Pekka Manninen

Perturbational ab initio calculations of relativistic contributions to nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the leading-order one-electron relativistic contributions to the nuclear magnetic resonance shielding tensor based on the Pauli Hamiltonian. The scalar relativistic and spin–orbit interaction effects, including both relativistic corrections to the wave function (“passive” relativistic effects) and relativistic magnetic perturbation operators (“active” effects), are considered for H2X (X=O, S, Se, Te, Po), HX (X=F, Cl, Br, I, At), and noble gas (Ne, Ar, Kr, Xe, Rn) systems. The perturbational corrections are calculated using linear and quadratic response theory applied to nonrelativistic reference states. We use the uncorrelated self-consistent field as well as correlated, multiconfigurational complete active space self-consistent field models. Results for the 1H and heavy-atom shielding constants and anisotropies are compared with Dirac–Hartree–Fock and quasirelativistic data.

Leading-order relativistic effects on nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.

Systematic Gaussian basis-set limit using completeness-optimized primitive sets. A case for magnetic properties

We discuss the connection between the completeness of a basis set, measured by the completeness profiles introduced by Chong (Can J Chem 1995, 73, 79) at a certain exponent interval, and the possibility of reproducing molecular properties that arise either in the region close to the atomic nuclei or in the valence region. We present a scheme for generating completeness‐optimized Gaussian basis sets, in which a preselected range of exponents is covered to an arbitrary accuracy. This is done by requiring Gaussian functions, the exponents of which are selected without reference to the atomic structure, to span the range with completeness profile as close to unity as wanted with as few functions as possible. The initial exponent range can be chosen suitable for calculations of molecular energetics or other valence‐like properties. By extending the exponent range, properties requiring augmentation of the basis at a given angular momentum value and/or in a given distance range from the nucleus may be straightforwardly and systematically treated. In this scheme a universal, element‐independent exponent set is generated in an automated way. The relation of basis‐set completeness and performance in the calculation of magnetizability, nuclear magnetic shielding, and spin–spin coupling is tested with the completeness‐optimized primitive sets and literature basis sets.

Coupled-cluster theory in a projected atomic orbital basis

We present a biorthogonal formulation of coupled-cluster (CC) theory using a redundant projected atomic orbital (PAO) basis. The biorthogonal formulation provides simple equations, where the projectors involved in the definition of the PAO basis are absorbed in the integrals. Explicit expressions for the coupled-cluster singles and doubles equations are derived in the PAO basis. The PAO CC equations can be written in a form identical to the standard molecular orbital CC equations, only with integrals that are related to the atomic orbital integrals through different transformation matrices. The dependence of cluster amplitudes, integrals, and correlation energy contributions on the distance between the participating atomic centers and on the number of involved atomic centers is illustrated in numerical case studies. It is also discussed how the present reformulation of the CC equations opens new possibilities for reducing the number of involved parameters and thereby the computational cost.

General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory

With low-order scaling correlated wave function theories in mind, we present second quantization formalism as well as biorthonormalization procedures for general--singular or nonsingular--bases. Of particular interest are the so-called projected atomic orbital bases, which are obtained from a set of atom-centered functions and feature a separation of occupied and virtual spaces. We demonstrate the formalism by deriving and implementing second-order Møller-Plesset perturbation theory in it, and discuss the convergence and preconditioning of the iterative amplitude equations in detail.

Perturbational calculations of parity-violating effects in nuclear-magnetic-resonance parameters.

We investigate the effects of the parity-violating electroweak interaction in the spectral parameters of nuclear magnetic resonance. Perturbational theory of parity-violating effects in the nuclear magnetic shielding is presented to the order of G(F)alpha, and in the indirect spin-spin coupling, to the order of G(F)alpha3. These leading-order parity-violating corrections are evaluated using analytical linear-response theory methods based on Hartree-Fock and density-functional theory reference states. Parity-violating contributions to spin-spin couplings are evaluated for the first time at the first-principles level. Calculations are carried out for two chiral halomethanes, bromochlorofluoromethane and bromofluoroiodomethane.

