Density functional theory of born couplings: Consequences for electron flow in Jahn–Teller molecules and superconductors

The dynamics of Jahn–Teller systems has recently been discussed in terms of generalized electronic charge and current densities in nuclear-coordinate space. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, was a crucial component of this formulation. Here, a densitybased treatment of Born couplings is derived from first-principles quantum mechanics beyond the Born–Oppenheimer approximation. Because of the degenerate electronic configuration of a Jahn–Teller molecule, there are an infinite number of ways in which the charge distribution can be oriented for the same energy, leading to a vanishing bond hardness for the molecule in the symmetric nuclear configuration. Further, the moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, leading to unhindered rotation of the charge cloud. This leads to the dynamical Jahn–Teller problem, namely, the coupling of electronic and nuclear motions through the Born coupling terms. Applications to superconductivity theory are discussed. © 1995 John Wiley & Sons, Inc.     

Pseudo Jahn–Teller effects of triphenylene dianion

Pseudo Jahn–Teller effects of triphenylene dianion were discussed by molecular orbital method. While the triplet ground state preferred a D_3h geometry, singlet states were subject to symmetry lowering to have C_2v geometries. The resultant geometries were rationalized to amplitude patterns of the degenerate frontier orbitals.     

Finding transition states when second-order Jahn–Teller instability occurs

When second-order Jahn–Teller couplings become strong along “streambeds” on potential energy surfaces, instability reflected in negative curvature along a symmetry-lowering distortion coordinate can take place. The point where such negative curvature sets in is usually not a transition state because the gradient of the potential is usually large there. In this paper, it is demonstrated how to use the local energy, local gradient, local Hessian, and knowledge of how quickly the curvature for the symmetry-breaking mode evolves along the streambed (i.e., the derivative of this curvature) to predict how far to move in the symmetry-breaking mode in search of the desired transition state. It is shown that the Hessian matrix evaluated at the symmetry-broken geometry suggested by this analysis has only one negative eigenvalue. Because this analysis is based on a local approximation to the potential, its predictions are, of course, approximate. As such, they only “suggest” the proper direction and magnitude that one should “step” to move toward a transition state. © 1993 John Wiley & Sons, Inc.     

Geometrical configurations of Pu4 and the Jahn–Teller effect

The present work has found seven stable geometrical configurations of Pu₄ using the density functional method Becke3LYP with relativistic effective core potentials (RECP). Based on the Jahn–Teller effect, vibronic interaction and the resolution of group representations, the analysis of the relationships among these various geometrical configurations is in fair agreement with the calculated results. It is found that the spin–polarization effect is rather important for the plutonium clusters and, in general, actinide element molecules.     

Dynamic nonlinear Jahn–Teller effect of the type E ⊗ ϵ

By applying the projection operator method it is shown that the complicated Hamiltonian of a E ? ? JT system with nonlinear coupling coefficients can be written in terms of two Hamiltonians which are simple to handle and transform according to irreducible representations E, A₁, and A₂ of C_3v point group. A variational approach is then used to calculate the ground state energy, using the Hamiltonian that transforms according to E, as an explicit function of the linear and nonlinear coupling parameters. The energies calculated in the strong coupling limit are finally compared with the corresponding previously calculated energies.     

Density functional theory for systems of very many atoms

The standard Kohn-Sham formulation of density functional theory (DFT ) is limited, for practical reasons, to systems of less than about 50-100 atoms. The computational effort scales as N, where N_at is the number of atoms and 2 < α > 3. (By comparison, conventional configuration interaction methods are limited to 5-10 atom systems.) This article deals with the prospect of practical methods that scale linearly in N_at and may thus allow calculations for systems of 10³-104 atoms. The physical reason (“near-sightedness”) for linear scaling is presented. Implementations of linear scaling DFT by the use of generalized Wannier functions or the one-particle density matrix are discussed. © 1995 John Wiley & Sons, Inc.     

Density functional theory of field theoretical systems

The field theoretical background of relativistic density functional theory is emphasized and its consequences for relativistic Kohn-Sham equations are shown. The local density approximation for the exchange energy functional is reviewed and the importance of relativistic corrections for an accurate representation of the exchange functional is demonstrated. © 1995 John Wiley & Sons, Inc.     

A Genuine Jahn–Teller System with Compressed Geometry and Quantum Effects Originating from Zero‐Point Motion

First‐principle calculations together with analysis of the experimental data found for 3d⁹ and 3d⁷ ions in cubic oxides proved that the center found in irradiated CaO:Ni²⁺ corresponds to Ni⁺ under a static Jahn–Teller effect displaying a compressed equilibrium geometry. It was also shown that the anomalous positive g_∥ shift (g_∥?g₀=0.065) measured at T=20 K obeys the superposition of the |3 z²?r²? and |x²?y²? states driven by quantum effects associated with the zero‐point motion, a mechanism first put forward by O'Brien for static Jahn–Teller systems and later extended by Ham to the dynamic Jahn–Teller case. To our knowledge, this is the first genuine Jahn–Teller system (i.e. in which exact degeneracy exists at the high‐symmetry configuration) exhibiting a compressed equilibrium geometry for which large quantum effects allow experimental observation of the effect predicted by O'Brien. Analysis of the calculated energy barriers for different Jahn–Teller systems allowed us to explain the origin of the compressed geometry observed for CaO:Ni⁺.     

Jahn–Teller Effect in Circulenes: X‐ray Diffraction Study of Coronene and Corannulene Radical Anions

Single‐crystal X‐ray diffraction studies of two polyaromatic radical anions crystallized as sodium salts, namely [Na(DME)₃]⁺[C₂₀H₁₀^?] ( 1 ) and [Na(DME)₃]⁺[C₂₄H₁₂^?] ( 2 ) are reported. This allowed the first structural evaluation of Jahn–Teller (JT) effects for monoreduced circulenes and a comparison between bowl‐shaped corannulene and planar coronene. The C_s and D_2h symmetrical distortions are found to fit the experimental data for C₂₀H₁₀^.? and C₂₄H₁₂^.?, respectively. The continuous symmetry measure (CSM) analysis was carried out to provide a quantitative measure of the JT distortions in 1 and 2 . In addition, the X‐ray crystallographic results were fully supported by DFT calculations.     

Density functional theory for triplet superconductors

The density functional theory of superconductivity is extended to triplet superconductors and superfluid helium 3. We prove a Hohenberg-Kohn-type theorem for these systems and derive effective single-particle equations. The latter include exchange and correlations in a formally exact way and allow the treatment of both electronic and phonon-induced superconductivity. The relation of this approach to the Bogolubov-de Gennes mean-field theory and to phenomenological theories based on Ginzburg-Landau functionals is discussed. © 1997 John Wiley & Sons, Inc.     

Density functional theory for Yukawa fluids

We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.     

Density functional theory for excited states

In this article, we justify the use of standard Kohn-Sham (KS ) band structure theory for the calculation of the low-energy spectrum of metals and the density of states. For the higher spectrum, one can start the KS excited-state calculations by using as the first-order approximation the spin orbitals of the ground state. We next deal with the problem of degenerate states by using the subspace theory minimum principle. © 1995 John Wiley & Sons, Inc.     

Orbit–orbit interaction in the NO–Fe(II)Hemoproteins studied by the low-temperature magnetic circular dichroism: Dynamic Jahn–Teller effect detected by MCD

This paper analyzes the low-temperature magnetic circular dichroism of NO–Fe(II)hemoproteins in detail. We include the Jahn–Teller effect in our consideration of the low-temperature MCD results.     

