Unitary group based open-shell coupled cluster theory: Application to van der Waals interactions of high-spin systems

When Gold Is Not Enough: Platinum Standard of Quantum Chemistry with N7 Cost

In this paper, we extend the rank-reduced coupled-cluster formalism to the calculation of non-iterative energy corrections due to quadruple excitations. There are two major components of the proposed formalism. The first is an approximate compression of the quadruple excitation amplitudes using the Tucker format. The second is a modified functional used for the evaluation of the corrections which gives exactly the same results for the exact amplitudes, but is less susceptible to errors resulting from the aforementioned compression. We show, both theoretically and numerically, that the computational cost of the proposed method scales as the seventh power of the system size. Using reference results for a set of small molecules, the method is calibrated to deliver relative accuracy of a few percent in energy corrections. To illustrate the potential of the theory, we calculate the isomerization energy of ortho/meta benzyne (C₆H₄) and the barrier height for the Cope rearrangement in bullvalene (C₁₀H₁₀). The method retains a near-black-box nature of the conventional coupled-cluster formalism and depends on only one additional parameter that controls the accuracy.

Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory

We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from standard restricted open-shell Hartree-Fock (ROHF) orbitals, which allows the unperturbed Hamiltonian operator to be defined in terms of a diagonal spin-free Fock operator. The HFC tensors are computed as a first-order property via implementation of an analytic derivative scheme. The required one-particle spin density matrix is computed by using one- and two-particle spin-free density matrices that are obtained from the analytic derivative implementation, in this way avoiding the use of any spin-dependent operator and maintaining spin adaptation of the CC wavefunction. Benchmark calculations of HFC tensors for a set of 21 radicals indicate reasonably good agreement of the COS-CCSD(T) results with experiment and a consistent improvement over the COS-CCSD method. We demonstrate that the accuracies of the isotropic hyperfine coupling constants obtained in unrestricted HF (UHF) reference based spin-orbital CCSD(T) calculations deteriorate when spin contamination in the UHF wavefunction is large, and the results may even become qualitatively incorrect when spin polarization is the driving mechanism. Within a similar noniterative perturbative treatment of triple excitations, the spin-adapted COS-CCSD(T) approach produces accurate results, thus ensuring cost-effectiveness together with reliability.

Symmetry-adapted perturbation theory utilizing density functional description of monomers for high-spin open-shell complexes

We present an implementation of symmetry-adapted perturbation theory (SAPT) to interactions of high-spin open-shell monomers forming high-spin dimers. The monomer spin-orbitals used in the expressions for the electrostatic and exchange contributions to the interaction energy are obtained from density functional theory using a spin-restricted formulation of the open-shell Kohn-Sham (ROKS) method. The dispersion and induction energies are expressed through the density-density response functions predicted by the time-dependent ROKS theory. The method was applied to several systems: NH...He, CN...Ne, H2O...HO2, and NH...NH. It provides accuracy comparable to that of the best previously available methods such as the open-shell coupled-cluster method with single, double, and noniterative triple excitations, RCCSD(T), with a significantly reduced computational cost.

Third-order interactions in symmetry-adapted perturbation theory

We present an extension of many-body symmetry-adapted perturbation theory (SAPT) by including all third-order polarization and exchange contributions obtained with the neglect of intramonomer correlation effects. The third-order polarization energy, which naturally decomposes into the induction, dispersion, and mixed, induction-dispersion components, is significantly quenched at short range by electron exchange effects. We propose a decomposition of the total third-order exchange energy into the exchange-induction, exchange-dispersion, and exchange-induction-dispersion contributions which provide the quenching for the corresponding individual polarization contributions. All components of the third-order energy have been expressed in terms of molecular integrals and orbital energies. The obtained formulas, valid for both dimer- and monomer-centered basis sets, have been implemented within the general closed-shell many-electron SAPT program. Test calculations for several small dimers have been performed and their results are presented. For dispersion-bound dimers, the inclusion of the third-order effects eliminates the need for a hybrid SAPT approach, involving supermolecular Hartree-Fock calculations. For dimers consisting of strongly polar monomers, the hybrid approach remains more accurate. It is shown that, due to the extent of the quenching, the third-order polarization effects should be included only together with their exchange counterparts. Furthermore, the latter have to be calculated exactly, rather than estimated by scaling the second-order values.

Automated generation of coupled-cluster diagrams: Implementation in the multireference state-specific coupled-cluster approach with the complete-active-space reference

An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled-cluster (CC) method with an arbitrary level of the electronic excitations has been developed. The method was implemented in the general case as well as for specific application in the state-specific multireference coupled-cluster theory (SSMRCC) based on the concept of a "formal reference state." The algorithm was tested in SSMRCC calculations describing dissociation of a single bond and in calculations describing simultaneous dissociation of two single bonds--the problem requiring up to six-particle excitations in the CC operator.