Koopmans' theorem for large molecular systems within density functional theory

It is shown that in density functional theory (DFT), Koopmans' theorem for a large molecular system can be stated as follows: The ionization energy of the system equals the negative of the highest occupied molecular orbital (HOMO) energy plus the Coulomb electrostatic energy of removing an electron from the system, or equivalently, the ionization energy of an N-electron system is the negative of the arithmetic average of the HOMO energy of this system and the lowest unoccupied molecular orbital (LUMO) energy of the (N - 1)-electron system. Relations between this DFT Koopmans' theorem and its existing counterparts in the literature are discussed. Some of the previous results are generalized and some are simplified. DFT calculation results of a fullerene molecule, a finite single-walled carbon nanotube and a finite boron nitride nanotube are presented, indicating that this Koopmans' theorem approximately holds, even if the orbital relaxation is taken into consideration.     

Face-integrated Fukui function: understanding wettability anisotropy of molecular crystals from density functional theory

Wettability is one of the anisotropic surface properties of molecular crystals that exhibit the structural variance of chemical moieties on various growth faces. The divergence in liquid-solid interactions at different faces is thought to be related to the inherent responding capacity or sensitivity of a solid surface to the perturbation in electronic structures and atomic positions as a result of the contact by a liquid. Since the Fukui function, according to density functional theory (DFT), is a local function for describing such sensitivity to the structural perturbation and is directly related to local softness, it has been proposed and tested to use an integrated Fukui function over a crystallographic plane for describing the anisotropy of solid-liquid interactions. It is found that the contact angle of a polar solvent, such as water, on a crystal surface shows an intimate connection to the integrated Fukui functions of the surface, illustrating an extension of Pearson's HSAB (hard and soft acids and bases) to crystal systems. The concept of face-integrated Fukui function and the approach to apply the HSAB with the DFT-based concepts may provide a powerful means for describing anisotropic properties, including wettability of organic crystals.     

Lattice density functional theory of molecular diffusion

A density functional theory of diffusion is developed for lattice fluids with molecular flux as a functional of the density distribution. The formalism coincides exactly with the generalized Ono-Kondo density functional theory when there is no gradient of chemical potential, i.e., at equilibrium. Away from equilibrium, it gives Fick's first law in the absence of a potential energy gradient, and it departs from Fickian behavior consistently with the Maxwell-Stefan formulation. The theory is applied to model a nanopore, predicting nonequilibrium phase transitions and the role of surface diffusion in the transport of capillary condensate.     

Mechanisms of Staudinger reactions within density functional theory

The Staudinger reactions of substituted phosphanes and azides have been investigated by using density functional theory. Four different initial reaction mechanisms have been found. All systems studied go through a cis-transition state rather than a trans-transition state or a one-step transition state. The one-step pathway of the phosphorus atom attacking the substituted nitrogen atom is always unfavorable energetically. Depending on the substituents on the azide and the phosphane, the reaction mechanism with the lowest initial reaction barrier can be classified into three categories: (1). like the parent reaction, PH(3) + N(3)H, the reaction goes through a cis-transition state, approaches a cis-intermediate, overcomes a PN-bond-shifting transition state, reaches a four-membered ring intermediate, dissociates N(2) by overcoming a small barrier, and results in the final products: N(2) and a phosphazene; (2). once reaching the cis-intermediate, the reaction goes through the N(2)-eliminating transition state and produces the final products; (3). the reaction has a concerted initial cis-transition state, in which the phosphorus atom attacks the first and the third nitrogen atoms of the azide simultaneously and reaches an intermediate, and then the reaction goes through similar steps of the first reaction mechanism. In contrast to the previous predictions on the relative stability of the unsubstituted cis-configured phosphazide intermediate and the unsubstituted trans-configured phosphazide intermediate, the total energy of the substituted trans-configured phosphazide intermediate is close to that of the substituted cis-configured phosphazide intermediate. The preference of the initial cis-transition state reaction pathway is thoroughly discussed. The relative stability of the cis- and the trans-intermediates is explored and analyzed with the aid of molecular orbitals. The effects of substituents and solvent effects on the reaction mechanisms of the Staudinger reactions are discussed in detail.     

