scholarly journals The Effect of Hartree-Fock Exchange on Scaling Relations and Reaction Energetics for C–H Activation Catalysts

2021 ◽  
Author(s):  
Vyshnavi Vennelakanti ◽  
Aditya Nandy ◽  
Heather Kulik
Keyword(s):  
Spin State ◽  
Density Functional ◽  
Large Scale ◽  
Predictive Power ◽  
Minimum Energy ◽  
Poor Performance ◽  
Closed Shell ◽  
Open Shell ◽  
Methanol Conversion ◽  
Hartree Fock

<p>High-throughput computational catalyst studies are typically carried out using density functional theory (DFT) with a single, approximate exchange-correlation functional. In open shell transition metal complexes (TMCs) that are promising for challenging reactions (e.g., C–H activation), the predictive power of DFT has been challenged, and properties are known to be strongly dependent on the admixture of Hartree-Fock (HF) exchange. We carry out a large-scale study of the effect of HF exchange on the predicted catalytic properties of over 1,200 mid-row (i.e., Cr, Mn, Fe, Co) 3<i>d </i>TMCs for direct methane-to-methanol conversion. Reaction energetic sensitivities across this set depend both on the catalytic rearrangement and ligand chemistry of the catalyst. These differences in sensitivities change both the absolute energetics predicted for a catalyst and its relative performance. Previous observations of the poor performance of global linear free energy relationships (LFERs) hold with both semi-local DFT widely employed in heterogeneous catalysis and hybrid DFT. Narrower metal/oxidation/spin-state specific LFERs perform better and are less sensitive to HF exchange than absolute reaction energetics, except in the case of some intermediate/high-spin states. Importantly, the interplay between spin-state dependent reaction energetics and exchange effects on spin-state ordering means that the choice of DFT functional strongly influences whether the minimum energy pathway is spin-conserved. Despite these caveats, LFERs involving catalysts that can be expected to have closed shell intermediates and low-spin ground states retain significant predictive power.</p>

scholarly journals The Effect of Hartree-Fock Exchange on Scaling Relations and Reaction Energetics for C–H Activation Catalysts

2021 ◽  
Author(s):  
Vyshnavi Vennelakanti ◽  
Aditya Nandy ◽  
Heather Kulik
Keyword(s):  
Spin State ◽  
Density Functional ◽  
Large Scale ◽  
Predictive Power ◽  
Minimum Energy ◽  
Poor Performance ◽  
Closed Shell ◽  
Open Shell ◽  
Methanol Conversion ◽  
Hartree Fock

<p>High-throughput computational catalyst studies are typically carried out using density functional theory (DFT) with a single, approximate exchange-correlation functional. In open shell transition metal complexes (TMCs) that are promising for challenging reactions (e.g., C–H activation), the predictive power of DFT has been challenged, and properties are known to be strongly dependent on the admixture of Hartree-Fock (HF) exchange. We carry out a large-scale study of the effect of HF exchange on the predicted catalytic properties of over 1,200 mid-row (i.e., Cr, Mn, Fe, Co) 3<i>d </i>TMCs for direct methane-to-methanol conversion. Reaction energetic sensitivities across this set depend both on the catalytic rearrangement and ligand chemistry of the catalyst. These differences in sensitivities change both the absolute energetics predicted for a catalyst and its relative performance. Previous observations of the poor performance of global linear free energy relationships (LFERs) hold with both semi-local DFT widely employed in heterogeneous catalysis and hybrid DFT. Narrower metal/oxidation/spin-state specific LFERs perform better and are less sensitive to HF exchange than absolute reaction energetics, except in the case of some intermediate/high-spin states. Importantly, the interplay between spin-state dependent reaction energetics and exchange effects on spin-state ordering means that the choice of DFT functional strongly influences whether the minimum energy pathway is spin-conserved. Despite these caveats, LFERs involving catalysts that can be expected to have closed shell intermediates and low-spin ground states retain significant predictive power.</p>

Self-consistent Field Orbital Methods

2020 ◽  
pp. 128-149
Author(s):  
Jochen Autschbach
Keyword(s):  
Density Functional ◽  
Slater Determinant ◽  
Closed Shell ◽  
Open Shell ◽  
Initial Guess ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Definition Of

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.

