The accuracy of dipole moments from spin-component scaled CC2 in ground and electronically excited states

The accuracy of dipole moments calculated from wave function methods based on second-order perturbation theory is investigated in the ground and electronically excited states. Results from the approximate coupled-cluster singles-and-doubles model, CC2, M?ller-Plesset perturbation theory, MP2, and the algebraic diagrammatic construction through second-order, ADC(2), are discussed together with the spin-component scaled and the scaled opposite-spin variants of these methods. The computed dipole moments show a very good correlation with data from high-resolution spectroscopy. Compared to the unscaled methods, the spin-component scaling increases the accuracy of the results and improves the robustness of the calculations. An accuracy about 0.2 to 0.1 D in the ground state and about 0.3 to 0.2 D in the electronically excited states can be achieved with these approaches.     

Ab initio calculation of the vibrational and electronic spectra of trans- and cis-azobenzene

We report accurate geometries and harmonic force fields for trans- and cis-azobenzene determined by second-order M?ller-Plesset perturbation theory. For the trans isomer, the planar structure with C(2h) symmetry, found in a recent gas electron diffraction experiment, is verified. The calculated vibrational spectra are compared with experimental data and density functional calculations. Important vibrational frequencies are localized and discussed. For both isomers, we report UV spectra calculated using the second-order approximate coupled-cluster singles-and-doubles model CC2 with accurate basis sets. Vertical excitation energies and oscillator strengths have been determined for the lowest singlet n(pi)* and (pi)(pi)* transitions. The results are compared with the available experimental data and second-order polarization propagator (SOPPA) and density functional (DFT) calculations. For both isomers, the CC2 results for the excitation energies into the S(1) and S(2) states agree within 0.1 eV with experimental gas-phase measurements.     

Improvement of the coupled-cluster singles and doubles method via scaling same- and opposite-spin components of the double excitation correlation energy

There has been much interest in cost-free improvements to second-order M?ller-Plesset perturbation theory (MP2) via scaling the same- and opposite-spin components of the correlation energy (spin-component scaled MP2). By scaling the same- and opposite-spin components of the double excitation correlation energy from the coupled-cluster of single and double excitations (CCSD) method, similar improvements can be achieved. Optimized for a set of 48 reaction energies, scaling factors were determined to be 1.13 and 1.27 for the same- and opposite-spin components, respectively. Preliminary results suggest that the spin-component scaled CCSD (SCS-CCSD) method will outperform all MP2 type methods considered for describing intermolecular interactions. Potential energy curves computed with the SCS-CCSD method for the sandwich benzene dimer and methane dimer reproduce the benchmark CCSD(T) potential curves with errors of only a few hundredths of 1 kcal mol(-1) for the minima. The performance of the SCS-CCSD method suggests that it is a reliable, lower cost alternative to the CCSD(T) method.     

Calculating stacking interactions in nucleic acid base-pair steps using spin-component scaling and local second order Møller-Plesset perturbation theory

Stacking interaction energies for ten B-DNA base-pair steps are computed with density fitted local second-order M?ller-Plesset perturbation theory (DF-LMP2), and with the spin-component scaled (SCS) and spin-component scaled for nucleobases (SCSN) variants of DF-LMP2. Comparison with existing CBS(T) reference data indicates larger than expected energy differences for both SCS variants. After an analysis of the errors involved, an alternative method of producing reference data is proposed where DF-LMP2/aug-cc-pVTZ and DF-LMP2/aug-cc-pVQZ energies for the whole complex are extrapolated to produce interaction energies that do not require many-body correction and show reduced error in estimation of the basis set limit. A literature correction term from coupled cluster theory with perturbative triples is then added to the DF-LMP2 estimated basis set limit. These new reference data are consistently around 1 kcal mol(-1) less than previous literature data. DF-SCSN-LMP2/aug-cc-pVTZ is found to reproduce the new reference interaction energies with a root mean square error (RMSE) of 0.71 kcal mol(-1), while SCS consistently underestimates the binding energy.     

A kinetic energy fitting metric for resolution of the identity second-order Møller-Plesset perturbation theory

A kinetic-energy-based fitting metric for application in the context of resolution of the identity second-order M?ller-Plesset perturbation theory is presented, which is derived from the Poisson equation. Preliminary tests of the applicability include the evaluation of the error in the correlation energy, compared to standard M?ller-Plesset perturbation theory, with respect to the auxiliary basis set employed. We comment on the potential merits of this fitting metric, compared to standard resolution of the identity second-order M?ller-Plesset perturbation theory, and discuss its scaling behavior in the limit of large molecules.     

Calculation of intermolecular interactions in the benzene dimer using coupled-cluster and local electron correlation methods

Potential energy curves for the parallel-displaced, T-shaped and sandwich structures of the benzene dimer are computed with density fitted local second-order M?ller-Plesset perturbation theory (DF-LMP2) as well as with the spin-component scaled (SCS) variant of DF-LMP2. While DF-LMP2 strongly overestimates the dispersion interaction, in common with canonical MP2, the DF-SCS-LMP2 interaction energies are in excellent agreement with the best available literature values along the entire potential energy curves. The DF-SCS-LMP2 dissociation energies for the three structures are also compared with new complete basis set estimates of the interaction energies obtained from accurate coupled cluster (CCSD(T)) and DF-SCS-MP2 calculations. Since LMP2 is essentially free of basis set superposition errors, counterpoise corrections are not required. As a result, DF-SCS-LMP2 is computationally inexpensive and represents an attractive method for the study of larger pi-stacked systems such as truncated sections of DNA.     

Computational studies of nonstoichiometric sodium auride clusters

The molecular structures of low-lying isomers of anionic and neutral sodium auride clusters have been studied computationally at the second-order M?ller-Plesset perturbation theory level using quadruple-ζ basis sets augmented with a double set of polarization functions. The first vertical detachment energies were calculated at the M?ller-Plesset level as the energy difference between the cluster anion and the corresponding neutral cluster. The photodetachment energies of higher-lying ionization channels were calculated by adding electronic excitation energies of the neutral clusters to the first vertical detachment energy. The excitation energies were calculated at the linear response approximate coupled-cluster singles and doubles level using the anionic cluster structures. The obtained ionization energies for NaAu(-), NaAu(2)(-), NaAu(3)(-), NaAu(4)(-), Na(2)Au(2)(-), Na(2)Au(3)(-), Na(3)Au(3)(-), and Na(2)Au(4)(-) were compared to values deduced from experimental photoelectron spectra. Comparison of the calculated photoelectron spectra for a few energetically low-lying isomers shows that the energetically lowest cluster structures obtained in the calculations do not always correspond to the clusters produced experimentally. Spin-component-scaled second-order M?ller-Plesset perturbation theory calculations shift the order of the isomers such that the observed clusters more often correspond to the energetically lowest structure, whereas the spin-component-scaled approach does not improve the photodetachment energies of the sodium aurides. The potential energy surface of the sodium aurides is very soft, with several low-lying isomers requiring an accurate electron correlation treatment. The calculations show that merely the energetic criterion is not a reliable means to identify the structures of the observed sodium auride clusters; other experimental information is needed to ensure a correct assignment of the cluster structures. The cluster structures of nonstoichiometric anionic sodium aurides have been determined by comparing calculated ionization energies for low-lying structures of the anionic clusters with experimental data.     

Accurate all-electron correlation energies for the closed-shell atoms from Ar to Rn and their relationship to the corresponding MP2 correlation energies

All-electron correlation energies E(c) are not very well-known for atoms with more than 18 electrons. Hence, coupled-cluster calculations in carefully designed basis sets are combined with fully converged second-order M?ller-Plesset perturbation theory (MP2) computations to obtain fairly accurate, nonrelativistic E(c) values for the 12 closed-shell atoms from Ar to Rn. These energies will be useful for the evaluation and parameterization of density functionals. The results show that MP2 overestimates ∣E(c)∣ for heavy atoms. Spin-component scaling of the MP2 correlation energy is used to provide a simple explanation for this overestimation.     

