Barrier heights, reaction energies and bond dissociation energies for RH + HO2 reactions with coupled-cluster theory, density functional theory and diffusion quantum Monte Carlo methods.

Hydrogen abstraction reactions by the HO2 radical from hydrocarbon molecules are an important class of reactions in the autoignition of hydrocarbon fuels. Performance of DLPNO-CC and DFT methods using three hybrids and four double hybrids as well as FN-DMC with the single-Slater-Jastrow trial wavefunction on barrier heights and reaction energies of RH + HO2 reactions as well as bond dissociation energies of the involved X-H molecules is evaluated by comparison with the highly accurate CCSD(T)-F12b/CBS results in this study. Our results show that the DLPNO-CCSD(T)-F12 method can achieve highly accurate barrier heights, reaction energies and X-H bond energies for RH + HO2 reactions at a relatively low computational cost, and it is applicable to the H-abstraction reactions of larger molecules. Among all DFAs, MN15 and the employed double hybrids can achieve accurate barrier heights and reaction energies with MADs of less than or around 2 kJ mol-1, but their error on X-H bond energies is more pronounced. Only DSD-BLYP and DSD-PBEB95 can provide X-H bond energies with MADs less than 4 kJ mol-1. Considering dispersion correction in DFT calculations does not improve these barrier heights and reaction energies. The error of FN-DMC on barrier heights and reaction energies is slightly larger than that of MN15 and those of double hybrids, but it can achieve results within chemical accuracy for these reactions and the X-H bond energies.

The effect of spin-orbit coupling on molecular properties: Potential energy curve, transition dipole moment and laser cooling scheme of NH.

The influence of spin-orbit coupling on the cooling of NH molecular laser is investigated based on the ab initio theory. The potential energy curves (PECs) and spectral constants for four Λ-S states (X3Σ-, a1Δ, b1Σ+ and A3Π) and eight Ω states [Formula: see text] a1Δ2, [Formula: see text] and [Formula: see text] ) of NH molecule are obtained by the multi-reference configuration interaction (MRCI) plus Davidson correction. The spectroscopic constants (Re, ωe, ωeχe, Be, De) are obtained by solving the one dimensional radial Schrödinger equation, and the results are almost the same as the previously reported data. In addition, the transition dipole moment, permanent dipole moment, Franck-Condon factors, and radiative lifetime of NH molecule are also acquired. Also, the effects of the intermediate state on the [Formula: see text] , [Formula: see text] and [Formula: see text] transitions are considered. The feasible laser cooling schemes using a single laser are formulated. In the proposed cooling scheme, there wavelengths for the [Formula: see text] are used, the main pump lasers are λ00 = 335.74 nm. The feasible transition is based on this. It is found that spin-orbit coupling has a significant effect on potential energy curves, permanent dipole moments, transition dipole moments and vibration energy levels.

Analytical energy gradients for ionized states using equation-of-motion coupled-cluster theory with spin-orbit coupling.

Spin-orbit coupling (SOC) may have a significant effect on the structure and harmonic frequencies of particularly heavy p-block element compounds. However, reports on analytical energy gradients with SOC are scarce, especially for excited states. In this work, we implemented analytical energy gradients for ionized states using the equation-of-motion coupled-cluster (CC) theory at the CC singles and doubles level (EOM-IP-CCSD) with SOC. Effects of SOC on structure and harmonic frequencies as well as properties for both the ground and some excited states of open-shell compounds with one unpaired electron can be investigated efficiently with the present implementation. A closed-shell reference is required in the calculations, and SOC is included in post-Hartree-Fock treatment. Relativistic effective core potentials are employed in dealing with both scalar relativistic effects and SOC, and we treat perturbations that are even under time reversal in this work. Both time-reversal symmetry and double point group symmetry for D2h * and its subgroups are exploited in the implementation. The method is applicable to states which can be reached by removing one electron from a closed-shell reference state. The results of some open-shell cations indicate the importance of SOC on structures and harmonic frequencies of heavy element compounds.

Properties of closed-shell superheavy element hydrides and halides using coupled-cluster method and density functional theory with spin-orbit coupling.

We report bond lengths, force constants, and dissociation energies for a series of closed-shell superheavy element monohydrides and halides at the singles and doubles level with perturbative triples (CCSD(T)) using recently developed relativistic effective core potentials in this work. CCSD(T) results with spin-orbit coupling (SOC) included in self-consistent field (SCF) calculations provide highly accurate estimates for properties of these molecules. Trends as well as SOC effects on properties of these molecules are presented. Performance of the coupled-cluster (CC) approach with SOC included in post-SCF calculations (SOC-CC) on these superheavy element molecules is evaluated. Our results show that SOC-CCSD results are in excellent agreement with those of KR-CCSD, while the error of SOC-CCSD(T) is larger, particularly for molecules containing element 114. Density functional theory results with various exchange-correlation (XC) functionals for these superheavy element molecules are also compared with those of CCSD(T). PBE0 is shown to be able to give rise to results that agree best with those of CCSD(T) in scalar-relativistic calculations among the investigated XC functionals. On the other hand, B97-3 is the best XC functional when SOC is considered in calculations.

Coupled-cluster method for open-shell heavy-element systems with spin-orbit coupling.

