Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

Adiabatic corrections to density functional theory energies and wave functions

The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT.     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.     

Equilibrium structure and Ti-catalyzed H2 desorption in NaAlH4 nanoparticles from density functional theory

Improving the hydrogen ab- and desorption kinetics in complex hydrides is essential if these materials are to be used as reversible hydrogen storage media in the transport sector. Although reductions in particle size and the addition of titanium based compounds have been found to improve the kinetics significantly, the physical understanding remains elusive. Density functional theory is used to calculate the energy of the potential low energy surfaces of NaAlH(4) to establish the equilibrium particle shape, and furthermore to determine the deposition energy of Ti/TiH(2) and the substitutional energy for Ti@Al and Ti@Na-sites on the exposed facets. The substitutional processes are energetically preferred and the Na-vacancy formation energy is found to be strongly reduced in the presence of Ti. The barrier for H(2) desorption is found to depend significantly on surface morphology and in particular on the presence of Ti, where the activation energy for H(2) desorption on NaAlH(4){001} surfaces can drop to 0.98 eV--in good agreement with the experimentally observed activation energy for dehydrogenation.     

Adiabatic versus nonadiabatic photoisomerization in photochromic ruthenium sulfoxide complexes: a mechanistic picture from density functional theory calculations

Polypyridine ruthenium sulfoxide complexes are intriguing compounds which can display both photochromic and electrochromic properties. These properties are based on the Ru-S → Ru-O linkage isomerization capability of the sulfoxide group. The photoisomerization mechanism is of particular importance in order to understand the photophysical properties of such molecules. Density functional theory calculations demonstrate that the main photoisomerization mechanism is nonadiabatic for the system under study in agreement with the experimental observations. Indeed, funnels for efficient radiationless decay back to the ground state are shown to be easily accessible compared to transition states on the adiabatic triplet potential energy surface. However, we highlight for the first time that triplet metal-centered states play a central role in the photoisomerization mechanism of these compounds.     

Effects of hydroxyl group on H2 dissociation on graphene: A density functional theory study

Graphene-based materials are promising for hydrogen production and storage. In this work, using density functional theory calculations, we explored how a hydroxyl group influences H₂ dissociation on graphene. Presence of the hydroxyl group makes the binding of H atom with graphene stronger, as the binding energy of H atom with the hydroxyl-modified graphene is higher than that with the pristine graphene. The para-site is the most favorable site for H₂ dissociation on both the pristine and hydroxyl-modified graphene. The energy barrier of H₂ dissociation at para-site on the pristine graphene is 3.10 eV whereas that on the hydroxyl-modified graphene is 2.46 eV, indicating a more facile H₂ dissociation on the hydroxyl-modified graphene.     

Applying density functional theory on tautomerism in 3,4-dihydropyrimidin-2(1H)-ones

In the present study, the density functional theory (DFT) and Gibbs free energy calculations were performed to investigate the stability and tautomerism of C4-substituted-3,4-dihydropyrimidin-2(1H)-ones. Three different forms are possible for the ethyl 3,4-dihydropyrimidinones (ethyl 4-aryl-6-methyl-3,4-dihydropyrimidin-2(1H)-one-5-carboxylates, ethyl 4-aryl-2-hydroxy-6-methyl-1,4-dihydropyrimidine-5-carboxylates and ethyl 4-aryl-2-hydroxy-6-methyl-3,4-dihydropyrimidine-5-carboxylates) forms that the most stable form is ethyl 4-aryl-6-methyl-3,4-dihydropyrimidin-2 (1H)-one-5-carboxylates (keto-form). The obtained data showed that the substitution on the C4-substitut position can be effective on the equilibrium constant (K _eq).     

Density functional theory: Approximating quasiparticle density functional

A constructive approach for deriving the approximating quasiparticle energy density functional is proposed. As a matter of fact, the proposed approach is the direct development of the Kohn–Sham quasiparticle concept and the Levy–Valone approach. The approach presented takes into account a pseudopotential character of the exchange-correlation part of the density functional and results in a system of functional equations to obtain ground-state energies of many-electron systems.     

