Effective Core Pseudopotentials Research Articles

Modeling stoichiometric and oxygen defective TiO2 anatase bulk and (101) surface: structural and electronic properties from hybrid DFT.

We present a periodic hybrid DFT investigation of the structural and electronic properties of both stoichiometric and oxygen-defective TiO2 anatase bulk and (101) surface, in singlet and triplet spin states. In all cases, an excellent agreement with available photoelectron spectroscopy data has been obtained, reproducing the offsets of the deep defect levels positions from the conduction band minimum of TiO2 created upon oxygen vacancy (VO) formation. For the bulk, different local structural polaronic distortions around the VO site have been evidenced depending on the spin state considered. Although a similar conclusion has been drawn for the defective surface for the nine different vacancy positions which have been considered, large migration of the twofold coordinated surface O atom has also been evidenced, up to the initial vacancy site in some cases. The very good agreement obtained with available experimental data regarding the offsets from the conduction band minimum of the deep defect levels positions both for the bulk and the (101) surface of TiO2 anatase is encouraging for the application of the proposed hybrid-based computational strategy to TiO2 surface-related processes such as TiO2-based photocatalysis in which oxygen vacancies are known to play a key role. All calculations have been performed with Crystal17, considering different hybrid functionals with both effective core pseudopotentials and all-electron atom-centered basis sets, as well as additional empirical dispersion effects with the D2 and D3 models.

A DFT study of graphene-FeNx (x = 4, 3, 2, 1) catalysts for acetylene hydrochlorination

In this paper, we used density functional theory (DFT) to systematically study the mechanism and activity of a graphene-FeNx (x = 4, 3, 2, 1) series of non-noble metal catalysts for acetylene hydrochlorination at the B3LYP/6–31 G** level, and the LANL2DZ effective core pseudo-potentials basis set was applied to Fe atom. Dispersion-corrected DFT-D3 was considered in the calculation. In the process of the graphene-FeNx catalytic reaction, all the catalysts adsorbed acetylene first and adsorbed hydrogen chloride later to form a co-adsorption structure. The calculation results displayed that with a decrease in doped nitrogen atoms in the catalyst, the activity of the reaction decreased successively. Graphene-FeN4 showed excellent catalytic performance, and its energy barrier was only 16.80 kcal/mol. Accordingly, it is a latent non-noble metal catalyst for hydrochlorination of acetylene.

Effect of Charge and Phosphine Ligands on the Electronic Structure of the Au8 Cluster.

In this work, we use density functional theory calculations with a hybrid exchange–correlation functional and effective core pseudopotentials to determine the geometry of bare and phosphine-protected Au8 nanoclusters and characterize their electronic structure. Au8 clusters were bonded to four and eight PH3 ligands in order to evaluate the effect of ligand concentration on the electronic structure, while different positional configurations were also tried for four ligands attached to the cluster. We show that the neutral clusters become more nucleophilic as the ligands bind to the clusters at stable sites. The ground-state planar configuration of Au8 is maintained depending on the concentration and position of ligands. The effect of ionizing to the +2 charge state results in disruption of planar geometry in some cases because of inoccupation of a molecular orbital with the Au–Au bonding character. Natural bond order charge analyses showed that Au atoms oxidize upon ionization, instead of phosphine. The net positive charge makes the clusters more electrophilic with a capacity to absorb electrons from nucleophiles depending on the concentration and position of ligands and on the concentration of low-coordinated gold atoms. Besides, ionization energies and electron affinities were calculated through different mechanisms, finding that both variables are much higher for charged systems and change inversely with the concentration of ligands.

Enhancing 4-propylheptane dissociation with nickel nanocluster based on molecular dynamics simulations

In the present work, a 0.4nm nickel cluster has been theoretically studied. Its equilibrium structural parameters have been calculated by the DFT method based on the PBEH1PBE hybrid functional and split-valence basis set Lanl2DZ including effective core potentials. We have systematically considered diverse spin states of this cluster and find out its ground state. The relative stability of these states depends on the HOMO–LUMO gap. The interaction of the Ni6 with 4-propylheptane С10Н22 has been studied to simulate the process of catalytic cracking of hydrocarbons. The optimization of this structure has been performed by the ωPBE/Lanl2DZ_ecp method (the TeraChem V.1.9 program package) with no symmetry restrictions; the electron shells of the metal were described by effective core pseudopotentials. For visualization and quantitative estimation of the bonding bonds between the nickel nanocluster and 4-propylheptane, the analysis of weak interactions based on RGD has been performed. To confirm the proposition about the formation of Ni–H bonds, we have scrutinized critical points of electronic density. Values of laplasian of electronic density and Bader atomic charge distribution in the global minimum of the total energy have been estimated by the AIMAll 15.05.18 program suite. Finally, we have simulated interaction of Ni6 with 4-propylheptane in terms of the Born–Oppenheimer ab initio molecular dynamics. The results of the molecular dynamics simulation provide pair radial distribution function CH at 1500°C and a detailed picture of the processes occurring in the system.