Structure of the ammonia dimer studied by density functional theory

Self-consistent Kohn–Sham density functional calculations have been carried out to study the structure of the ammonia dimer. The local-density approximation yields unusually large binding energy and short internitrogen distance compared with the experimental and more accurate theoretical data. The results from the Becke–Perdew gradient-corrected functionals are generally in good agreement with those at the SCF MP 2 level when the geometry is fully optimized with various large basis sets. With our best estimation, the staggered quasi-linear structure (C_s) is 0.6 kcal/mol lower in energy than the symmetric cyclic one (C_2h). The hydrogen-bonded N—H bond in the staggered quasi-linear structure is found to be 0.008 Å longer than the N—H bond in ammonia. In our calculations, we could not find the minima on the energy surface corresponding to the two asymmetric cyclic structures suggested by microwave spectra and coupled pair functional calculations. © 1994 John Wiley & Sons, Inc.     

Energy ranking of molecular crystals using density functional theory calculations and an empirical van der waals correction

By combination of high level density functional theory (DFT) calculations with an empirical van der Waals correction, a hybrid method has been designed and parametrized that provides unprecedented accuracy for the structure optimization and the energy ranking of molecular crystals. All DFT calculations are carried out using the VASP program. The van der Waals correction is expressed as the sum over atom-atom pair potentials with each pair potential for two atoms A and B being the product of an asymptotic C(6,A,B)/r(6) term and a damping function d(A,B)(r). Empirical parameters are provided for the elements H, C, N, O, F, Cl, and S. Following Wu and Yang, the C(6) coefficients have been determined by least-squares fitting to molecular C(6) coefficients derived by Meath and co-workers from dipole oscillator strength distributions. The damping functions d(A,B)(r) guarantee the crossover from the asymptotic C(6,A,B)/r(6) behavior at large interatomic distances to a constant interaction energy at short distances. The careful parametrization of the damping functions is of crucial importance to obtain the correct balance between the DFT part of the lattice energy and the contribution from the empirical van der Waals correction. The damping functions have been adjusted to yield the best possible agreement between the unit cells of a set of experimental low temperature crystal structures and their counterparts obtained by lattice energy optimization using the hybrid method. On average, the experimental and the calculated unit cell lengths deviate by 1%. To assess the performance of the hybrid method with respect to the lattice energy ranking of molecular crystals, various crystal packings of ethane, ethylene, acetylene, methanol, acetic acid, and urea have been generated with Accelrys' Polymorph Predictor in a first step and optimized with the hybrid method in a second step. In five out of six cases, the experimentally observed low-temperature crystal structure corresponds to the most stable calculated structure.     

Computational study of water and ammonia dimers with density functional theory methods

The structures and energies for the dimerization of water and ammonia molecules were computed with density functional theory (DFT) and ab initio methods. For all studies the same 6-311+G(2d,2p) basis set was used. Two linear hydrogen-bonded and cyclic ammonia dimer structures were computed and their relative stability is discussed. From the systematic studies, hybrid DFT methods were selected as reliable for computing the parameters of these types of van der Waals' complex.     

Double excitations within time-dependent density functional theory linear response

Within the adiabatic approximation, time-dependent density functional theory yields only single excitations. Near states of double excitation character, the exact exchange-correlation kernel has a strong dependence on frequency. We derive the exact frequency-dependent kernel when a double excitation mixes with a single excitation, well separated from the other excitations, in the limit that the electron--electron interaction is weak. Building on this, we construct a nonempirical approximation for the general case, and illustrate our results on a simple model.     

Validation of dispersion-corrected density functional theory approaches for ionic liquid systems

The performance of several general gradient approximation, meta general gradient approximation, and hybrid functionals is tested against M?ller-Plesset perturbation theory second-order for ionic liquid systems. Additionally, two dispersion-corrected approaches (addition of van der Waals forces by a 1/r(6) term and employing a dispersion-corrected atom-center dispersion pseudopotential) were studied. For the 1-butyl-3-methylimidazolium cation neglecting dispersion results in different trends for structural stabilities. The two applied correction schemes for density functional theory improve the results tremendously. Investigating several 1-butyl-3-methylimidazolium dicianamide ion pairs shows a mean absolute deviation from M?ller-Plesset perturbation theory of 35.7 kJ/mol for Hartree-Fock and up to 33.2 kJ/mol for the density functional theory methods. The dispersion-corrected methods reduce the mean absolute deviation to less than 10 kJ/mol. Comparing adducts of the 1-ethyl-3-methylimidazolium dicianamide ion pair with Diels-Alder educts (cyclopentadiene and methylacrylate) shows similar energetic differences as for the ion pairs. Furthermore large deviations in geometries for the intermolecular distances were found for the Hartree-Fock approach (mean absolute deviation: 190 pm) and density functional theory (mean absolute deviation up to 178 pm) while for the dispersion-corrected methods the mean absolute deviation is less than 50 pm.     