He2+2: A comparison between Hartree–Fock and density functional techniques

A comparison of Roothaan-Hartree–Fock methods (both restricted and unrestricted) with density functional ones (LCAO -Xα and cellular MS -Xαβ) is made using as test case the He²₂ + molecular ion. It is shown the analogy that exists between RHF and symmetry-adapted LCAO -Xα potential energy curves, as well as between UHF and symmetry-unconstrained LCAO -Xα ones. The influence of symmetry adaptation on the overall behavior of the potential energy curve is also discussed. Finally, the difference in the behavior of the LCAO -Xα and cellular MS -Xαβ calculations is explained as an artifact of the space partitioning in the latter technique. It is concluded that LCAO -Xα method is superior to cellular MS -Xαβ because it requires less effort to reach the same results and that the general behavior is similar to UHF , although the former affords a better equilibrium bond distance and a worse energy barrier than the latter.     

Hybrid density functional theory investigation of a series of alloxan-based thiosemicarbazones and semicarbazones

Recently, the synthesis and the NMR characterization of a series of eight alloxan-based thiosemicarbazones and semicarbazones were reported. These compounds exhibit a strongly hydrogenbonded hydrazinic proton that is a part of a characteristic six-membered ring. This proton is highly deshielded and resonates far downfield in the proton NMR spectra. In this report, mPW1PW91/6-31+G(d,p) calculations have been used to investigate the structure and other molecular properties of this series of eight compounds. The relationship between the ¹H and ¹³C NMR chemical shifts and various geometric parameters was investigated, and linear relationships for proton peaks that are involved in hydrogen-bond interactions were found.     

Structure and bonding in the PtCO isoelectronic series

The equilibrium geometries and harmonic frequencies of PtXY, XY = CO, N₂, CN⁻ and NO⁺, in the ¹∑⁺ state have been calculated by the ab initio self-consistent field method with gradients using appropriate effective core potentials. An analogous analysis was also carried out on the free ligands for comparison purposes. The ligands are compared with respect to changes in X-Y bond lengths and stretch frequencies upon complexation, and Pt-XY bond lengths, stretch frequencies and bond energies. The calculated results for PtCO and PtN₂ are compared with matrix-isolated infrared spectra.     

硅沸石团簇分子与H_2O相互作用的密度泛函研究

采用密度泛函广义梯度近似(GGA)的PW91方法和全电子基组DNP对硅沸石单元晶胞分子簇进行几何结构优化。通过键长、电子结构参数和Fukui指数计算,了解团簇Al取代前后的变化。通过键能、吸附能、偶极距等考察H2O分子与团簇模型上的相互作用。结果表明:团簇分子在Al取代之后,给电子能力变弱。与H2O作用后,结合能减小,稳定性变弱;Si/Al-O平均键长增长,Al离子增加了团簇分子的极化作用。     

A density functional theory study of molecular and dissociative adsorption of H2 on active sites in mordenite

Adsorption and chemisorption of H2 in mordenite is studied using ab initio density functional theory (DFT) calculations. The geometries of the adsorption complex, the adsorption energies, stretching frequencies, and the capacity to dissociate the adsorbed molecule are compared for different active sites. The active centers include a Br?nsted acid site, a three-coordinated surface Al site, and Lewis sites formed by extraframework cations: Na+, Cu+, Ag+, Zn2+, Cu2+, Ga3+, and Al3+. Adsorption properties of cations are compared for a location of the cation in the five-membered ring. This location differs from the location in the six-membered ring observed for hydrated cations. The five-membered ring, however, represents a stable location of the bare cation. In this position any cation exhibits higher reactivity compared with the location in the six-membered ring and is well accessible by molecules adsorbed in the main channel of the zeolite. Calculated adsorption energies range from 4 to 87 kJ/mol, depending on electronegativity and ionic radius of the cation and the stability of the cation-zeolite complex. The largest adsorption energy is observed for Cu+ and the lowest for Al3+ integrated into the interstitial site of the zeolite framework. A linear dependence is observed between the stretching frequency and the bond length of the adsorbed H2 molecule. The capacity of the metal-exchanged zeolite to dissociate the H2 molecule does not correlate with the adsorption energy. Dissociation is not possible on single Cu+ cation. The best performance is observed for the Ga3+, Zn2+, and Al3+ extraframework cations, in good agreement with experimental data.     