Density functional theory and Hartree–Fock-density functional theory calculations of O, S, and Ge quadrupole coupling constants

The performance of several density functional theory and Hartree–Fock density functional theory methods in conjunction with Pople type bases for the calculation of ¹⁷O, ³³S, and ⁷³Ge quadrupole coupling constants in gaseous state molecules was investigated.Assessment of the several models was made by linear regression analysis of the calculated gradient of the molecular electric field versus the experimental nuclear quadrupole coupling constant (NQCCs). Calculations for oxygen on six molecules with the B3LYP/6-311++G(3df,3p) model yield a residual standard deviation of 0.057 MHz (1.4%); for sulfur on 12 molecules with the B3LYP/6-311G(3df,3p) model, 0.42 MHz (1.8%); and for germanium on nine molecules with the B3P86/6-311G(2d) model, 0.83 MHz (1.0%).In the case of germyl acetylene, our calculations indicate that the experimental NQCC reported some time ago by Thomas and Laurie [J. Chem. Phys. 44 (1966) 2602] was incorrectly assigned with respect to algebraic sign.Predictions are made of the ¹⁷O and ³³S NQCCs in furan, 4H-pyran-4-one, 4H-pyran-4-thione, and 4H-thiapyran-4-thione; and of the ⁷³Ge NQCC in germyl bromide.     

An Unusual Stable Mononuclear MnIII Bis‐terpyridine Complex Exhibiting Jahn–Teller Compression: Electrochemical Synthesis,Physical Characterisation and Theoretical Study

The mononuclear manganese bis‐terpyridine complex [Mn(tolyl‐terpy)₂](X)₃ ( 1 (X)₃; X=BF₄, ClO₄, PF₆; tolyl‐terpy=4′‐(4‐methylphenyl)‐2,2′:6′,2“‐terpyridine), containing Mn in the unusual +III oxidation state, has been isolated and characterised. The 1 ³⁺ ion is a rare example of a mononuclear Mn^III complex stabilised solely by neutral N ligands. Complex 1 ³⁺ is obtained by electrochemical oxidation of the corresponding Mn^II compound 1 ²⁺ in anhydrous acetonitrile. Under these conditions the cyclic voltammogram of 1 ²⁺ exhibits not only the well‐known Mn^II/Mn^III oxidation at E_1/2=+0.91 V versus Ag/Ag⁺ (+1.21 V vs. SCE) but also a second metal‐based oxidation process corresponding to Mn^III/Mn^IV at E_1/2=+1.63 V (+1.93 V vs. SCE). Single crystals of 1 (PF₆)₃?2 CH₃CN were obtained by an electrocrystallisation procedure. X‐ray analysis unambiguously revealed its tetragonally compressed octahedral geometry and high‐spin character. The electronic properties of 1 ³⁺ were investigated in detail by magnetic measurements and theoretical calculations, from which a D value of +4.82 cm^?1 was precisely determined. Density functional and complete active space self consistent field ab initio calculations both correctly predict a positive sign of D, in agreement with the compressed tetragonal distortion observed in the X‐ray structure of 1 (PF₆)₃?2 CH₃CN. The different contributions to D were calculated, and the results show that 1) the spin–orbit coupling part (+2.593 cm^?1) is predominant compared to the spin–spin interaction (+1.075 cm^?1) and 2) the excited triplet states make the dominant contribution to the total D value.     

Density functional theory of chemical reactivity indices in some ion—molecule reaction systems

Three isoelectronic reactions, proton transfer (PT ), hydrogen abstraction (HA ), and electron transfer (ET ), of NH⁺₃ with NH,₃ H₂O, and HF have been studied using ab initio molecular orbital calculations. For the reaction of NH⁺₃ + H₂O, the energy of the transition state (TS) is higher than that of the reactants. This is consistent with the experimental observation that the rate constant is less than the average dipole orientation (ADO) rate constant. It seems reasonable that the reaction rate for the reaction NH⁺₃ + H₂O would hardly depend on the v₂ mode of NH⁺₃ at least for low-lying excited states (E_int≤ 0.714 eV) of the v₂ mode, because the v₂ mode contributes mainly to the normal mode orthogonal to the reaction coordinate at the TS . This is consistent with experimental observation. A similar prediction can be made for the NH⁺₃ + HF reaction. The electron-transfer processes for the HA reactions have been examined in terms of the intrinsic reaction coordinate (IRC ). The order of reactivity with NH⁺₃ is NH₃ > H₂O > HF. It is found that the degree of the electron transfer and the reactivity are correlated with the absolute hardness (η) of NH₃, H₂O, and HF. This is in accord with the softness as the chemical reactivity index in the density functional theory. © 1996 John Wiley & Sons, Inc.