Solvent effects on the S(N)2 reaction: Application of the density functional theory-based effective fragment potential method

The performance of the density functional theory (DFT)-based effective fragment potential (EFP) method is assessed using the S(N)2 reaction: Cl- + nH2O + CH3Br = CH3Cl + Br- + nH2O. The effect of the systematic addition of water molecules on the structures and relative energies of all species involved in the reaction has been studied. The EFP1 method is compared with second-order perturbation theory (MP2) and DFT results for n = 1, 2, and 3, and EFP1 results are also presented for four water molecules. The incremental hydration effects on the barrier height are the same for all methods. However, only full MP2 or MP2 with EFP1 solvent molecules are able to provide an accurate treatment of the transition state (TS) and hence the central barriers. Full DFT and DFT with EFP1 solvent molecules both predict central barriers that are too small. The results illustrate that the EFP1-based DFT method gives reliable results when combined with an accurate quantum mechanical (QM) method, so it may be used as an efficient alternative to fully QM methods in the treatment of larger microsolvated systems.     

What makes an N12 cage stable?

Much recent attention has been given to molecules containing only nitrogen atoms. Such molecules N(x) can undergo the reaction N(x) --> (x/2)N(2), which is very exothermic. These molecules are potential candidates for high energy density materials (HEDM). However, many all-nitrogen molecules dissociate too easily to be stable, practical energy sources. It is important to know which nitrogen molecules will be stable and which will not. In the current study, a variety of N(12) cages with all single bonds are examined by theoretical calculations to determine which ones are the most thermodynamically stable. Calculations are carried out using Hartree-Fock (HF) theory, gradient-corrected density functional theory (DFT), and Moller-Plesset perturbation theory (MP2 and MP4). Relative energies among the various isomers are calculated and trends are examined in order to determine which structural features lead to the most energetically favorable molecules.     

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order M?ller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.     

Formation and bonding of alane clusters on Al(111) surfaces studied by infrared absorption spectroscopy and theoretical modeling

Alanes are believed to be the mass transport intermediate in many hydrogen storage reactions and thus important for understanding rehydrogenation kinetics for alanates and AlH3. Combining density functional theory (DFT) and surface infrared (IR) spectroscopy, we provide atomistic details about the formation of alanes on the Al(111) surface, a model environment for the rehydrogenation reactions. At low coverage, DFT predicts a 2-fold bridge site adsorption for atomic hydrogen at 1150 cm(-1), which is too weak to be detected by IR but was previously observed in electron energy loss spectroscopy. At higher coverage, steps are the most favorable adsorption sites for atomic H adsorption, and it is likely that the AlH3 molecules form (initially strongly bound to steps) at saturation. With increasing exposures AlH3 is extracted from the step edge and becomes highly mobile on the terraces in a weakly bound state, accounting for step etching observed in previous STM studies. The mobility of these weakly bound AlH3 molecules is the key factor leading to the growth of larger alanes through AlH3 oligomerization. The subsequent decomposition and desorption of alanes is also investigated and compared to previous temperature programmed desorption studies.     

Symmetric ring puckering potential in thietane‐1,1‐dioxide compared with experiment and analysis of theoretical vibrational spectra

We studied the ring puckering potential in thietane‐1,1‐dioxide with different methods, using a suitable basis set, 6‐311+G**. We obtained a barrier to ring puckering of 153 cal/mol with the DFT/B3LYP (Becke3 exchange–Lee, Yang, