Liangyou Fan

The influence of self‐consistency on nonlocal density functional calculations

A self‐consistent nonlocal density functional method (NL‐SCF) based on the gradient corrected exchange term by Becke [Phys. Rev. A 33, 2786(1988)] and a gradient corrected correlation term by Perdew [Phys. Rev. B 33, 8822(1986)] has been implemented into the hfs‐lcao‐program by Baerends et al. [Chem. Phys. 2, 41(1973)]. An expression for the variational potential corresponding to Becke’s gradient correction has been derived. A detailed analysis is given of the change in density δρ induced by the gradient corrections. It is shown that δρ is 2 orders of magnitude smaller than the deformation density Δρ=ρmolecule−ρatom. The dipole moments calculated by NL‐SCF differ as a consequence only modestly from dipole moments obtained by the local density approximation (LDA), in which the gradient corrections are absent. The importance of self‐consistency for calculations on bond distances, bond energies, and vibrational frequencies are assessed by comparing results from NL‐SCF calculations with data obtained by a per...

Optimization of molecular structures by self-consistent and nonlocal density-functional theory

An algorithm for the calculation of energy gradients has been implemented into the linear combination of atomic orbitals‐Hartree–Fock–Slater (LCAO‐HFS) program due to Baerends et al. [Chem. Phys. 2, 41 (1973)], and tested in connection with geometry optimizations of transition‐metal complexes, organic molecules and compounds of main group elements. The algorithm is based on a self‐consistent nonlocal density‐functional method (NL‐SCF) combining the nonlocal exchange correction by Becke [Phys. Rev. A 38, 3098 (1988)] with the nonlocal correlation correction by Perdew [Phys. Rev. B 33, 8822 (1986)]. It is shown that nonlocal corrections to the local‐density approximation (LDA) improves the calculated metal‐ligand bond distances considerably. Full optimizations of MnO−4, Cr(CO)6, Mo(CO)6, Fe(CO)5, Ni(CO)4, HMn(CO)5, HCo(CO)4, Fe(C5H5)2, and C5H5NiNO revealed that the LDA underestimates metal‐ligand bond distances by an average of 0.05 A, whereas nonlocal corrections, on the average, reduce the error to 0.01 ...

Application of density functional theory to infrared absorption intensity calculations on main group molecules

Approximate density functional theory has been evaluated as a practical tool for calculations on infrared vibrational frequencies and absorption intensities. The density functional schemes included the local density approximation (LDA) by Gunnarson [Phys. Rev. B 10, 1319 (1974)] as well as a self‐consistent nonlocal density functional method (LDA/NL) in which the gradient corrected exchange term by Becke [Phys. Rev. A 38, 3098 (1988)] and the gradient corrected correlation term by Perdew [Phys. Rev. B 33, 8822 (1986)] has been added to LDA. The LDA and LDA/NL schemes have been applied to calculations on the infrared vibrational frequencies and absorption intensities of H2O, NH3, H2CO, C2H4, CH3OH and oxirane. The calculations were carried out with two basis sets of respectively double‐ζ plus polarization (DZP) and triple‐ζ plus polarization (TZP) quality. The study has demonstrated that vibrational frequencies are relatively insensitive to the level of density functional theory as well as to the choice of...

An implementation of the coupled perturbed Kohn-Sham equations: perturbation due to nuclear displacements

Abstract The Coupled Perturbed Kohn-Sham equations have been implemented in the Amsterdam Density Functional program package. Our implementation differs from previous ones in many ways. This program uses density fitting to calculate the Coulomb and exchange integrals. Further, all matrix elements of the Fock type matrix and its derivatives are calculated by numerical integration. The frozen core approximation is also implemented. Our implementation is approximately 10 times faster than a finite difference algorithm, and the absolute CPU times also compare favorably with other reported implementations.

A combined density functional and intrinsic reaction coordinate study on the ground state energy surface of H2CO

Approximate density functional theory (DFT) has been used to study four elementary processes on the singlet ground state energy surface of H2CO. The elementary steps include the elimination of H2 and CO from formaldehyde, the transformation of formaldehyde to trans‐hydroxymethylene, the isomerization of trans‐hydroxymethylene to cis‐hydroxymethylene, and the 1,2 elimination of H2 from cis‐hydroxymethylene. The DFT studies were based on the local density approximation (LDA) as well as a nonlocal self‐consistent field (NL‐SCF) extension in which Perdew’s correlation correction and Becke’s exchange correction were added to LDA. Fully optimized structures as well as harmonic vibrational frequencies have been evaluated for all of the stationary points corresponding to the reactants, products, and transition states for the four reactions within the LDA and NL‐SCF approximations. The four reactions have in addition been studied by the intrinsic reaction coordinate (IRC) method in which stationary points on the p...