Ab initio and long-range studies of the electronic transition dipole moments among the low-lying states of Rb2 and Cs2 molecules

The spin allowed electronic transition dipole moments (ETDM) of rubidium and cesium dimers are calculated among the states converging to the lowest three dissociation limits. The ETDM functions are evaluated for a wide range of internuclear distances R in the basis of the spin-averaged wavefunctions corresponding to pure Hund׳s coupling case (a) by using small (including the 8 subvalence +1 valence electrons) effective core pseudopotentials (ECP). The dynamic correlation is accounted for in a large scale multi-reference configuration interaction (MR-CI) method applied to only two valence electrons. The core-polarization potentials (CPP) are implemented to implicitly take the residual core–valence effect into account. The reliability of the present EDTM functions is discussed through comparison with preceding ab initio calculations and their long range perturbation theory counterparts. The achieved accuracy allowed us to quantitatively support the asymptotic behavior of the ETDM functions predicted in Marinescu and Dalgarno (1995 [4]). The long R-range transition moments could be useful to optimize stimulated Raman processes employed in ultracold molecule production.

Theoretical study of spin–orbit and Coriolis coupling among the low-lying states of Rb2 and Cs2

The spin–orbit (SO) and angular (Coriolis) coupling matrix elements of rubidium and cesium dimers have been calculated between the states converging to the lowest three dissociation limits. The relevant quasi-relativistic matrix elements were evaluated for a wide range of internuclear distances and density grid in the basis of the spin-averaged wave functions corresponding to pure Hund’s coupling case (a). Both shape and energy consistent small (9-electrons) effective core pseudopotentials were used to monitor a sensitivity of the matrix elements to the particular basis set. The dynamic correlation has been taken accounted by a large scale multi-reference configuration interaction method which was applied for only two valence electrons. The l-independent core-polarization potentials were employed to take into account the residual core-valence effect. The assessment of current accuracy of the present ab initio functions is discussed by a comparison with preceding calculations and their empirical counterparts.

Non-adiabatic dynamics modeling framework for materials in extreme conditions

Modeling non-adiabatic phenomena and materials at extremes has been a long-standing challenge for computational chemistry and materials science, particularly for systems that undergo irreversible phase transformations due to significant electronic excitations. Ab initio and existing quantum mechanics approximations to the Schrödinger equation have been limited to ground-state descriptions or few excited electronic states, less than 100 atoms, and sub-picosecond timescales of dynamics evolution. Recently, the electron force field (eFF) introduced by Su and Goddard (2007) presented a cost-efficient alternative to describe the dynamics of electronic and nuclear degrees of freedom. eFF describes an N-electron wave function as a Hartree product of one-electron floating spherical Gaussian wave packets propagating via the time-dependent Schrödinger equation under a mixed quantum–classical Hamiltonian evaluated as sum of self- and pairwise potential interactions. Local Pauli potential corrections replace the need for explicit anti-symmetrization of total electronic wavefunction, a wavefunction kinetic energy term accounts for Heisenberg’s uncertainty, and classical electrostatics complete the total eFF energy expression. However, due to the spherical symmetry of the underlying Gaussian basis functions, the original eFF formulation is limited to low-Z numbers with electrons of predominant s-character. To overcome this, we introduce here a formal set of potential form extensions that enable accurate description of p-block elements in the periodic table. The extensions consist of a model representing the core electrons of an atom together with the nucleus as a single pseudo particle with wave-like behavior, interacting with valence electrons, nuclei, and other cores through effective core pseudopotentials (ECPs). We demonstrate and validate the ECP extensions for complex bonding structures, geometries and energetics of systems with p-block character (containing silicon, oxygen, carbon, or aluminum atoms and combination thereof) and apply them to study materials under extreme mechanical loading conditions.

General Multiobjective Force Field Optimization Framework, with Application to Reactive Force Fields for Silicon Carbide.

