Calculation of Verdet constants with time-dependent density functional theory: implementation and results for small molecules

We report the implementation of a method by which to calculate Verdet constants for molecules. The method is based on gauge-including atomic orbitals (GIAOs) and density functional theory. Calculations based on this method afford magneto-optical rotations of the right magnitude for the molecules H2, N2, CO, HF, CH4, C2H2, H2O, and CS2. The results are in satisfactory agreement with experiment. We investigate the dependency of the results on the gauge origin if GIAOs are not chosen, the convergence of the results with the size of the basis set for AOs and GIAOs, and for H2O and CS2 a comparison of gas-phase and liquid phase values. For the small molecules studied here, large polarized basis sets with diffuse functions are required to obtain well converged results. The use of an asymptotically correct Kohn-Sham potential is advantageous.     

A well-tempered density functional theory of electrons in molecules

This Invited Article reports extensions of a recently developed approach to density functional theory with correct long-range behavior (R. Baer and D. Neuhauser, Phys. Rev. Lett., 2005, 94, 043002). The central quantities are a splitting functional gamma[n] and a complementary exchange-correlation functional E[n]. We give a practical method for determining the value of gamma in molecules, assuming an approximation for E is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent gamma and an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond lengths of the molecules in the G2(1) database. The optimized values are gamma = 0.5 a and w = 0.1. We then examine the performance of this slightly semi-empirical functional for a variety of molecular properties, comparing to related works and experiment. We show that this approach can be used for describing in a satisfactory manner a broad range of molecular properties, be they static or dynamic. Most satisfactory is the ability to describe valence, Rydberg and inter-molecular charge-transfer excitations.     

The local structure of protonated water from x-ray absorption and density functional theory

We present a combined x-ray absorption spectroscopy/computational study of water in hydrochloric acid (HCl) solutions of varying concentration to address the structure and bonding of excess protons and their effect on the hydrogen bonding network in liquid water. Intensity variations and energy shifts indicate changes in the hydrogen bonding structure in water as well as the local structure of the protonated complex as a function of the concentration of protons. In particular, in highly acidic solutions we find a dominance of the Eigen form, H(3)O(+), while the proton is less localized to a specific water under less acidic conditions.     

Molecular density functional theory of solvation: from polar solvents to water

A classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, limited to two-body correlations, the unknown excess term of the functional approximated by the angular-dependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss-Legendre angular grid for orientations to provide the solvation structure and free-energy. This two-step procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around H-bonded solutes, such as spherical ions. This can be corrected by introducing suitable three-body correlation terms that restore both an accurate hydration structure and a satisfactory energetics.     

Bidentate reagents form cyclic organic-Cr(VI) molecules for aiding in the removal of Cr(VI) from water: density functional theory and experimental results

Hexavalent chromium, Cr(VI), in the form of chromate (CrO₄ ^2?) or dichromate (Cr₂O₇ ^2?) is a well-described carcinogen found in the drinking water in many parts of the country at levels deemed unsafe by the U.S. Environmental Protection Agency and the World Health Organization. We report on the ability of bidentate organic molecules containing diols or diamines to capture chromate ions from aqueous sources by forming cyclic organic-Cr(VI) carbonates or ureas. After their formation, the cyclic organic-Cr(VI) molecules are readily absorbed onto granulated activated charcoal to facilitate Cr(VI) removal. Using density functional theory, E ₀ values for the reactions of diols and diamines with chromate were calculated and correlated with the experimental findings of Cr(VI) removal.     