The coupled-cluster approach with spin-orbit coupling (SOC) included in post-self-consistent field treatment (SOC-CC) using relativistic effective core potentials is extended to spatially non-degenerate open-shell systems in this work. The unrestricted Hartree-Fock determinant corresponding to the scalar relativistic Hamiltonian is employed as the reference and the open-shell SOC-CC approach is implemented at the CC singles and doubles (CCSD) level as well as at the CCSD level augmented by a perturbative treatment of triple excitations (CCSD(T)). Due to the breaking of time-reversal symmetry and spatial symmetry, this open-shell SOC-CC approach is rather expensive compared with the closed-shell SOC-CC approach. The open-shell SOC-CC approach is applied to some open-shell atoms and diatomic molecules with s1, p3, σ1, or π2 configuration. Our results indicate that rather accurate results can be achieved with the open-shell SOC-CCSD(T) approach for these systems. Dissociation energies for some closed-shell molecules containing heavy IIIA or VIIA atoms are also calculated using the closed-shell SOC-CC approach, where energies of the IIIA or VIIA atoms are obtained from those of the closed-shell ions and experimental ionization potentials or electron affinities. SOC-CCSD(T) approach affords reliable dissociation energies for these molecules. Furthermore, scalar-relativistic CCSD(T) approach with the same strategy can also provide reasonable dissociation energies for the 5th row IIIA or VIIA molecules, while the error becomes pronounced for the 6th row elements.

Combining the spin-separated exact two-component relativistic Hamiltonian with the equation-of-motion coupled-cluster method for the treatment of spin-orbit splittings of light and heavy elements.

The spin-separated exact two-component (X2C) relativistic Hamiltonian [sf-X2C+so-DKHn, J. Chem. Phys., 2012, 137, 154114] is combined with the equation-of-motion coupled-cluster method with singles and doubles (EOM-CCSD) for the treatment of spin-orbit splittings of open-shell molecular systems. Scalar relativistic effects are treated to infinite order from the outset via the spin-free part of the X2C Hamiltonian (sf-X2C), whereas the spin-orbit couplings (SOC) are handled at the CC level via the first-order Douglas-Kroll-Hess (DKH) type of spin-orbit operator (so-DKH1). Since the exponential of single excitations, i.e., exp(T1), introduces sufficient spin orbital relaxations, the inclusion of SOC at the CC level is essentially the same in accuracy as the inclusion of SOC from the outset in terms of the two-component spinors determined variationally by the sf-X2C+so-DKH1 Hamiltonian, but is computationally more efficient. Therefore, such an approach (denoted as sf-X2C-EOM-CCSD(SOC)) can achieve uniform accuracy for the spin-orbit splittings of both light and heavy elements. For light elements, the treatment of SOC can even be postponed until the EOM step (denoted as sf-X2C-EOM(SOC)-CCSD), so as to further reduce the computational cost. To reveal the efficacy of sf-X2C-EOM-CCSD(SOC) and sf-X2C-EOM(SOC)-CCSD, the spin-orbit splittings of the 2Π states of monohydrides up to the sixth row of the periodic table are investigated. The results show that sf-X2C-EOM-CCSD(SOC) predicts very accurate results (within 5%) for elements up to the fifth row, whereas sf-X2C-EOM(SOC)-CCSD is useful only for light elements (up to the third row but with some exceptions). For comparison, the sf-X2C-S-TD-DFT-SOC approach [spin-adapted open-shell time-dependent density functional theory, Mol. Phys., 2013, 111, 3741] is applied to the same systems. The overall accuracy (1-10%) is satisfactory.

Spin-orbit coupling with approximate equation-of-motion coupled-cluster method for ionization potential and electron attachment.

Various approximate approaches to calculate cluster amplitudes in equation-of-motion coupled-cluster (EOM-CC) approaches for ionization potentials (IP) and electron affinities (EA) with spin-orbit coupling (SOC) included in post self-consistent field (SCF) calculations are proposed to reduce computational effort. Our results indicate that EOM-CC based on cluster amplitudes from the approximate method CCSD-1, where the singles equation is the same as that in CCSD and the doubles amplitudes are approximated with MP2, is able to provide reasonable IPs and EAs when SOC is not present compared with CCSD results. It is an economical approach for calculating IPs and EAs and is not as sensitive to strong correlation as CC2. When SOC is included, the approximate method CCSD-3, where the same singles equation as that in SOC-CCSD is used and the doubles equation of scalar-relativistic CCSD is employed, gives rise to IPs and EAs that are in closest agreement with those of CCSD. However, SO splitting with EOM-CC from CC2 generally agrees best with that with CCSD, while that of CCSD-1 and CCSD-3 is less accurate. This indicates that a balanced treatment of SOC effects on both single and double excitation amplitudes is required to achieve reliable SO splitting.

Spin-Orbit Effects in Closed-Shell Heavy and Superheavy Element Monohydrides and Monofluorides with Coupled-Cluster Theory.

Bond lengths and force constants of a set of closed-shell sixth-row and superheavy element monohydrides and monofluorides are calculated in this work. Kramers restricted coupled-cluster approaches (KR-CC) with spin-orbit coupling (SOC) included at the self-consistent field (SCF) level as well as CC approaches with SOC included in post-SCF treatment (SOC-CC) are employed in calculations. Recently published relativistic effective core potentials are employed, and highly accurate results for superheavy element molecules are achieved with KR-CCSD(T). SOC effects on bond lengths and force constants of these molecules are investigated. Effects of electron correlation are shown to be affected by SOC to a large extent for some superheavy element molecules. Bond lengths and force constants with SOC-CC agree very well with those of KR-CC for most of the sixth-row element molecules. As for superheavy element molecules, SOC-CCSD is able to afford results that are in good agreement with those of KR-CCSD except for 111F, while the error of SOC-CCSD(T) is more pronounced. Large error would be encountered with SOC-CC approaches for molecules when both SOC and electron correlation effects are sizable.