First-principles-based force fields prepared from large quantum mechanical data sets are now the norm in predictive molecular dynamics simulations for complex chemical processes, as opposed to force fields fitted solely from phenomenological data. In principle, the former allow improved accuracy and transferability over a wider range of molecular compositions, interactions, and environmental conditions unexplored by experiments. That is, assuming they have been optimally prepared from a diverse training set. The trade-off has been force field engines that are functionally complex, with a large number of nonbonded and bonded analytical forms that give rise to rather large parameter search spaces. To address this problem, we have developed GARFfield (genetic algorithm-based reactive force field optimizer method), a hybrid multiobjective Pareto-optimal parameter development scheme based on genetic algorithms, hill-climbing routines and conjugate-gradient minimization. To demonstrate the capabilities of GARFfield we use it to develop two very different force fields: (1) the ReaxFF reactive force field for modeling the adiabatic reactive dynamics of silicon carbide growth from an methyltrichlorosilane precursor and (2) the SiC electron force field with effective core pseudopotentials for modeling nonadiabatic dynamic phenomena with highly excited electronic states. The flexible and open architecture of GARFfield enables efficient and fast parallel optimization of parameters from quantum mechanical data sets for demanding applications like ReaxFF, electronic fast forward (or electron force field), and others including atomistic reactive charge-optimized many-body interatomic potentials, Morse, and coarse-grain force fields.

A quantum chemical study of the structure and energy of β-diketonates. XVII. Internal rotation of radical substituents in β-diketonate molecules

A quantum chemical study of the internal rotation of CX3 (X = H, F, CH3) radical substituents in scandium and calcium β-diketonate complexes is performed. Calculations are carried out using the GAUSSIAN-03 program at the HF and DFT/B3LYP levels with relativistic effective core pseudo-potentials and valence double zeta basis sets. Analytical expressions V(φ) are obtained that describe the potential energy variation during the rotation of CX3 groups. The rotation of CH3 and CF3 groups is shown to be described by a simple potential of the form V = V0/2 + V3cos(3φ), while for the description of the rotation of tert-butyl groups it is required to use a more complex function V = V0/2 + V3cos(3φ) + V6cos(6φ). Based on the obtained expressions for V(φ), the effective torsion angles φef of the rotation of CX3 groups are calculated for different temperatures. It is shown that φef obtained based on the quantum chemical calculations are close to the values obtained in electron diffraction experiments.

Theoretical Study of the Low Lying States of Ga2X (X = P, As)

Since the low lying electronic states of Ga(2)X (X = P, As) are nearly degenerate, an accurate determination of the electronic structure of these states was incomplete in the previous works. In this study, the geometry optimization and vibrational frequency calculation have been performed at the various levels of theory, using the effective core pseudopotentials of the Ga and As atoms and the associated cc-pVTZ basis sets. The ground state of Ga(2)P is found to be the (2)A' state correlating with the (2)B(2) state in C(2v) structure, which lies 0.031 eV above the global minimum at the RCCSD(T) level. The equilibrium of the (2)A(1) state is optimized above that of the (2)B(2) state, and the (2)B(1) state, predicted previously as the ground state, has a stable minimum above the optimized geometries of the former states. Concerning the low lying states of Ga(2)As, our results confirm in general the previous studies. Because all the states of both compounds can be considered monoconfigurational around their equilibrium, the RCCSD(T) method is well adapted to acurrately describe both systems. In turn, we have applied our obtained information to analyze the Ga(2)P(-) and Ga(2)As(-) anion photoelectron spectra, to which it remains difficult to appropriately assign the low lying states of Ga(2)P and Ga(2)As. As a consequence, our analysis supports the previous assignment for Ga(2)P, but contrasts partially to that for Ga(2)As.

An AB Initio Study of the Electronic and Geometric Structure of BIS-of Dipivaloylmethane With Manganese, IRON, and Cobalt

An ab initio study of the structure of Mn(thd)2, Fe(thd)2, and Co(thd)2 complexes in different electronic states is carried out. Quantum chemical calculations are performed using the PC GAMESS program with relativistic effective core pseudopotentials and Gaussian valence triple-zeta basis sets. Calculation methods: DFT/ROB3LYP and CASSCF followed by the inclusion of dynamic electron correlation through multiconfiguration quasi-degenerate second order perturbation theory (MCQDPT2). All three complexes are shown to have a low-spin electronic ground state with a planar structure of the bicyclic fragment at D2h molecular symmetry. The M—O bond is mainly ionic, and M(thd)2 molecules can be considered as an M2+ cation coordinated by two negatively charged bidentate ligands.

