Calculation of nonadiabatic couplings in density-functional theory

This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.     

Time-dependent density-functional theory calculations of triplet-triplet absorption

We present density-functional theory calculations of triplet-triplet absorption by three different approaches based on time-dependent density-functional theory (DFT): unrestricted DFT linear response, open-shell restricted DFT linear response applied to the triplet state, and quadratic response with triplet excitations applied to the ground state. Comparison is also made with corresponding results obtained by Hartree-Fock and multiconfiguration self-consistent-field response theory. Two main conclusions concerning triplet-triplet transitions are drawn in this study: First, the very good agreement between unrestricted and restricted DFT results indicates that spin contamination of the triplet state is not a serious problem when computing triplet-triplet spectra of common organic molecules. Second, DFT response calculations of triplet-triplet transitions can be affected by triplet instability problems, especially for the combination of DFT quadratic response with functionals containing fractional exact Hartree-Fock exchange.     

Single molecule conductivity: the role of junction-orbital degeneracy in the artificially high currents predicted by ab initio approaches

A priori evaluations, using Hartree-Fock self-consistent-field (SCF) theory or density-functional theory (DFT), of the current passing between two electrodes through a single bridging molecule result in predicted conductivities that may be up to one to two orders of magnitude larger than observed ones. We demonstrate that this is, in part, often due to the improper application of the computational methods. Conductivity is shown to arise from tunneling between junction states of the electrodes through the molecule; these states are inherently either quasi two-fold or four-fold degenerate and always comprise the (highest occupied molecular orbital) HOMO band at the Fermi energy of the system. Frequently, in previous cluster based molecular conduction calculations, closed-shell SCF or Kohn-Sham DFT methods have been applied to systems that we demonstrate to be intrinsically open shell in nature. Such calculations are shown to induce artificial HOMO-LUMO (LUMO-lowest unoccupied molecular orbital) band splittings that Landauer-based formalisms for steady-state conduction interpret as arising from extremely rapid through-molecule tunneling at the Fermi energy, hence, overestimating the low-voltage conductivity. It is demonstrated that these shortcomings can be eliminated, dramatically reducing calculated current magnitudes, through the alternate use of electronic-structure calculations based on the spin-restricted open-shell formalism and related multiconfigurational SCF of DFT approaches. Further, we demonstrate that most anomalies arising in DFT implementations arise through the use of hybrid density functionals such as B3LYP. While the enhanced band-gap properties of these functionals have made them the defacto standard in molecular conductivity calculations, we demonstrate that it also makes them particularly susceptible to open-shell anomalies.     

Density-functional theory with effective potential expressed as a mapping of the external potential: applications to open-shell molecules

In this paper we apply the direct-mapping density-functional theory (DFT) to open-shell systems, in order to get many-electron wave functions having the same transformation properties as the eigenstates of the exact Hamiltonians. Such a case is that of spin, where in order to get the magnetic properties, the many-particle states must be eigenstates not only of S(z) but also of S2. In this theory the Kohn and Sham [Phys. Rev. A 140, 1133 (1965)] potential is expressed directly as a mapping of the external potential. The total energies of the molecules calculated were satisfactory as their relative deviations (deltaEE) from the exact Hartree-Fock ones were of the order of 10(-4). This accuracy is much higher than that of the standard DFT in its local exchange potential approximation. This method does not need an approximate density as input, as the effective potential is derived directly from the external potential.     

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration Kohn-Sham density-functional theory and applications to d1 and d2 systems with octahedral and tetrahedral symmetries

A method for calculating the UV-vis spectra of molecules with spatially degenerate ground states using time-dependent density-functional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration Kohn-Sham TDDFT (TRICKS-TDDFT) method avoids the difficulties caused by the multireference nature of spatially degenerate states by rather than utilizing the ground state instead taking a nondegenerate excited state with desirable properties as the reference for the TDDFT calculation. The scope and practical application of the method are discussed. Like all open-shell TDDFT calculations this method at times suffers from the inability to produce transitions to states that are eigenfunctions of the total spin operator. A technique for alleviating this difficulty to some extent is proposed. The applicability and accuracy of the TRICKS-TDDFT method is demonstrated through example calculations of several d(1) and d(2) transition metal complexes with tetrahedral and octahedral symmetries. For the most part, the results of these calculations are similar in quality to to those obtained from standard TDDFT calculations.     