Embedding wave function theory in density functional theory

We present a framework for embedding a highly accurate coupled-cluster calculation within a larger density functional calculation. We use a perturbative buffer to help insulate the coupled-cluster region from the rest of the system. Regions are defined, not in real space, but in Hilbert space, though connection between the two can be made by spatial localization of single-particle orbitals. Relations between our embedding approach and some similar techniques are discussed. We present results for small sample systems for which we can extract essentially exact results, demonstrating that our approach seems to work quite well and is generally more reliable than some of the related approaches due to the introduction of additional interaction terms.     

Adiabatic electron affinities of the polyhydrated adenine-thymine base pair: a density functional study

Adiabatic electron affinities (AEAs) of the adenine-thymine (AT) base pair surrounded by 5 and 13 water molecules have been studied by density functional theory (DFT). Geometries of neutral AT x nH2O and anionic (AT x nH2O)- complexes (n = 5 and 13) were fully optimized, and vibrational frequency analysis was performed at the B3LYP/6-31+G** level of theory. The optimized structures of the neutral (AT x nH2O) and (AT x nH2O)- complexes were found to be somewhat nonplanar. Some of the water molecules are displaced away from the AT ring plane and linked with one another by hydrogen bonds. The optimized structures of the complexes are found to be in a satisfactory agreement with the observed experimental and molecular dynamics simulation results. In the optimized anionic complexes, the thymine (T) moiety was found to be puckered, whereas the adenine (A) moiety remained almost planar. Natural population analysis (NPA) performed using the B3LYP/6-31+G** method shows that the thymine moiety in the anionic (AT x nH2O)- complexes (n = 5 and 13) has most of the excess electronic charge, i.e., approximately -0.87 and approximately -0.81 (in the unit of magnitude of the electronic charge), respectively. The zero-point energy corrected adiabatic electron affinities of the hydrated AT base pair were found to be positive both for n = 5 and 13 and have the values of 0.97 and 0.92 eV, respectively, which are almost three times the AEA of the AT base pair. The results show that the presence of water molecules appreciably enhances the EA of the base pair.     

A density functional theory study of the dissociation of H2 on gold clusters: importance of fluxionality and ensemble effects

Density functional theory was employed to calculate the adsorption/dissociation of H2 on gold surfaces, Au(111) and Au(100), and on gold particles from 0.7 (Au14) to 1.2 nm (Au29). Flat surfaces of the bulk metal were not active towards H2, but a different effect was observed in gold nanoclusters, where the hydrogen was adsorbed through a dissociative pathway. Several parameters such as the coordination of the Au atoms, ensemble effects and fluxionality of the particle were analyzed to explain the observed activity. The effect of the employed functional was also studied. The flexibility of the structure, i.e., its adaptability towards the adsorbate, plays a key role in the bonding and dissociation of H2. The interaction with hydrogen leads to drastic changes in the structure of the Au nanoparticles. Furthermore, it appears that not only low coordinated Au atoms are needed because H2 adsorption/dissociation was only observed when a cooperation between several (4) active Au atoms was allowed.     

A finite-temperature density functional study of electron self-trapping in 3He and 4He

We introduce a compact finite-temperature density functional model to study electron self-trapping in both liquid and vapor (3)He and (4)He. This model can quantitatively reproduce the most essential thermodynamic properties of (3)He and (4)He along their liquid-vapor coexistence lines. The structures and energetics of self-trapped electron bubbles on the 1S ground state and 1P excited state are particularly investigated. Our results show that 1S and 1P bubbles exist in liquid at any temperature, whereas 1S bubbles exist in vapor only above 1.6 K in (3)He and above 2.8 K in (4)He, 1P bubbles exist in vapor only above 2.5 K in (3)He and 4.0 K in (4)He. An initially spherical 1P bubble is unstable against deformation towards a peanut shape. In liquid, a peanut-shaped 1P bubble is held from fission by surface tension until reaching the liquid-vapor critical point, whereas in vapor it always splits into two smaller bubbles. The existence of 1P bubbles in finite-temperature liquid helium and their fission instability in helium vapor reveal interesting physics in this system.     

Molecular fragments in density functional theory

The second-order density functional approach to the partitioning of the molecular density of Cedillo, Chattaraj, and Parr (Int. J. Quantum Chem. 2000, 77, 403-407) is used, together with a local assumption for the function that projects the total density into its components, to show that the distribution function adopts a stockholders form, in terms of the local softness of the isolated fragments, and that the molecular Fukui function is distributed in the molecular fragments in the same proportion as the electronic density.