The application of density functional theory to the optimization of transition state structures. I. Organic migration reactions

We present here the first determination of transition state structures based on Hartree–Fock–Slater (HFS) density functional calculations. The optimization of the transition state structures utilized the analytical energy gradients evaluated by a recently developed method. The transition state structures obtained by the HFS method are similar to those determined by ab initio methods in which electron correlation is partly taken into account. The energy barrier for the CH3NC→CH3CN isomerization process, corrected for the zero‐point energy, is 40.1 kcal mol−1 which is in good agreement with the experimental value of 38.4 kcal mol−1. Experimental barriers are not available for the HNC→HCN and N2H2(trans)→N2H2(cis) isomerization processes. However, the barriers calculated by the HFS method are in good accordance with the barriers obtained from electron‐correlation calculations. Furthermore, the vibrational frequencies calculated by the HFS method are in good agreement either with experiments in the case of st...

A density functional study on the insertion mechanism and chain termination in Kaminsky-type catalysts; comparison of frontside and backside attack☆

Abstract Non-local density functional (DF) calculations have been carried out on the reaction of ethylene with Cp 2 Zr + , which serves as a model for the resting state between two insertions. The β-agostic Cp 2 Zr + Et is 47.0 kJ mol −1 more stable than the α-agostic conformer. Frontside insertion of the olefin can take place after rotation around the ZrC α -bond forming the α-agostic Cp 2 Zr + Et. An α-agostic π-complex is formed with a complexation energy of 81.1 kJ mol −1 and the frontside transition state has an activation energy of 2 kJ mol −1 relative to the π-complex. The reaction is exothermic by 118.9 kJ mol −1 . Without rotation around the ZrC α bond a β-agostic π-complex is formed and H-transfer from the polymer chain end to the olefin takes place. This reaction leads to chain termination with an activation barrier of 29.8 kJ mol −1 . An alternative path for the olefin insertion starts with a backside attack of the olefin. The activation barrier for the backside insertion is 28.9 kJ mol −1 and the reaction is exothermic by 24.9 kJ mol −1 relative to the π-complex. Backside insertion does not involve inversion at the metal centre. The formation of syndiotactic polypropene in the case of the backside insertion can only be explained with chain-end control. Comparison of three chain termination processes (β-hydride elimination, C-H activation and H-exchange) indicates that H-exchange is the most probable reaction. β-Elimination is strongly endothermic and frontside C-H-activation makes a rotation around ZrC α necessary.

A Combined Density Functional and Molecular Mechanics Study on Olefin Polymerization by Metallocene Catalysts

A study based on density functional theory (DFT) and molecular mechanics is presented on processes related to ethylene polymerization by metallocenes. The study makes use of Cp2Zr-CH 3 + as the model catalysts and all calculations are based on the AMOL program system. Calculations have been carried out on the energy profile for the insertion reaction: Cp2M-CH3 1a + H2C = CH2 → Cp2M-CH2CH2CH3 1d. The computational study has shown that a π-ethylene complex with a very shallow potential well is involved as an intermediate in the insertion process. Also the barrier to insertion is modest and amounts to less than 1 kcal/mol. The propyl complex, 1d, can adopt several conformations including structures in which a C-H bond is involved in a β-agostic interaction, or a γ-agostic interaction with the metal center. The structure with a β-agostic interaction is the most stable. Our study does support the view that α-agostic interactions are important for the stability of 1a. It is suggested that the experimental barrier of activation for the propagation in olefin polymerization is due to the rearrangement of 1d in order to free the coordination site for the next insertion, rather than the actual insertion. Two chain terminating steps have been studied, involving β-hydrogen elimination: Cp2Zr+-CH2CH3 → Cp2Zr+-H + H2C = CH2, and C-H activation: Cp2Zr+-CH3 + H2C = CH2→Cp2Zr+-CH = CH2 + CH4. The β-hydrogen elimination reaction is endothermic by 42 kcal/mol whereas the C-H activation reaction is exothermic by 14.7 kcal/mol. It is concluded that β-hydride elimination is unlikely a dominant chain termination step based on thermodynamic and kinetic considerations.

The Application of Nonlocal and Self-Consistent Density Functional Theory to Molecular Problems

A self consistent nonlocal density functional method (NL-SCF) based on the gradient corrected exchange term by Becke [Phys. Rev. A38, 3098(1988)] and a gradient corrected correlation term by Perdew [Phys. Rev. B33, 8822(1986)] has been implemented into the LCAO-HFS program by Baerends et al. [Chem. Phys. 2, 41(1973)]. An expression for the variational potential corresponding to Becke’s gradient correction has been derived. A detailed analysis is given of the change in density, 5p, induced by the gradient corrections. It is shown that δp is two orders of magnitude smaller than the deformation density Δρ = ρmolecule -ρatom. The dipole moments calculated by NL-SCF differ as a consequence only modestly from dipole moments obtained by the Local Density Approximation (LDA) in which the gradient corrections are absent. The importance of self-consistency for calculations on bond distances, bond energies and vibrational frequencies are assessed by comparing results from NL-SCF calculations with data obtained by a perturbative approach (NL-P) in which densities obtained from LDA calculation were used in the evaluation of the gradient corrections. It is further shown that results from calculations on metal-ligand bond distances and bond energies are improved considerably by nonlocal corrections.