Universal mathematical identities in density functional theory: results from three different spin-resolved representations

This paper supersedes previous theoretical approaches to conceptual DFT because it provides a unified and systematic approach to all of the commonly considered formulations of conceptual DFT, and even provides the essential mathematical framework for new formulations. Global, local, and nonlocal chemical reactivity indicators associated with the "closed-system representation" ([N(alpha),N(beta),nu(alpha)(r),nu(beta)(r)]) of spin-polarized density functional theory (SP-DFT) are derived. The links between these indicators and the ones associated with the "open-system representation" ([mu(alpha),mu(beta),nu(alpha)(r),nu(beta)(r)]) are derived, including the spin-resolved Berkowitz-Parr identity. The Legendre transform to the "density representation" ([rho(alpha)(r),rho(beta)(r)]) is performed, and the spin-resolved Harbola-Chattaraj-Cedillo-Parr identities linking the density representation to the closed-system and open-system representations are derived. Taken together, these results provide the framework for understanding chemical reactions from both the electron-following perspective (using either the closed-system or the open-system representation) and electron-preceding perspective (density representation). A powerful matrix-vector notation is developed; with this notation, identities in conceptual DFT become universal. Specifically, this notation allows the fundamental identities in conventional (spin-free) conceptual DFT, the [N(alpha),N(beta)] representation, and the [N=N(alpha)+N(beta),N(S)=N(alpha)-N(beta)] representation to be written in exactly the same forms. In cases where spin transfer and electron transfer are coupled (e.g., radical+molecule reactions), we believe that the [N(alpha),N(beta)] representation may be more useful than the more common [N,N(S)] representation.     

Vibrational corrections to geometries of transition metal complexes from density functional theory

Zero-point vibrational corrections are computed at the BP86/AE1 level for the set of 50 transition-metal/ligand bonds that have recently been proposed as testing ground for DFT methods, because of the availability of precise experimental gas-phase geometries (Bühl and Kabrede, J Chem Theory Comput 2006, 2, 1282). These corrections are indicated to be transferable to a large extent between various density-functional/basis-set combinations, so that they can be used to estimate zero-point averaged r0g distances from re values optimized at other theoretical levels. Applying this approach to a number of popular DFT levels does not, in general, improve their overall accuracy in terms of mean and standard deviations from experiment. The hybrid variant of the meta-functional TPSS is confirmed as promising choice for computing structures of transition-metal complexes.     

Density functional theory study on the bridge structure in dimeric aluminum (III) water complexes

Density-functional theory methods were used to investigate the structure of dimeric aluminum (III) water complexes as a function of bridging group. The possibilities of oxygen, water, and hydroxyl bridge ligands and a variety of structural arrangements, such as cis/trans, with respect to the relative position of hydroxyl ligands, were considered. Within the limit of our computational level, we found that electrostatic repulsion between hydroxyls is important in deciding the polyaluminum structure. Although the structures of aluminum-hexaaquo predominate, species with small number of charges or a large number of hydroxyl ligands have a tendency toward a five-coordinate trigonal bipyramidal configuration. Because water is electronically neutral, it cannot provide enough negative charges as a bridge ligand to stabilize two Al(III) molecules. The energy differences among many configurational isomers of hydroxyl Al are so small that they may coexist and convert into each other easily at room temperature.     

Ammonia production at the FeMo cofactor of nitrogenase: results from density functional theory

Biological nitrogen fixation has been investigated beginning with the monoprotonated dinitrogen bound to the FeMo cofactor of nitrogenase up to the formation of the two ammonia molecules. The energy differences of the relevant intermediates, the reaction barriers, and potentially relevant side branches are presented. During the catalytic conversion, nitrogen bridges two Fe atoms of the central cage, replacing a sulfur bridge present before dinitrogen binds to the cofactor. A transformation from cis- to trans-diazene has been found. The strongly exothermic cleavage of the dinitrogen bond takes place, while the Fe atoms are bridged by a single nitrogen atom. The dissociation of the second ammonia from the cofactor is facilitated by the closing of the sulfur bridge following an intramolecular proton transfer. This closes the catalytic cycle.     