Ab initio Study of HZnF

On the basis of highly correlated ab initio calculations, an accurate determination of the electronic structure and of the rovibrational spectroscopy has been performed for the electronic ground state of the HZnF system. Using effective core pseudopotentials for the Zn and F atoms and associated aug-cc-pVQZ basis sets, we have calculated, at the multireference configuration interaction level including the Davidson correction, the three-dimensional potential energy surface of the X(1)Sigma(+) ground state. The rovibrational energy levels have been obtained variationally, and the results have been discussed and compared with existing experimental data on the ground state of the close system HZnCl, which exhibits a complicated vibration-rotation spectrum. Our analysis shows that the nature of the H-ZnF bond is quite similar to that of the H-ZnCl bond, according to their bond lengths, harmonic frequencies of the H-Zn stretching mode, and dissociation energies into H and ZnF/ZnCl. The ab initio study of the electronic ground and excited states of ZnH and ZnH(+) are also presented using similar level of calculations. Characteristic constants are given for the first bounded electronic states correlating to the first two dissociation asymptotes of the neutral and ionic diatomics.

Density Functional Study on Relative Energies, Structures, and Bonding of Low-lying Electronic States of Lutetium Dimer

Low-lying electronic states of the lutetium dimer (Lu2) were studied based on density functional theory (DFT) using ten different density functionals together with three different relativistic effective core pseudopotentials (RECPs). Relative state energies, equilibrium bond lengths, vibrational frequencies, and ground-state dissociation energies were evaluated. It was found that the ground state is a triplet state irrespective of the type of functional and RECP used. This result is in contrast with a previous DFT calculation which gave a singlet ground state for Lu2. By comparing with the high-level ab initio and available experimental results, it is evident that the hybrid-GGA functionals combined with the Stuttgart small-core RECP yield the best overall agreement for the properties under study. The effects of HartreeFock exchange in B3LYP functional on the calculated bond length and dissociation energy of the ground state were examined, and rationalized in terms of 5d participation in LuLu covalent bonding.

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case ( a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X 1 Σ + and a 3 Σ + states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ + states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3) 3 Σ + states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ -doubling constants of the (1,2) 1 Π states and magnetic g -factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.

Ab initiostudy of the low lying electronic states of ZnF and ZnF−

Highly correlated ab initio calculations have been performed for an accurate determination of the electronic structure and of the spectroscopy of the low lying electronic states of the ZnF system. Using effective core pseudopotentials and aug-cc-pVQZ basis sets for both atoms, the potential curves, the dipole moment functions, and the transition dipole moments between relevant electronic states have been calculated at the multireference-configuration-interaction level. The spectroscopic constants calculated for the X(2)Sigma(+) ground state are in good agreement with the most recent theoretical and experimental values. It is shown that, besides the X(2)Sigma(+) ground state, the B(2)Sigma(+), the C(2)Pi, and the D(2)Sigma(+) states are bound. The A(2)Pi state, which has been mentioned in previous works, is not bound but its potential presents a shoulder in the Franck-Condon region of the X(2)Sigma(+) ground state. All of the low lying quartet states are found to be repulsive. The absorption transitions from the v=0 level of the X(2)Sigma(+) ground state toward the three bound states have been evaluated and the spectra are presented. The potential energy of the ZnF(-) molecular anion has been determined in the vicinity of its equilibrium geometry and the electronic affinity of ZnF (EA=1.843 eV with the zero energy point correction) has been calculated in agreement with the photoelectron spectroscopy experiments.

Toward a physical understanding of electron‐sharing two‐center bonds. I. General aspects

In 1916, Lewis and Kossel laid the empirical ground for the electronic theory of valence, whose quantum theoretical foundation was uncovered only slowly. We can now base the classification of the various traditional chemical bond types in a threefold manner on the one- and two-electron terms of the quantum-physical Hamiltonian (kinetic, atomic core attraction, electron repulsion). Bond formation is explained by splitting up the real process into two physical steps: (i) interaction of undeformed atoms and (ii) relaxation of this nonstationary system. We aim at a flexible bond energy partitioning scheme that can avoid cancellation of large terms of opposite sign. The driving force of covalent bonding is a lowering of the quantum kinetic energy density by sharing. The driving force of heteropolar bonding is a lowering of potential energy density by charge rearrangement in the valence shell. Although both mechanisms are quantum mechanical in nature, we can easily visualize them, since they are of one-electron type. They are however tempered by two-electron correlations. The richness of chemistry, owing to the diversity of atomic cores and valence shells, becomes intuitively understandable with the help of effective core pseudopotentials for the valence shells. Common conceptual difficulties in understanding chemical bonds arise from quantum kinematic aspects as well as from paradoxical though classical relaxation phenomena. On this conceptual basis, a dozen different bond types in diatomic molecules will be analyzed in the following article. We can therefore examine common features as well as specific differences of various bonding mechanisms.