Polaronic and Bipolaronic Enhancement of Second Hyperpolarizabilities in Dithienyl Polyenes from Ab Initio Quantum Methods

1999 ◽  
Vol 597 ◽  
Author(s):  
Steven Trohalaki ◽  
Robert J. Zellmer ◽  
Ruth Pachter
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Valence Bond ◽  
Closed Shell ◽  
Functional Theory ◽  
Molecular Conformations ◽  
Hartree Fock ◽  
Molecular Charge ◽  
Field Methodology ◽  
Moller Plesset

AbstractSpangler and He [1,2] have shown that dithienyl polyenes form extremely stable bipolaronic dications when oxidatively doped in solution. Previous theoretical studies applied empirical methods to predict bipolaronic enhancement of hyperpolarizabilities for simple polyenes [3,4]. Here, we employ density functional theory to optimize the gas-phase molecular conformations of neutral, cationic, and dicationic forms of a series of dithienyl polyenes, where the number of ethene units, N, is varied from 1–5. Ab initio Hartree-Fock, generalized valence bond, configuration interaction, and Møller-Plesset calculations demonstrate that the dications are farily well described with a closed shell and therefore have little biradicaloid character. Second hyperpolarizabilities, γ, are subsequently calculated using ab initio Hartree-Fock theory and a finite field methodology. As expected, γ increases with the number of ethene units for a given molecular charge. The cations also show the largest increase in γ with N. For a given value of N, the cations display the largest γ values. However, if we treat the dication as a triplet, which might be present in solution, then it displays the largest γ.

Large- Scale ab initio Simulations of Fe-doped SrTiO3 Perovskites

2002 ◽  
Vol 731 ◽  
Author(s):  
R.A. Evarestov ◽  
R.I. Eglitis ◽  
S. Piskunov ◽  
E. A. Kotomin ◽  
G. Borstel
Keyword(s):  
Energy Level ◽  
Ab Initio ◽  
High Spin ◽  
Spin State ◽  
Large Scale ◽  
Covalent Bonding ◽  
Hartree Fock ◽  
Ab Initio Simulations ◽  
Displacement Mode ◽  
Jahn Teller

AbstractUsing the Unrestricted Hartree-Fock method and supercells containing up to 160 atoms, we calculated the energy level positions in the gap and atomic geometry for the Fe4+ impurity substituting for a host Ti atom in SrTiO3. In agreement with experiment, the high spin (S=2) state is much lower in energy than the zero-spin state. The energy level positions strongly depend on the asymmetric displacement mode of the six nearest O ions which is a combination of the Jahn-Teller and breathing modes. A considerable covalent bonding between the Fe ion and four nearest O ions takes place.

scholarly journals Vibrationally and Spin-Orbit-Resolved Inner-Shell X-ray Absorption Spectroscopy of the NH+ Molecular Ion: Measurements and ab Initio Calculations

Atoms ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 67
Author(s):  
Stéphane Carniato ◽  
Jean-Marc Bizau ◽  
Denis Cubaynes ◽  
Eugene T. Kennedy ◽  
Ségolène Guilbaud ◽  
...  
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Theoretical Calculations ◽  
High Sensitivity ◽  
Open Shell ◽  
Field Configuration ◽  
High Spectral Resolution ◽  
Spin Orbit ◽  
Molecular Ion ◽  
Hartree Fock

This article presents N2+ fragment yields following nitrogen K-shell photo-absorption in the NH+ molecular ion measured at the SOLEIL synchrotron radiation facility in the photon energy region 390–450 eV. The combination of the high sensitivity of the merged-beam, multi-analysis ion apparatus (MAIA) with the high spectral resolution of the PLEIADES beamline helped to resolve experimentally vibrational structures of highly excited [N1s−1H]*+ electronic states with closed or open-shell configurations. The assignment of the observed spectral features was achieved with the help of density functional theory (DFT) and post-Hartree Fock Multiconfiguration Self-Consistent-Field/Configuration Interaction (MCSCF/CI) ab-initio theoretical calculations of the N1s core-to-valence and core-to-Rydberg excitations, including vibrational dynamics. New resonances were identified compared to previous work, owing to detailed molecular modeling of the vibrational, spin-orbit coupling and metastable state effects on the spectra. The latter are evidenced by spectral contributions from the 4Σ− electronic state which lies 0.07 eV above the NH+2Π ground state.

Quadrupole polarizabilities and Sternheimer antishielding factors in the density functional theory

1982 ◽  
Vol 60 (2) ◽  
pp. 210-221 ◽  
Author(s):  
M. J. Stott ◽  
E. Zaremba ◽  
D. Zobin
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Closed Shell ◽  
Energy Functional ◽  
Functional Theory ◽  
Hartree Fock ◽  
Shielding Factor ◽  
The Density Functional Theory

The quadrupole polarizability and Sternheimer antishielding factor have been calculated for selected closed-shell atoms and ions using the density functional theory. In most cases, the results agree favourably with coupled Hartree–Fock calculations. However, for atoms with valence (d-shells the local density approximation used in the calculations is found to be inadequate. Our results suggest that refinements to the exchange-correlation energy functional are required in order to obtain accurate values for the polarizability and shielding factor of (d-shell atoms within a density functional approach.

Simplified Non-Empirical Unrestricted Hartree-Fock Approximation (SUHF) for the Calculation of Electronic Ground State Properties of Molecules with Closed and Open Valence Shells. I. Method

1993 ◽  
Vol 48 (7) ◽  
pp. 829-833
Author(s):  
Wolfhard Koch
Keyword(s):  
Electron Correlation ◽  
Ground State ◽  
Atomic Orbital ◽  
Closed Shell ◽  
Open Shell ◽  
Polyatomic Molecules ◽  
Correlation Effects ◽  
Hartree Fock ◽  
Electron Correlation Effects ◽  
Electronic Ground

Abstract Focusing on relative stabilities of electronic states with different spin multiplicities of polyatomic molecules, a simplified unrestricted Hartree-Fock (SUHF) procedure is described. Using different orbitals for different spins (DODS), electron correlation effects of both closed-shell and open-shell systems are expected to be taken into account in the simplest way. While working within a symmetrically orthogonalized (Löwdin) basis we make use of the NDDO approximation (neglect of diatomic differential overlap) concerning the evaluation of electron repulsion and nuclear attraction integrals. Originally, a locally orthogonalized all-electron atomic orbital set of Slater type is considered. The approximation method is completely non-empirical. Rotational invariance is fully retained.

scholarly journals Covariant density functional theory: predictive power and first attempts of a microscopic derivation

2018 ◽  
Vol 178 ◽  
pp. 02001
Author(s):  
Peter Ring
Keyword(s):  
Nuclear Matter ◽  
Density Functional ◽  
Predictive Power ◽  
Tensor Force ◽  
Density Functionals ◽  
Functional Theory ◽  
Hartree Fock ◽  
Microscopic Derivation ◽  
Nuclear Systems ◽  
Covariant Density

We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

Balancing DFT Interaction Energies in Charged Dimers Precursors to Organic Semiconductors

2019 ◽  
Author(s):  
Alberto Fabrizio ◽  
Riccardo Petraglia ◽  
Clemence Corminboeuf
Keyword(s):  
Organic Semiconductors ◽  
Density Functional ◽  
Radical Cations ◽  
Closed Shell ◽  
Open Shell ◽  
Binding Energies ◽  
Interaction Energies ◽  
Functional Theory ◽  
Energy Profiles ◽  
London Dispersion

Accurately describing intermolecular interactions within the framework of Kohn-Sham density functional theory (KS-DFT) has resulted in numerous benchmark databases over the past two decades. By far, the largest efforts have been spent on closed-shell, neutral dimers for which today, the interaction energies and geometries can be accurately reproduced by various combinations of dispersion-corrected density functional approximations (DFAs). In sharp contrast, charged, open-shell dimers remain a challenge as illustrated by the analysis of the OREL26rad benchmark set consisting of pi-dimer radical cations. Aside from the methodological aspect, achieving a proper description of radical cationic complexes is appealing due to their role as models for charge carriers in organic semiconductors. In the interest of providing an assessment of more realistic dimer systems, we construct a dataset of large radical cationic dimers (CryOrel) and jointly train the 19 parameters of a dispersion corrected, range-separated hybrid density functional (wB97X-dDsC), with the objective of providing the maximum balance between the treatment of long-range London dispersion and reduction of the delocalization error. These conditions are essential to obtain accurate energy profiles and binding energies of charged, open-shell dimers. Comparisons with the performance of the parent wB97X functional series and state-of-the-art wavefunction based methods are provided. <br>

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