Dissociation of sulfur oxoacids by two water molecules studied using ab initio and density functional theory calculations

Using ab initio [SCS‐MP2 and CCSD(T)] and density functional theory (M062X) calculations, we have studied the geometries and energies of sulfur oxoacids H₂S_mO₆ (m = 2–4) and their monohydrated and dihydrated clusters. When including the results from previously reported disulfuric acid (H₂S₂O₇) cases, the gas phase acidity is ordered as H₂S₂O₆ < H₂S₃O₆ < H₂S₂O₇ < H₂S₄O₆. The intramolecular H‐bonding, which may indicate the degree of structural flexibility in this molecular series, is an important factor for the order of the gas phase acidity. All these sulfur oxoacids show dissociated (or deprotonated) geometries with only two water molecules, although the energies of the dissociated conformers are ranked differently. All of the dissociated conformers form a unique H‐bonding network structure in which the protonated first water (H₃O⁺) is triply H‐bonded to each oxygen atom of two SO₃ moieties as well as the second water, which in turn is H‐bonded to a SO₃ moiety. H₂S₃O₆ has the best molecular flexibility for adopting such an H‐bonding network structure, and thereby all the low‐lying conformers of H₂S₃O₆(H₂O)₂ are dissociated. In contrast, the least flexible H₂S₂O₆ forms such a structure with a high strain, and dissociation of H₂S₂O₆(H₂O)₂ is found from the third lowest conformer. Although the gas phase acidity of H₂S₄O₆ is the highest in this series, the lowest dissociated conformer and the lowest undissociated conformer of H₂S₄O₆(H₂O)₂ are very close in energy. This is because forming the H‐bonding network structure is somewhat difficult due to the large distance between the two SO₃ moieties.     

Polydisperse telechelic polymers at interfaces: analytic results and density functional theory

We use a recently developed continuum theory to expand on an exact treatment of the interfacial properties of telechelic polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. A new surface adsorption transition is identified for ideal telechelic chains, wherein the central block is an equilibrium polymer. This transition occurs in the limit of strong end adsorption. Additionally, closed expressions are derived for the ideal continuum telechelic chain in contact with two large spheres, using the Derjaguin approximation. We analyze the interactions between colloids as a function of polydispersity and molecular weight, and the results are compared with polymer density functional theory in the dilute limit. Significant variations in polymer mediated forces are observed as a function of polydispersity, molecuar weight, and chain stiffness.     

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.     

Complexation behavior of trivalent actinides and lanthanides with 1,10-phenanthroline-2,9-dicarboxylic acid based ligands: insight from density functional theory

We have investigated the complexation behavior of preorganized 1,10-phenanthroline-2,9-dicarboxylic acid (PDA) based ligands with trivalent lanthanides and actinides using density functional theory with various GGA type exchange-correlation functionals and different basis sets. New ligands have been designed from PDA through functionalization with soft donor atoms such as sulfur, resulting in mono-thio-dicarboxylic acids (TCA/TCA1) and di-thio-dicarboxylic acid (THIO). It has been found that selectivity in terms of complexation energy of actinides over lanthanides is the maximum with TCA1 where the metal-ligand binding is through the O atoms. This unusual feature where a softer actinide metal ion is bonded strongly with hard donor oxygen atoms has been explained using the popular chemical concepts, viz., Pearson's Hard-Soft-Acid-Base (HSAB) principle and the frontier orbital theory of chemical reactivity as proposed by Fukui. Detailed analysis within the framework of the HSAB principle indicates that the presence of softer nitrogen atoms in the phenanthroline moiety (which also act as donors to the metal ion) has a profound influence in changing the soft nature of the actinide ion, which in turn binds with the hard oxygen atoms in a stronger way as compared to the valence isoelectronic lanthanide ion. Also, the trends in the variation of calculated values of the metal-ligand bond distances and the corresponding complex formation energies have been rationalized using the Fukui reactivity indices corresponding to the metal ions and the donor sites. All the calculations have also been done in the presence of solvent. The "intra-ligand synergistic effect" demonstrated here for PDA or TCA1 with soft and hard donor centers might be very important in designing new ligands for selective extraction of various metal ions in a competitive environment. However, for TCA and THIO ligands with only soft donor centers, "intra-ligand synergism" may not be very efficient although reports are available demonstrating soft-soft inter-ligand synergism. Nevertheless, in the case of TCA and THIO complexes, a shorter Am-S bond distance in conjunction with lower metal ion charge and a higher percentage of orbital interaction energy corroborate the presence of a higher degree of covalency in Am-S bonds, which in turn may be responsible for selectivity towards Am(3+).     

