scholarly journals Hyperfine Coupling Constants in Local Exact Two-Component Theory

2021 ◽  
Author(s):  
Yannick J. Franzke ◽  
Jason M. Yu
Keyword(s):  
Single Molecule ◽  
Density Functional ◽  
Hyperfine Coupling ◽  
Scalar Potential ◽  
Coupling Constants ◽  
Basis Set ◽  
Basis Sets ◽  
Spin Orbit ◽  
Finite Nucleus ◽  
Two Component

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, i.e. the derivatives of the unitary decoupling transformation are considered. This requires solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened-nuclear spin--orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12--17 transition-metal compounds. The error introduced by DLU is negligible and the DLU-X2C Hamiltonian accurately reproduces its four-component ``fully'' relativistic parent results. Functionals with a large amount of Hartree--Fock exchange such as CAM-QTP-02 and omega-B97X-D are generally favorable. The pure density functional r2SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-zeta bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C6Cl5)4]- with more than 4700 primitive basis functions and four rare-earth single molecule magnets: [La(OAr*)3]-, [Lu(NR2)3]-, [Lu(OAr*)3]-, and [TbPc2]-. Here, the spin--orbit DLU-X2C Hamiltonian results in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

Hyperfine Coupling Constants in Local Exact Two-Component Theory

2021 ◽  
Author(s):  
Yannick J. Franzke ◽  
Jason M. Yu
Keyword(s):  
Single Molecule ◽  
Density Functional ◽  
Hyperfine Coupling ◽  
Scalar Potential ◽  
Coupling Constants ◽  
Basis Set ◽  
Basis Sets ◽  
Spin Orbit ◽  
Finite Nucleus ◽  
Two Component

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, i.e. the derivatives of the unitary decoupling transformation are considered. This requires solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened-nuclear spin--orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12--17 transition-metal compounds. The error introduced by DLU is negligible and the DLU-X2C Hamiltonian accurately reproduces its four-component ``fully'' relativistic parent results. Functionals with a large amount of Hartree--Fock exchange such as CAM-QTP-02 and omega-B97X-D are generally favorable. The pure density functional r2SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-zeta bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C6Cl5)4]- with more than 4700 primitive basis functions and four rare-earth single molecule magnets: [La(OAr*)3]-, [Lu(NR2)3]-, [Lu(OAr*)3]-, and [TbPc2]-. Here, the spin--orbit DLU-X2C Hamiltonian results in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

A density functional theory approach to the magnetic properties of a coupled single-molecule magnet (Mn7)2 complex — An entangled qubit pair candidate

2013 ◽  
Vol 91 (9) ◽  
pp. 866-871 ◽  
Author(s):  
Silvia Gómez-Coca ◽  
Eliseo Ruiz
Keyword(s):  
Density Functional Theory ◽  
Single Molecule ◽  
Exchange Coupling ◽  
Density Functional ◽  
Relative Strength ◽  
Coupling Constants ◽  
Basis Set ◽  
Theory Approach ◽  
Functional Theory ◽  
Spin Configuration

The exchange coupling constants of a Mn14 complex constituted by two weakly coupled Mn7 moieties were calculated using two different density functional theory (DFT) approaches: the Perdew–Burke–Ernzerhof (PBE) functional with a numerical basis set and the hybrid Becke, three-parameter Lee–Yang–Parr (B3LYP) functional employed with a Gaussian basis set. The sign and relative strength of the exchange coupling constants calculated with both methods were consistent; as expected, the values calculated with the PBE functional were slightly overestimated, as corroborated by comparison with the experimental magnetic susceptibility curve. Both methods gave a ground spin configuration of S = 3/2 for the Mn7 moiety, which was weakly antiferromagnetically coupled with the other Mn7 fragment, leading to an S = 0 ground spin configuration for the entire Mn14 complex.

COMPARATIVE QUANTUM STUDY ON TERT-BUTYL RADICAL AND CATION

2011 ◽  
Vol 10 (03) ◽  
pp. 325-348 ◽  
Author(s):  
ANNA IGNACZAK
Keyword(s):  
Density Functional ◽  
Structural Parameters ◽  
Coupling Constants ◽  
Basis Set ◽  
Basis Sets ◽  
Inversion Barrier ◽  
Gaussian Basis Sets ◽  
Dft Methods ◽  
Tert Butyl ◽  
Butyl Radical

Detailed comparative analysis of properties of the tert-butyl radical and cation is performed using 14 density functional (DFT) methods combined with double-zeta and triple-zeta quality Gaussian basis sets with polarization and diffuse functions. Stability of different conformers is discussed. Structural parameters, dipole moment, adiabatic ionization potential (IP), inversion barrier and isotropic hyperfine coupling constants are examined and compared to values obtained at the standard MP2 level and to experimental data available. All methods indicate that that the CC bond in the radical is longer than in the cation by about 0.033 Å. The IP values are found to be very sensitive to the method used and range from 612 to 709 kJ/mol, but majority oscillate around 646÷656 kJ/mol. Calculated inversion barrier for the radical is higher than the experimental estimate of 2.68 kJ/mol; with the 6-311++G** basis set and most DFT methods it is predicted in the range 3.86÷4.82 kJ/mol. All DFT methods predict for the out-of-plane CC3 bending mode of the radical the frequency around 260 cm-1, while in the cation the corresponding frequency is higher by about 180 cm-1.

scholarly journals Factors Governing the Chemical Stability and NMR Parameters of Uracil Tautomers and Its 5-Halogen Derivatives

Molecules ◽  
2020 ◽  
Vol 25 (17) ◽  
pp. 3931 ◽  
Author(s):  
Kacper Rzepiela ◽  
Aneta Buczek ◽  
Teobald Kupka ◽  
Małgorzata A. Broda
Keyword(s):  
Electrostatic Interactions ◽  
Density Functional ◽  
Chemical Shifts ◽  
Polarizable Continuum Model ◽  
Coupling Constants ◽  
Spin Coupling ◽  
Basis Set ◽  
Basis Sets ◽  
Nmr Parameters ◽  
Solvent Model

We report on the density functional theory (DFT) modelling of structural, energetic and NMR parameters of uracil and its derivatives (5-halogenouracil (5XU), X = F, Cl, Br and I) in vacuum and in water using the polarizable continuum model (PCM) and the solvent model density (SMD) approach. On the basis of the obtained results, we conclude that the intramolecular electrostatic interactions are the main factors governing the stability of the six tautomeric forms of uracil and 5XU. Two indices of aromaticity, the harmonic oscillator model of aromaticity (HOMA), satisfying the geometric criterion, and the nuclear independent chemical shift (NICS), were applied to evaluate the aromaticity of uracil and its derivatives in the gas phase and water. The values of these parameters showed that the most stable tautomer is the least aromatic. A good performance of newly designed xOPBE density functional in combination with both large aug-cc-pVQZ and small STO(1M)−3G basis sets for predicting chemical shifts of uracil and 5-fluorouracil in vacuum and water was observed. As a practical alternative for calculating the chemical shifts of challenging heterocyclic compounds, we also propose B3LYP calculations with small STO(1M)−3G basis set. The indirect spin–spin coupling constants predicted by B3LYP/aug-cc-pVQZ(mixed) method reproduce the experimental data for uracil and 5-fluorouracil well.

scholarly journals Magnetic Exchange Interactions in Binuclear and Tetranuclear Iron (III) Complexes Described by Spin-Flip DFT and Heisenberg Effective Hamiltonians

2021 ◽  
Author(s):  
Saikiran Kotaru ◽  
Maristella Alessio ◽  
Anna I. Krylov
Keyword(s):  
Single Molecule ◽  
Density Functional ◽  
Exchange Interactions ◽  
Coupling Constants ◽  
Basis Set ◽  
Energy Separation ◽  
Ionic Character ◽  
Binuclear Complexes ◽  
Effective Spin ◽  
Spin Flip

Low-energy spectra of single-molecule magnets (SMMs) are often described by the Heisenberg Hamiltonian. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For the series of binuclear complexes with J-values ranging from -6 to -132 cm−1 , our benchmark calculations using the short-range hybrid LRC-ωPBEh functional and 6-31G(d,p) basis set agree well (mean absolute error of 4.7 cm−1) with the experimentally derived values. For the tetranuclear SMMs, the computed J constants are within 6 cm−1 from the values extracted from the experiment. We explore the range of applicability of the Heisenberg model by analyzing the radical character in the binuclear iron (III) complexes using natural orbitals (NO) and their occupations. On the basis of the number of effectively unpaired electrons and the NO occupancies, we attribute larger errors observed in strongly anti-ferromagnetic species to an increased ionic character. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

scholarly journals Magnetic Exchange Interactions in Binuclear and Tetranuclear Iron (III) Complexes Described by Spin-Flip DFT and Heisenberg Effective Hamiltonians

2021 ◽  
Author(s):  
Saikiran Kotaru ◽  
Maristella Alessio ◽  
Anna I. Krylov
Keyword(s):  
Single Molecule ◽  
Density Functional ◽  
Exchange Interactions ◽  
Coupling Constants ◽  
Basis Set ◽  
Energy Separation ◽  
Ionic Character ◽  
Binuclear Complexes ◽  
Effective Spin ◽  
Spin Flip