Energies of ions in water and nanopores within density functional theory

Accurate calculations of electrostatic potentials and treatment of substrate polarizability are critical for predicting the permeation of ions inside water-filled nanopores. The ab initio molecular dynamics method, based on density functional theory (DFT), accounts for the polarizability of materials, water, and solutes, and it should be the method of choice for predicting accurate electrostatic energies of ions. In practice, DFT coupled with the use of periodic boundary conditions in a charged system leads to large energy shifts. Results obtained using different DFT packages may vary because of the way pseudopotentials and long-range electrostatics are implemented. Using maximally localized Wannier functions, we apply robust corrections that yield relatively unambiguous ion energies in select molecular and aqueous systems and inside carbon nanotubes. Large binding energies are predicted for ions in metallic carbon nanotube arrays, while Na+ and Cl- energies are found to exhibit asymmetry in water that is smaller than but comparable with those computed using nonpolarizable water force fields.     

Condensed phase ionic polarizabilities from plane wave density functional theory calculations

A method is presented to allow the calculation of the dipole polarizabilities of ions and molecules in a condensed-phase coordination environment. These values will be useful for understanding the optical properties of materials and for developing simulation potentials which incorporate polarization effects. The reported values are derived from plane wave density functional theory calculations, though the method itself will apply to first-principles calculations on periodic systems more generally. After reporting results of test calculations on atoms to validate the procedure, values for the polarizabilities of the oxide ion and various cations in a range of materials are reported and compared with experimental information as well as previous theoretical results.     

Modified corrections for London forces in solid-state density functional theory calculations of structure and lattice dynamics of molecular crystals

Dispersion forces are critical for defining the crystal structures and vibrational potentials of molecular crystals. It is, therefore, important to include corrections for these forces in periodic density functional theory (DFT) calculations of lattice vibrational frequencies. In this study, DFT was augmented with a correction term for London-type dispersion forces in the simulations of the structures and terahertz (THz) vibrational spectra of the dispersion-bound solids naphthalene and durene. The parameters of the correction term were modified to best reproduce the experimental crystal structures and THz spectra. It was found that the accurate reproduction of the lattice dimensions by adjusting the magnitude of the applied dispersion forces resulted in the highest-quality fit of the calculated vibrational modes with the observed THz absorptions. The method presented for the modification of the dispersion corrections provides a practical approach to accurately simulating the THz spectra of molecular crystals, accounting for inherent systematic errors imposed by computational and experimental factors.     

Density functional theory study of hydrogen bonding in ionic molecular materials

Crystal structures are usually described in geometric terms. However, it is the energetics of intermolecular interactions that determine the chemical and physical properties of molecular materials.(1) In this paper, we use density functional theory (DFT) in combination with numerical basis sets to analyze the hydrogen bonding interactions in a family of novel ionic molecular materials. We find that the calculated binding energies are consistent with those of other ionic hydrogen bonded systems. We also examine electron density distributions for the systems of interest to gain insight into the nature of the hydrogen bonding interaction and investigate the effects of different aspects of the crystal field on the geometry of the hydrogen bond.     

Ab initio and density functional theory reinvestigation of gas-phase sulfuric acid monohydrate and ammonium hydrogen sulfate