NMR tensors in planar hydrocarbons of increasing size

(13)C nuclear shielding and (13)C-(13)C spin-spin coupling tensors were calculated using density functional theory linear response methods for a series of planar hydrocarbons. As calculation of the spin-spin coupling is computationally demanding for large molecules due to demands placed on basis-set quality, novel, compact completeness-optimized (co) basis sets of high quality were employed. To maximize the predictive value of the data, the convergence of the co basis sets was compared to well-known basis-set families. The selection of the exchange-correlation functional was performed based on the available experimental data and coupled-cluster calculations for ethene and benzene. The series of hydrocarbons, benzene, coronene, circumcoronene and circumcircumcoronene, was chosen to simulate increasingly large fragments of carbon nanosheets. It was found that the nuclear shielding and the one-, two-, and three-bond spin-spin coupling constants, as well as the corresponding anisotropies with respect to the direction normal to the plane, approach convergence as the number of carbon atoms in the fragment is increased. Predictions of the investigated properties can then be done for the limit of large planar hydrocarbons or carbon nanosheets. From the results obtained with a judicious choice of the functional, PBE, and co basis close to convergence, limiting values are estimated as follows: sigma = 54 +/- 1 ppm [corresponding to the chemical shift of 134 ppm with methane (CH(4)) as a reference], Deltasigma = 207 +/- 4 ppm, (1)J = 59.0 +/- 0.5 Hz, Delta(1)J = -1.5 +/- 0.5 Hz, (2)J = 0.2 +/- 0.4 Hz, Delta(2)J = -4.6 +/- 0.2 Hz, (3)J = 6 +/- 1 Hz, and Delta(3)J = 3 +/- 1 Hz.

Laser-induced nuclear magnetic resonance splitting in hydrocarbons

Irradiation of matter with circularly polarized light (CPL) shifts all nuclear magnetic resonance (NMR) lines. The phenomenon arises from the second-order interaction of the electron cloud with the optical field, combined with the orbital hyperfine interaction. The shift occurs in opposite directions for right and left CPL, and rapid switching between them will split the resonance lines into two. We present ab initio and density functional theory predictions of laser-induced NMR splittings for hydrocarbon systems with different sizes: ethene, benzene, coronene, fullerene, and circumcoronene. Due to the computationally challenging nature of the effect, traditional basis sets could not be used for the larger systems. A novel method for generating basis sets, mathematical completeness optimization, was employed. As expected, the magnitude of the spectral splitting increases with the laser beam frequency and polarizability of the system. Massive amplification of the effect is also observed close to the optical excitation energies. A much larger laser-induced splitting is found for the largest of the present molecules than for the previously investigated noble gas atoms or small molecules. The laser intensity required for experimental detection of the effect is discussed.

Magnetic field dependence of nuclear magnetic shielding in closed-shell atomic systems

Abstract We present a response theory formulation for the dependence of nuclear magnetic shielding on the external magnetic field B 0 in closed-shell atomic systems. The dependence appears in even powers of B 0 , and we include terms up to the sixth power of the field. Calculations are carried out for the field-dependence coefficient τ for noble gas atoms as well as halogen and alkali metal ions, based on a nonrelativistic reference state, using self-consistent field (SCF) and correlated multiconfigurational SCF linear and nonlinear response methods.

Completeness-optimized basis sets: application to ground-state electron momentum densities.

In the current work we apply the completeness-optimization paradigm [P. Manninen and J. Vaara, J. Comput. Chem. 27, 434 (2006)] to investigate the basis set convergence of the moments of the ground-state electron momentum density at the self-consistent field level of theory. We present a black-box completeness-optimization algorithm that can be used to generate computationally efficient basis sets for computing any property at any level of theory. We show that the complete basis set (CBS) limit of the moments of the electron momentum density can be reached more cost effectively using completeness-optimized basis sets than using conventional, energy-optimized Gaussian basis sets. By using the established CBS limits, we generate a series of smaller basis sets which can be used to systematically approach the CBS and to perform calculations on larger, experimentally interesting systems.