Generalized van Vleck perturbation theory (GVVPT2) study of the excited states of benzene and the azabenzenes

Generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structures is applied to examine the azabenzene series: benzene, pyridine, pyrazine, symmetric triazine and symmetric tetrazine. The spectra of azabenzenes are complex with large numbers of excited states at low energies comprising n --> pi* and pi --> pi* excited states and also doubly excited states of the n,n --> pi*,pi* type. The calculations are complicated due to strong correlation effects in the nitrogen lone-pair orbitals and the pi electrons. This study is the first to use GVVPT2 on conjugated systems. Comparison is made with experimental data and complete active space second-order perturbation theory, equation of motion coupled cluster and similarity transformed equation of motion coupled cluster theory data. Using polarized valence double split basis sets for benzene and pyrazine (cc-pVDZ) and pyridine (ANO-S) and polarized triple split basis sets (ANO-L) for triazine and tetrazine, the n --> pi* and pi --> pi* states are computed with an average error of 0.28 eV in comparison with available experimental data.     

Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the-identity approximation

We present an implementation of static and frequency-dependent polarizabilities for the approximate coupled cluster singles and doubles model CC2 and static polarizabilities for second-order Mo?ller-Plesset perturbation theory. Both are combined with the resolution-of-the-identity approximation for electron repulsion integrals to achieve unprecedented low operation counts, input-output, and disc space demands. To avoid the storage of double excitation amplitudes during the calculation of derivatives of density matrices, we employ in addition a numerical Laplace transformation for orbital energy denominators. It is shown that the error introduced by this approximation is negligible already with a small number of sampling points. Thereby an implementation of second-order one-particle properties is realized, which avoids completely the storage of quantities scaling with the fourth power of the system size. The implementation is tested on a set of organic molecules including large fused aromatic ring systems and the C(60) fullerene. It is demonstrated that exploiting symmetry and shared memory parallelization, second-order properties for such systems can be evaluated at the CC2 and MP2 level within a few hours of calculation time. As large scale applications, we present results for the 7-, 9-, and 11-ring helicenes.     

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and M?ller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.     

How accurate is the density functional theory combined with symmetry-adapted perturbation theory approach for CH-pi and pi-pi interactions? A comparison to supermolecular calculations for the acetylene-benzene dimer

Five different orientations of the acetylene-benzene dimer including the T-shaped global minimum structure are used to assess the accuracy of the density functional theory combined with symmetry adapted perturbation theory (DFT-SAPT) approach in its density-fitting implementation (DF-DFT-SAPT) for the study of CH-pi and pi-pi interactions. The results are compared with the outcome of counterpoise corrected supermolecular calculations employing second-order M?ller-Plesset (MP2), spin-component scaled MP2 (SCS-MP2) and single and double excitation coupled cluster theory including perturbative triple excitations (CCSD(T)). For all considered orientations MP2 predicts much deeper potential energy curves with considerably shifted minima compared to CCSD(T) and DFT-SAPT. In spite of being an improvement over the results of MP2, SCS-MP2 tends to underestimate the well depth while DFT-SAPT, employing an asymptotically corrected hybrid exchange-correlation potential in conjunction with the adiabatic local density approximation for the exchange-correlation kernel, is found to be in excellent agreement with CCSD(T). Furthermore, DFT-SAPT provides a detailed understanding of the importance of the electrostatic, induction and dispersion contributions to the total interaction energy and their repulsive exchange corrections.     

Ab initio calculations of electronically excited states of cyano-substituted polyacetylene cations

The transition energies for the lowest energy pi --> pi* electronic excitations are calculated with the complete active space self-consistent field method (CASSCF) and with the complete active space second-order perturbation theory method (CASPT2) for the linear cyano-substituted polyacetylene cations, H-Cn-CN+, n = 4-11, and NC-Cn-CN+, n = 2-10. These systems are models for an important class of interstellar species. We demonstrate the utility of the theoretical calculations in assigning the experimental spectra.     

Redshift and blueshift of the Ar-H vibrational stretching frequency in complexes of FArH and acetylene

Two planar hydrogen-bonded complexes of FArH and acetylene were found to be stable using second-order M?ller-Plesset perturbation theory (MP2) with 6-311++G(2d,2p) basis sets. The more stable complex involves bonding between the F atom of FArH and a H atom of acetylene, while the other isomer is a T-shaped complex with the H atom of FArH bonded to the center of the CC bond of acetylene; the zero-point energy corrected dissociation energies are 29 and 27 kJ mol(-1), respectively. Interestingly, the Ar-H harmonic vibrational stretching frequency is blueshifted in the more stable isomer and redshifted in the less stable form. The electron density rearrangement of FArH on complexation was investigated and used to explain these unusual findings.     