We have calculated the thermochemical parameters for the reactions H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O and H(2)SO(4) + NH(3) <--> H(2)SO(4).NH(3) using the B3LYP and PW91 functionals, MP2 perturbation theory and four different basis sets. Different methods and basis sets yield very different results with respect to, for example, the reaction free energies. A large part, but not all, of these differences are caused by basis set superposition error (BSSE), which is on the order of 1-3 kcal mol(-1) for most method/basis set combinations used in previous studies. Complete basis set extrapolation (CBS) calculations using the cc-pV(X+d)Z and aug-cc-pV(X+d)Z basis sets (with X = D, T, Q) at the B3LYP level indicate that if BSSE errors of less than 0.2 kcal mol(-1) are desired in uncorrected calculations, basis sets of at least aug-cc-pV(T+d)Z quality should be used. The use of additional augmented basis functions is also shown to be important, as the BSSE error is significant for the nonaugmented basis sets even at the quadruple-zeta level. The effect of anharmonic corrections to the zero-point energies and thermal contributions to the free energy are shown to be around 0.4 kcal mol(-1) for the H(2)SO(4).H(2)O cluster at 298 K. Single-point CCSD(T) calculations for the H(2)SO(4).H(2)O cluster also indicate that B3LYP and MP2 calculations reproduce the CCSD(T) energies well, whereas the PW91 results are significantly overbinding. However, basis-set limit extrapolations at the CCSD(T) level indicate that the B3LYP binding energies are too low by ca. 1-2 kcal/mol. This probably explains the difference of about 2 kcal mol(-1) for the free energy of the H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O reaction between the counterpoise-corrected B3LYP calculations with large basis sets and the diffusion-based experimental values of S. M. Ball, D. R. Hanson, F. L Eisele and P. H. McMurry (J. Phys. Chem. A. 2000, 104, 1715). Topological analysis of the electronic charge density based on the quantum theory of atoms in molecules (QTAIM) shows that different method/basis set combinations lead to qualitatively different bonding patterns for the H(2)SO(4).NH(3) cluster. Using QTAIM analysis, we have also defined a proton transfer degree parameter which may be useful in further studies.     

Performance of dispersion-corrected density functional theory for the interactions in ionic liquids

Potential energy curves for the dissociation of cation-anion associates representing the building units of ionic liquids have been computed with dispersion corrected DFT methods. Non-local van der Waals density functionals (DFT-NL) for the first time as well as an atom pair-wise correction method (DFT-D3) have been tested. Reference data have been computed at the extrapolated MP2/CBS and estimated CCSD(T)/CBS levels of theory. The investigated systems are combined from two cations (1-butyl-3-methylimidazolium and tributyl(methyl)posphonium) and three anions (chloride, dicyanamide, acetate). We find substantial stabilization from London dispersion energy near equilibrium of 5-7 kcal mol(-1) (about 5-6% of the interaction energy). Equilibrium distances are shortened by 0.03-0.09 ? and fundamental (inter-fragment) vibrational frequencies (which are in the range 140-180 cm(-1)) are increased by typically 10 cm(-1) when dispersion corrections are made. The dispersion-corrected hybrid functional potentials are in general in excellent agreement with the corresponding CCSD(T) reference data (typical deviations of about 1-2%). The DFT-D3 method performs unexpectedly well presumably because of cancellation of errors between the dispersion coefficients of the cations and anions. Due to self-interaction error, semi-local density functionals exhibit severe SCF convergence problems, and provide artificial charge-transfer and inaccurate interaction energies for larger inter-fragment distances. Although these problems may be alleviated in condensed phase simulations by effective Coulomb screening, only dispersion-corrected hybrid functionals with larger amounts of Fock-exchange can in general be recommended for such ionic systems.     

Intrinsic nucleofugality scale within the framework of density functional reactivity theory

Nucleofugality is a measure of the quality of a leaving group in substitution and elimination reactions. In a conceptual DFT context, the nucleofugality is calculated for an elaborate set of common organic leaving groups, both in the gas phase and in two organic solvents (dichloromethane and methanol). An intrinsic nucleofugality scale is constructed showing fair agreement with the classical trends in leaving group capacity in organic chemistry. The correlation of the results with acidities (tabulated pK(a) values) on one hand and experimental solvolysis reaction rate constants (kinetic parameters) on the other hand is discussed. Finally, a conceptual DFT based formula is derived, describing the influence of the solvation energy on the nucleofugality; excellent correlations were found with explicit calculations for the studied leaving groups.     

Assignment of the lowest-lying THz absorption signatures in biotin and lactose monohydrate by solid-state density functional theory

The narrow terahertz (THz) features in crystalline biotin and lactose monohydrate observed in recent experimental studies are considered by solid-state density functional theory (DFT) calculations. The lowest-frequency THz features in both solid-state biotin and lactose monohydrate are assigned to external hindered rotational modes and not to the lowest-frequency internal modes predicted from isolated-molecule calculations. The motions of the molecules associated with these narrow THz features and the interactions between molecules in the hydrogen-bonded networks of these molecular crystals are discussed, and comparisons are made to similar studies on molecular crystals not exhibiting strong intermolecular interactions.