Low-energy spectra of single-molecule magnets (SMMs) are often described by the Heisenberg Hamiltonian. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For the series of binuclear complexes with J-values ranging from -6 to -132 cm−1 , our benchmark calculations using the short-range hybrid LRC-ωPBEh functional and 6-31G(d,p) basis set agree well (mean absolute error of 4.7 cm−1) with the experimentally derived values. For the tetranuclear SMMs, the computed J constants are within 6 cm−1 from the values extracted from the experiment. We explore the range of applicability of the Heisenberg model by analyzing the radical character in the binuclear iron (III) complexes using natural orbitals (NO) and their occupations. On the basis of the number of effectively unpaired electrons and the NO occupancies, we attribute larger errors observed in strongly anti-ferromagnetic species to an increased ionic character. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

Theoretical Study of the Vertical Electronic Spectra, Electron-Spin g-Factors and Hyperfine Coupling Constants of the (C2v) Cyclic Radicals C3+, Si3+, C3− and Si3−

2003 ◽  
Vol 217 (3) ◽  
pp. 265-288 ◽  
Author(s):  
P. J. Bruna ◽  
F. Grein
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Bound States ◽  
Hyperfine Coupling ◽  
Coupling Constants ◽  
Basis Sets ◽  
Dft Methods ◽  
Functional Theory ◽  
Hyperfine Coupling Constants ◽  
Vertical Transition

AbstractThe vertical transition energies and Δg-values of cyclic C3+, Si3+ (X2B2), C3− (12A1, metastable) and Si3− (X2A1) are studied with ROHF MOs, multireference (MRDCI) wavefunctions and 6-311+G(2d) basis sets. Si3− has at least eight bound states. For each radical, the in-plane components of the g shift, Δgyy and Δgzz (with gii = ge + Δgii), have similar negative values (about −1200 ppm for C3+, C3− and about −8000 ppm for Si3+, Si3−). The Δgxx’s are larger in magnitude, negative for C3+, Si3+ (−11000 and −72000 ppm) but positive for C3−, Si3− (8000 and 165000 ppm). The hyperfine coupling constants Aiso, Adip are evaluated with ab initio CISD, QCISD, CCD, MP4SDQ methods as well as with density functional theory (DFT) methods (SVWN, B3LYP, B3PW91, PW91PW91), using a spin-unrestricted formalism; several basis sets are considered. Both approaches give internally consistent Aiso’s and Adip’s for each X3− center, with the (positive) s-spin-density at each basal atom (average Aiso (MHz) = 75 for C3− and −25 for Si3−) being smaller than at the apical center (275 and −95 MHz). The results are less satisfactory for X3+. All treatments agree, more or less, in a larger (positive) s-density at the basal atoms (Aiso(MHz) from 300 to 700 for C3+, and −80 to −150 for Si3+), whereas the s-contribution at the apical center depends on the method: for C3+, it is positive with ab initio but negative with DFT, whereas for Si3+ the opposite trend is found; as well, Adip(X3+) shows unusually large discrepancies for each center. For these radicals, literature values of Aiso and Adip are not available, either from experimental or multireference ab initio studies, to allow for comparisons with our results.

Benchmark of Simplified Time-Dependent Density Functional Theory for UV-Vis Spectral Properties of Porphyrinoids

2019 ◽  
Author(s):  
Kamal Batra ◽  
Stefan Zahn ◽  
Thomas Heine
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Large Scale ◽  
Absolute Error ◽  
Time Dependent ◽  
Basis Set ◽  
Basis Sets ◽  
Functional Theory ◽  
Framework Materials ◽  
Dependent Density

<p>We thoroughly benchmark time-dependent density- functional theory for the predictive calculation of UV/Vis spectra of porphyrin derivatives. With the aim to provide an approach that is computationally feasible for large-scale applications such as biological systems or molecular framework materials, albeit performing with high accuracy for the Q-bands, we compare the results given by various computational protocols, including basis sets, density-functionals (including gradient corrected local functionals, hybrids, double hybrids and range-separated functionals), and various variants of time-dependent density-functional theory, including the simplified Tamm-Dancoff approximation. An excellent choice for these calculations is the range-separated functional CAM-B3LYP in combination with the simplified Tamm-Dancoff approximation and a basis set of double-ζ quality def2-SVP (mean absolute error [MAE] of ~0.05 eV). This is not surpassed by more expensive approaches, not even by double hybrid functionals, and solely systematic excitation energy scaling slightly improves the results (MAE ~0.04 eV). </p>

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

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