Are insertion compounds of CH2CHF and the rare gases stable? A computational study

Ab initio calculations, using second-order M?ller-Plesset perturbation theory with a 6-311+ +G(2d,2p) basis set, predict the stability of two novel compounds of monofluoroethene, CH2CHF, with the rare-gas atoms Ar and Kr. The dissociation energies to the lowest-energy fragmentation products, CH2CHF + Rg (Rg = Ar,Kr), were computed to be -528 and -449 kJ mol(-1), respectively, at the coupled-cluster singles, doubles, and triples level of theory. Possible transition states (at second-order M?ller-Plesset theory) via a C-Rg-F bending mode for these fragmentation reactions were also located with barrier heights of about 76 and 106 kJ mol(-1), for the Ar- and Kr-containing species, respectively. However, the Ar-containing species may not exist at all as it is less stable than the fragments CH2CH + F + Ar at the higher level of theory and may possibly dissociate via this route.     

Electronic spectra and photodissociation of vinyl chloride: a symmetry-adapted cluster configuration interaction study

The vertical absorption spectrum and photodissociation mechanism of vinyl chloride (VC) were studied by using symmetry-adapted cluster configuration interaction theory. The important vertical pi --> pi* excitation was intensively examined with various basis sets up to aug-cc-pVTZ augmented with appropriate Rydberg functions. The excitation energy for pi --> pi* transition obtained in the present study, 6.96 eV, agrees well with the experimental value, 6.7-6.9 eV. Calculated excitation energies along with the oscillator strengths clarify that the main excitation in VC is the pi --> pi* excitation. Contrary to the earlier theoretical reports, the results obtained here support that the C-Cl bond dissociation takes place through the n(Cl-)sigma(C-Cl)* state.     

An atomic orbital-based reformulation of energy gradients in second-order Møller-Plesset perturbation theory

A fully atomic orbital (AO)-based reformulation of second-order M?ller-Plesset perturbation theory (MP2) energy gradients is introduced, which provides the basis for reducing the computational scaling with the molecular size from the fifth power to linear. Our formulation avoids any transformation between the AO and the molecular orbital (MO) basis and employs pseudodensity matrices similar to the AO-MP2 energy expressions within the Laplace scheme for energies. The explicit computation of perturbed one-particle density matrices emerging in the new AO-based gradient expression is avoided by reformulating the Z-vector method of Handy and Schaefer [J. Chem. Phys. 81, 5031 (1984)] within a density matrix-based scheme.     

Improved perturbative treatment of electronic energies from a minimal-norm approach to many-body perturbation theory

We propose a zeroth-order Hamiltonian for many-body perturbation theory based on the unitary decomposition of the two-particle reduced Hamiltonian. For the zeroth-order Hamiltonian constrained to be diagonal in the Hartree-Fock basis set, the two-particle reduced perturbation matrix is chosen to have a minimal Frobenius norm. When compared with the M?ller-Plesset partitioning, the method yields more accurate second-order energies.     

Hydrogen peroxide clusters: the role of open book motif in cage and helical structures

Hartree-Fock (HF) calculations using 6-31G*, 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets show that hydrogen peroxide molecular clusters tend to form hydrogen-bonded cyclic and cage structures along the lines expected of a molecule which can act as a proton donor as well as an acceptor. These results are reiterated by density functional theoretic (DFT) calculations with B3LYP parametrization and also by second-order M?ller-Plesset perturbation (MP2) theory using 6-31G* and 6-311++G(d,p) basis sets. Trends in stabilization energies and geometrical parameters obtained at the HF level using 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are similar to those obtained from HF/6-31G* calculation. In addition, the HF calculations suggest the formation of stable helical structures for larger clusters, provided the neighbors form an open book structure.     

Interaction energy contributions of H-bonded and stacked structures of the AT and GC DNA base pairs from the combined density functional theory and intermolecular perturbation theory approach

Stacked and Watson-Crick structures of DNA base pairs are investigated with the DFT-SAPT variant of intermolecular perturbation theory, yielding a rigorous decomposition of the interaction energy into electrostatic, induction, dispersion, and exchange contributions. Their interplay in the various structures is analyzed. Total interaction energies extrapolated to the complete basis set limit are compared with corresponding second-order M?ller-Plesset and estimated coupled-cluster theory results.