Self-interaction error in density functional theory: a mean-field correction for molecules and large systems

Corrections to the self-interaction error which is rooted in all standard exchange-correlation functionals in the density functional theory (DFT) have become the object of an increasing interest. After an introduction reminding the origin of the self-interaction error in the DFT formalism, and a brief review of the self-interaction free approximations, we present a simple, yet effective, self-consistent method to correct this error. The model is based on an average density self-interaction correction (ADSIC), where both exchange and Coulomb contributions are screened by a fraction of the electron density. The ansatz on which the method is built makes it particularly appealing, due to its simplicity and its favorable scaling with the size of the system. We have tested the ADSIC approach on one of the classical pathological problem for density functional theory: the direct estimation of the ionization potential from orbital eigenvalues. A large set of different chemical systems, ranging from simple atoms to large fullerenes, has been considered as test cases. Our results show that the ADSIC approach provides good numerical values for all the molecular systems, the agreement with the experimental values increasing, due to its average ansatz, with the size (conjugation) of the systems.     

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.     

Ring complexes of S-nitrosothiols with CU+: a density functional theory study

The density functional theory (DFT) method B3P86/6-311+G(2df,p) has been employed to investigate the complexes formed upon interaction of Cu(+) with nitrosylated cysteine (CysNO) and its decarboxylated (H(2)NCH(2)CH(2)SNO) and deaminated (HOOCCH(2)CH(2)SNO) derivatives. Optimized structures, relative enthalpies and relative free energies have been calculated and compared. In addition, the effects of binding an H(2)O molecule to the Cu(+) centre in the resulting complexes have also been considered. It is found that the most stable complexes are formed when Cu(+) coordinates to the S-nitrosothiol via S of the SNO group. This results in dramatic lengthenings of the SN bond with concomitant shortening of the NO bond. In contrast, when Cu(+) coordinates via the nitrogen of the SNO group, a shortening of the SN bond with lengthening of the NO bond is observed. These effects are tempered by the electron donating ability of other functional groups also coordinated with the Cu(+) centre in the complexes and on the coordination state of the Cu(+) ion.     

Proton affinities of molecules containing nitrogen and oxygen: Comparing density functional results to experiment

Summary Proton affinities were calculated using density functional theory for 11 small molecules whose primary protonation site is on nitrogen, and eight small molecules that protonate on oxygen. Calculations were performed using both the local spin density approximation and nonlocal gradient corrections to the exchange correlation functional. The results were not sensitive to whether the nonlocal gradient correction was implemented on the final local spin density optimized geometry or whether the correction was included in the self-consistent calculation of the energy at each optimization step. Although negligible basis set dependence was found using the analytic Gaussian basis sets, numerical basis sets required augmentation by a double set of polarization functions to achieve reasonable agreement with experiment. All calculations systematically underestimated oxygen proton affinities.     

Influence of the central metal on the structural,electronic, and spectroscopic properties of naphthalocyanine complexes: density functional theory calculations

A series of metal naphthalocyanine complexes (M = TiO²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Ru²⁺) have been investigated using density functional theory (DFT) and time-dependent DFT methods in vacuo and in the solvent dimethylsulfoxide in order to evaluate the influence of the different metal atoms on the geometries and optical properties of their complexes. The optimized geometries for the complexes without an axial ligand exhibit planar conformations. Most of the absorption bands of the metal complexes are blue-shifted compared to those of the metal-free naphthalocyanine, both in vacuo and in the solvent. The various transition metals could gradually tune the electronic and spectroscopic properties of their naphthalocyanine complexes, which may provide valuable information for tuning the properties of naphthalocyanine complexes for various applications.