Bimetallic Clusters Pt6Au: Geometric and Electronic Structures within Density Functional Theory.

Within density functional theory at the general gradient approximation for exchange and correlation (BPW91) and the relativistic 19-electron Los Alamos National Laboratory effective core pseudopotentials and basis sets (3s3p2d), the geometric and electronic structures of Pt6Au bimetallic clusters have been studied in detail in comparison with Pt7. A total of 38 conformations for Pt6Au are located. The most stable conformation for Pt6Au is a sextet with an edge- and face-capped trigonal bipyramid, in which the Au atom caps an edge of the trigonal bipyramid. Pt6Au, in general, prefers a three-dimensional geometry and high spin electronic state with multireference character. The electronic impact of the doping of Au in Pt clusters on the overall chemical activity of the doped bimetallic cluster is not as significant as that of the doping of Pt in Au clusters; however, the doping of Au lowers the chemical activity, thus enhancing the chemoselectivity in the gas phase, of PtAu bimetallic clusters.

Bimetallic Clusters Pt6Au: Geometric and Electronic Structures within Density Functional Theory

Within density functional theory at the general gradient approximation for exchange and correlation (BPW91) and the relativistic 19-electron Los Alamos National Laboratory effective core pseudopotentials and basis sets (3s3p2d), the geometric and electronic structures of Pt(6)Au bimetallic clusters have been studied in detail in comparison with Pt(7). A total of 38 conformations for Pt(6)Au are located. The most stable conformation for Pt(6)Au is a sextet with an edge- and face-capped trigonal bipyramid, in which the Au atom caps an edge of the trigonal bipyramid. Pt(6)Au, in general, prefers a three-dimensional geometry and high spin electronic state with multireference character. The electronic impact of the doping of Au in Pt clusters on the overall chemical activity of the doped bimetallic cluster is not as significant as that of the doping of Pt in Au clusters; however, the doping of Au lowers the chemical activity, thus enhancing the chemoselectivity in the gas phase, of PtAu bimetallic clusters.

The open-shell interaction of He with the B 3Piu(0+) state of Br2: an ab initio study and its comparison with a diatomics-in-molecule perturbation model.

The interaction of He with Br2 in electronically excited B 3Piu state is investigated using spin-unrestricted single and double coupled-cluster approach with noniterative perturbative treatment of triple excitations. Internal electrons of the Br atom are described by effective core pseudopotentials. The validity of this approach is analyzed by comparing the lowest 2Sigma+ and 2Pi electronic states of the HeBr molecule with those obtained in all electron calculations [J. Chem. Phys. 115, 10438 (2001)]. In this context, we examine the performance of different basis sets and saturation with bond functions. The comparison of theoretical blue-shifts with the experiment provides confidence about the present ab initio calculations. In addition, He-Br results of ab initio calculations at the same level are used to obtain approximate He-Br2 (3Piu) interactions in the framework of the diatomics-in-molecule first order perturbation theory (IDIM-PT1) [J. Chem. Phys. 104, 9913 (1996)]. Overall, the IDIM-PT1 model results show a good agreement with the ab initio ones, being the main difference the sensitivity to the elongation of the Br-Br bond.

Ab initio study of 2H-MoS2using Hay and Wadt effective core pseudo-potentials for modelling the (101̄0) surface structure

Periodic Hartree–Fock and DFT methods were employed to calculate the geometric and electronic properties of bulk 2H-MoS2 and of its catalytically important (100) edge structure. The core electrons of molybdenum and sulfur were represented by the effective core pseudo-potentials, developed by Hay and Wadt. For the calculations (100) type surface structures were generated by cutting sections from an 2H-MoS2 crystal, which consists of four, six or eight rows of molybdenum and sulfur atoms. The calculated elastic constants follow the experimental constants and show that 2H-MoS2 is an anisotropic covalent compound held together by weak dispersion interactions between neighbouring S-Mo-S units. The relaxation of the (100) surface of 2H-MoS2 leads to an inner relaxation of the Mo atoms and the formation of weakly coupled surface S-S species. As a result of the surface relaxation, the electronic charge of the surface states is different to that of the bulk states: empty Mo d states move into the band gap, and the surface becomes a better electron acceptor. In all calculations the model consisting of six rows of sulfur and molybdenum atoms is the most favourable one, because it provides an accurate description of the 2H-MoS2 surface structure and enables calculations at reasonable computation time. The calculations based on pseudo-potentials are in good agreement with all-electron calculations and confirm that, in contrast to the semiconducting bulk, the (100) 2H-MoS2 surface has metallic properties.