On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants.

M Natalia C Zarycz,Stephan P A Sauer,Patricio F Provasi

doi:10.1063/1.4937572

Abstract

It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH4, NH3, H2O, SiH4, PH3, SH2, C2H2, C2H4, and C2H6. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.

Highlights

Whether the number of excitedstates can be truncated in the sum-overstates expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals
The excitedstates were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J
Though, that there are four contributions to the SSCC: the Fermi contact (FC) and the spin-dipolar (SD), which come from the interaction of the nuclear magnetic moments with the spin of the electrons, as well as the diamagnetic spin orbital (DSO) and the paramagnetic spin orbital (PSO), which are due to the interaction of the nuclear spins with the orbital angular momentum of the electrons

Summary

Introduction

Whether the number of excited (pseudo)states can be truncated in the sum-overstates expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. The third class of approaches proposed by Cremer and co-workers essentially obtains the contribution of a given orbital indirectly by removing the contribution of this orbital in the coupled perturbed DFT calculations Compared to the latter two approaches the SOS or CLOPPA approach offers the advantage that the coupling constants can be analyzed in terms of a simultaneous interaction of both nuclei with the orbitals leading to coupling pathways and that one can understand the couplings in terms of contributions from different excited states. One should note that the purpose of such a truncated SOS approach is by no means to replace the more efficient linear response approach for the calculation of total coupling constants, but to reduce the computational cost in the localized orbital analysis of coupling constants via the IPPP-CLOPPA method in order to make IPPP-CLOPPA studies feasible for larger molecules

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Conclusion