Open-shell localized Hartree-Fock method based on the generalized adiabatic connection Kohn-Sham formalism for a self-consistent treatment of excited states

An effective exact-exchange Kohn-Sham approach for the treatment of excited electronic states, the generalized adiabatic connection open-shell localized Hartree-Fock (GAC-OSLHF) method is presented. The GAC-OSLHF method is based on the generalized adiabatic connection Kohn-Sham formalism and therefore capable of treating excited electronic states, which are not the energetically lowest of their symmetry. The method is self-interaction free and allows for a fully self-consistent computation of excited valence as well as Rydberg states. Results for atoms and small- and medium-size molecules are presented and compared to restricted open-shell Hartree-Fock (ROHF) and time-dependent density-functional results as well as to experimental data. While GAC-OSLHF and ROHF results are quite close to each other, the GAC-OSLHF method shows a much better convergence behavior. Moreover, the GAC-OSLHF method as a Kohn-Sham method, in contrast to the ROHF approach, represents a framework which allows also for a treatment of correlation besides an exchange by appropriate functionals. In contrast to the common time-dependent density-functional methods, the GAC-OSLHF approach is capable of treating doubly or multiply excited states and can be easily applied to molecules with an open-shell ground state. On the nodal planes of the energetically highest occupied orbital, the local multiplicative GAC-OSLHF exchange potential asymptotically approaches a different, i.e., nonzero, value than in other regions, an asymptotic behavior which is known from exact Kohn-Sham exchange potentials of ground states of molecules.     

Gamma-point lattice free energy estimates from O1 force calculations

We present a new method for estimating the vibrational free energy of crystal (and molecular) structures employing only a single force calculation, for a particularly displaced configuration, in addition to the calculation of the ground state configuration. This displacement vector is the sum of the phonon eigenvectors obtained from a fast-relative to, e.g., density-functional theory (DFT)-Hessian calculation using interatomic potentials. These potentials are based here on effective charges obtained from a DFT calculation of the ground state electronic charge density but could also be based on other, e.g., empiric approaches.     

DFT description of the electronic structure and spectromagnetic properties of strongly correlated electronic systems: NiII, CuII and ZnII o-dioxolene complexes

The spectroscopic and magnetic properties of dioxolene complexes of zinc, copper and nickel were studied by DFT calculations on model complexes of formulas [(NH(3))(4)M(II)(SQ)](+) (M=Zn, Ni; SQ=semiquinonato) and [(NH(3))(2)Cu(II)(SQ)](+). Standard approaches such as time-dependent DFT (TDDFT), the Slater transition state (STS), and broken symmetry (BS) were found to be unable to completely account for the physical properties of the systems, and complete active space-configuration interaction (CAS-CI) calculations based on the Kohn-Sham (KS) orbitals was applied. The CAS-CI energies, properly corrected with multireference perturbation theory (MR-PT), were found to be in good agreement with experimental data. We present here a calculation protocol that has a low CPU cost/accuracy ratio and seems to be very promising for interpreting the properties of strongly correlated electronic systems in complexes of real chemical size.     

A dual-level approach to density-functional theory

An efficient approximate scheme for density-functional theory (DFT) calculations, which eliminates the time-consuming self-consistent-field (SCF) procedure, is proposed using a dual-level DFT approach. In this approach, dual levels of basis sets and exchange-correlation functionals are adopted. The dual-level DFT approach is based on the idea that the total electron density in the ground state can be represented in terms of the density evaluated using the low-quality basis set and the low-cost exchange-correlation functional. Since the SCF procedure is avoided in the total energy evaluation, the dual-level DFT approach drastically reduces the computational cost. The applications of several dual-level DFT calculations to molecular systems show that our approach is more efficient than the self-consistent DFT approach with a moderate accuracy.     

Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

Proton-coupled electron transfer of the phenoxyl/phenol couple: effect of Hartree-Fock exchange on transition structures

Proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) reactions of the phenoxyl/phenol couple are studied theoretically by using wave function theory (WFT) as well as DFT methods. At the complete active space self-consistent field (CASSCF) level, geometry optimization is found to give two transition states (TSs); one is the PCET type with two benzene rings being nearly coplanar, and the other is the HAT type with two benzene rings taking a stacking structure. Geometry optimization at the (semilocal) DFT level, on the other hand, is found to give only one transition state (i.e., the PCET-type one) and fail to obtain the stacking TS structure. By comparing various levels of theories (including long-range corrected DFT functionals), we demonstrate that the Hartree-Fock exchange at long range plays a critical role in obtaining the sufficient stacking stabilization of the present open-shell system, and that the sole addition of empirical dispersion correction to semilocal DFT functionals may not be adequate for describing such a stacking interaction. Next, we investigate the solvent effect on the PCET and HAT TS thus obtained using the reference interaction site model self-consistent field (RISM-SCF) method. The results suggest that the free energy barrier increases with increasing polarity of the solvent, and that the solvent effects are stronger for the PCET TS than the stacking HAT TS pathway. The reason for this is discussed based on the dipole moment of different TS structures in solution.     

Stable Tetrabenzo-Chichibabin's Hydrocarbons: Tunable Ground State and Unusual Transition between Their Closed-Shell and Open-Shell Resonance Forms

Stable open-shell polycyclic aromatic hydrocarbons (PAHs) are of fundamental interest due to their unique electronic, optical, and magnetic properties and promising applications in materials sciences. Chichibabin's hydrocarbon as a classical open-shell PAH has been investigated for a long time. However, most of the studies are complicated by their inherent high reactivity. In this work, two new stable benzannulated Chichibabin's hydrocarbons 1-CS and 2-OS were prepared, and their electronic structure and geometry in the ground state were studied by various experiments (steady-state and transient absorption spectra, NMR, electron spin resonance (ESR), superconducting quantum interference device (SQUID), FT Raman, X-ray crystallographic etc.) and density function theory (DFT) calculations. 1-CS and 2-OS exhibited tunable ground states, with a closed-shell quinoidal structure for 1-CS and an open-shell biradical form for 2-OS. Their corresponding excited-state forms 1-OS and 2-CS were also chemically approached and showed different decay processes. The biradical 1-OS displayed an unusually slow decay to the ground state (1-CS) due to a large energy barrier (95 ± 2.5 kJ/mol) arising from severe steric hindrance during the transition from an orthogonal biradical form to a butterfly-like quinoidal form. The quick transition from the quinoidal 2-CS (excited state) to the orthogonal biradicaloid 2-OS (ground state) happened during the attempted synthesis of 2-CS. Compounds 1-CS and 2-OS can be oxidized into stable dications by FeCl(3) and/or concentrated H(2)SO(4). The open-shell 2-OS also exhibited a large two-photon absorption (TPA) cross section (760 GM at 1200 nm).     

A flexible implementation of frozen-density embedding for use in multilevel simulations

A new implementation of frozen-density embedding (FDE) in the Amsterdam Density Functional (ADF) program package is presented. FDE is based on a subsystem formulation of density-functional theory (DFT), in which a large system is assembled from an arbitrary number of subsystems, which are coupled by an effective embedding potential. The new implementation allows both an optimization of all subsystems as a linear-scaling alternative to a conventional DFT treatment, the calculation of one active fragment in the presence of a frozen environment, and intermediate setups, in which individual subsystems are fully optimized, partially optimized, or completely frozen. It is shown how this flexible setup can facilitate the application of FDE in multilevel simulations.     

Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory

Open-shell singlet diradicals are difficult to model accurately within conventional Kohn-Sham (KS) density-functional theory (DFT). These methods are hampered by spin contamination because the KS determinant wave function is neither a pure spin state nor an eigenfunction of the S(2) operator. Here we present a theoretical foray for using single-reference closed-shell ground states to describe diradicals by fractional-spin DFT (FS-DFT). This approach allows direct, self-consistent calculation of electronic properties using the electron density corresponding to the proper spin eigenfunction. The resulting FS-DFT approach is benchmarked against diradical singlet-triplet gaps for atoms and small molecules. We have also applied FS-DFT to the singlet-triplet gaps of hydrocarbon polyacenes.     

Different forms of perturbation theory for the calculation of the correlation energy

Different forms of perturbation theory for the calculation of correlation energy in both closed-and open-shell systems are discussed. For closed-shell systems, Epstein–Nesbet perturbation theory is compared with Møller–Plesset (MP ) perturbation theory based on canonical Hartree–Fock orbitals and with MP theory based on internally consistent SCF orbitals. The traditional MP theory gives superior results despite its use of an inferior zeroth-order Hamiltonian. This behavior is rationalized in terms of the larger denominators present in the traditional MP theory. These conclusions are used to support the restricted open-shell perturbation methods proposed recently by Murray and Davidson, and these new methods are compared with spin-restricted Epstein–Nesbet theory and the unrestricted MP (UMP ) approach. © 1992 John Wiley & Sons, Inc.     

Theoretical study of the electronic spectra of square-planar platinum (II) complexes based on the two-component relativistic time-dependent density-functional theory

In the present work the electronic spectra of [PtCl(4)](2-), [PtBr(4)](2-), and [Pt(CN)(4)](2-) are studied with a recently proposed relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. The contribution to the double group excited states in terms of singlet and triplet single group excited states is estimated through the inner product of the transition density matrix obtained from two-component and scalar relativistic TDDFT calculations to better understand the double group excited states. Spin-orbital coupling effects are found to be very important in order to simulate the electronic spectra of these complexes. The results show that the two-component TDDFT formalism can afford excitation energies with high accuracy for the transition-metal systems studied here when use is made of a proper XC potential.     

Scaling the Coulomb interaction in calculations of electron spectra of transition metal complexes

A simple technique of scaling two-electron integrals in ab initio calculations of the electronically excited states of transition metal complexes is proposed. This technique uses the fact that one-center two-electron integrals depend linearly on the scaling factor when Slater type functions are subjected to scaling transformation. This leads to a linear dependence of the d—d transition energy on the “scale” of Coulomb interaction, which allows one to affect the calculation result by varying the Slater exponential. To test the technique, ab initio configuration interaction and full active space calculations of the low excited states of the CrF ₆ ^3- , MnF ₆ ^2- , and VF ₆ ^3- complexes are performed. For transition elements, a basis of Slater type effective functions chosen from the optical spectra of the atoms and ions of transition elements is used. It is shown that in the STO-6G basis with effective exponentials, experimental transitions are reproduced with an accuracy of about 2000 cm^-1 even with the use of small active space determined by the orbitals localized on the central atom of the complex.     

Modeling carbon nanostructures with the self-consistent charge density-functional tight-binding method: vibrational spectra and electronic structure of C(28), C(60), and C(70)

The self-consistent charge density-functional tight-binding (SCC-DFTB) method is employed for studying various molecular properties of small fullerenes: C(28), C(60), and C(70). The computed bond distances, vibrational infrared and Raman spectra, vibrational densities of states, and electronic densities of states are compared with experiment (where available) and density-functional theory (DFT) calculations using various basis sets. The presented DFT benchmark calculations using the correlation-consistent polarized valence triple zeta basis set are at present the most extensive calculations on harmonic frequencies of these species. Possible limitations of the SCC-DFTB method for the prediction of molecular vibrational and optical properties are discussed. The presented results suggest that SCC-DFTB is a computationally feasible and reliable method for predicting vibrational and electronic properties of such carbon nanostructures comparable in accuracy with small to medium size basis set DFT calculations at the computational cost of standard semiempirical methods.