0000000000083859
AUTHOR
Lan Cheng
The route to high accuracy in ab initio calculations of Cu quadrupole-coupling constants.
We report nonrelativistic and scalar-relativistic coupled-cluster calculations of the copper quadrupole-coupling constants for eleven small copper-containing compounds. It is shown to be necessary to treat both electron-correlation and scalar-relativistic effects on the same footing even for a qualitatively correct description, because both effects are significant and are strongly coupled in the case of Cu electric-field gradients. We show that the three scalar-relativistic schemes employed in the present study--the leading order of direct perturbation theory, the spin-free exact two-component theory in its one-electron variant, and the spin-free Dirac-Coulomb approach--provide accurate tre…
Analytic second derivatives for the spin-free exact two-component theory
The formulation and implementation of the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c-1e scheme, the four-component one-electron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting "electrons-only" two-component Hamiltonian is then used together with untransformed two-electron interactions. The derivatives of the two-component Hamiltonian can thus be obtained by means of simple manipulations of the parent four-component Hamiltonian integrals and derivative integrals. The SF version of X2c-1e can furthermore exp…
Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order.
A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison …
Coupled-cluster techniques for computational chemistry: The CFOUR program package
An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of …
Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory.
This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations …
Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules
Benchmark scalar-relativistic coupled-cluster calculations for dissociation energies of the 20 diatomic molecules containing 3d transition metals in the 3dMLBE20 database ( J. Chem. Theory Comput. 2015 , 11 , 2036 ) are reported. Electron correlation and basis set effects are systematically studied. The agreement between theory and experiment is in general satisfactory. For a subset of 16 molecules, the standard deviation between computational and experimental values is 9 kJ/mol with the maximum deviation being 15 kJ/mol. The discrepancies between theory and experiment remain substantial (more than 20 kJ/mol) for VH, CrH, CoH, and FeH. To explore the source of the latter discrepancies, the …
Analytical evaluation of first-order electrical properties based on the spin-free Dirac-Coulomb Hamiltonian.
We report an analytical scheme for the calculation of first-order electrical properties using the spin-free Dirac-Coulomb (SFDC) Hamiltonian, thereby exploiting the well-developed density-matrix formulations in nonrelativistic coupled-cluster (CC) derivative theory. Orbital relaxation effects are fully accounted for by including the relaxation of the correlated orbitals with respect to orbitals of all types, viz., frozen-core, occupied, virtual, and negative energy state orbitals. To demonstrate the applicability of the presented scheme, we report benchmark calculations for first-order electrical properties of the hydrogen halides, HX with X = F, Cl, Br, I, At, and a first application to th…
Relativistic coupled-cluster calculations on XeF6: Delicate interplay between electron-correlation and basis-set effects
A systematic relativistic coupled-cluster study is reported on the harmonic vibrational frequencies of the O(h), C(3v), and C(2v) conformers of XeF6, with scalar-relativistic effects efficiently treated using the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). Atomic natural orbital type basis sets recontracted for the SFX2C-1e scheme have been shown to provide rapid basis-set convergence for the vibrational frequencies. SFX2C-1e as well as complementary pseudopotential based computations consistently predicts that both O(h) and C(3v) structures are local minima on the potential energy surface, while the C(2v) structure is a transition state. Qualitative disagre…
The bromine nuclear quadrupole moment revisited
For the bromine atom and the hydrogen bromide molecule, we report results for the electric-field gradient at the bromine nucleus based on quantum-chemical calculations. Highly accurate values are obtained by using coupled-cluster methods for the treatment of electron correlation, by minimising remaining basis-set effects through the use of large atomic-orbital sets, and by taking into account relativistic effects. For hydrogen bromide, zero-point vibrational corrections are considered as well. The obtained results for the bromine electric-field gradients are used to derive values for the Br-79 quadrupole moment: 308.1 and 309.3 mb based on data for the bromine atom and hydrogen bromide, res…
Perturbative treatment of spin-orbit-coupling within spin-free exact two-component theory using equation-of-motion coupled-cluster methods.
A scheme is reported for the perturbative calculation of spin-orbit coupling (SOC) within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) in combination with the equation-of-motion coupled-cluster singles and doubles method. Benchmark calculations of the spin-orbit splittings in 2Π and 2P radicals show that the accurate inclusion of scalar-relativistic effects using the SFX2C-1e scheme extends the applicability of the perturbative treatment of SOC to molecules that contain heavy elements. The contributions from relaxation of the coupled-cluster amplitudes are shown to be relatively small; significant contributions from correlating the inner-core orbitals are …
Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian.
We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The "picture-change" effect in the calculation of p…
Treatment of scalar-relativistic effects on nuclear magnetic shieldings using a spin-free exact-two-component approach.
A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin…