorbed on small clusters from various anatase surface planes are modeled in this study. We show that large basis sets with diffuse functions and high levels of electron correlation are needed to model the electron attached states of CO 2, which may play a role in its photoreduction. Density functional theory (DFT) calculations of CO 2 adsorbed on small TiO 2 clusters (Ti 2O 9H 10) extracted from the (010), (001), and (101) surface plane structures point to the formation of different adsorbed species depending on crystal face atomic structure. The calculated infrared (IR) spectral properties of these species are compared against experimental data. We find favorable agreement for the existence of three different surface complexes. The formation of different surfa...