Analytic gradients for spin multiplets in natural orbital functional theory

Time evolution of natural orbitals in ab initio molecular dynamics

This work combines for the first time ab initio molecular dynamics (AIMD) within the Born-Oppenheimer approximation with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is its ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N(4S) + H2(1Σ) → NH(3Σ) + H(2S) is taken as a validation test. Collision energy influences on integral cross sections for different initial rovibrational states of H2 and rotational-state distributions of the NH product are discussed, showing a good agreement with previous high-quality theoretical results.

Outstanding improvement in removing the delocalization error by global natural orbital functional

This work assesses the performance of the recently proposed global natural orbital functional (GNOF) against the charge delocalization error. GNOF provides a good balance between static and dynamic electronic correlations leading to accurate total energies while preserving spin, even for systems with a highly multi-configurational character. Several analyses were applied to the functional, namely, (i) how the charge is distributed in super-systems of two fragments, (ii) the stability of ionization potentials while increasing the system size, and (iii) potential energy curves of a neutral and charged diatomic system. GNOF was found to practically eliminate the charge delocalization error in many of the studied systems or greatly improve the results obtained previously with PNOF7.

Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

The relative stability of the singlet, triplet, and quintet spin states of iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wave function-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double-ζ basis set as used in this work, this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s, and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via second-order Møller-Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.

Spectroscopic properties of open shell diatomic molecules using Piris natural orbital functionals

Spectroscopic properties such as equilibrium distances, vibrational constants, rotational constants, dissociation energies, and excitation energies are calculated for nine heteronuclear diatomic molecules (PH, NF, NH, NO, CS, AlF, ClF, BeO and CF) using an interactive pair model (PNOF7s), that has been generalized for spin multiplet states, and its second order perturbation variant, NOF-MP2, which was also generalized for multiplets. The results obtained are compared with Complete Active Space (CASSCF) and Complete Active Space Perturbation Theory (CASPT2). It is shown that the potential energy curves provided by the PNOF functional for open shell diatomic molecules are in acceptable agreement with those from CASSCF and CASPT2. The spectroscopic constants depending at most on the second derivative of the potential energy are in good agreement with experiment, while those requiring the evaluation of the third and fourth derivatives show larger deviations from experiment and from those predicted by CASPT2. Thus, it is shown that the PNOF functional extension to multiplets is an alternative approach in predicting spectroscopic constants of molecules where static correlation plays an important role, like the open shell heteronuclear diatomic molecules studied in this work.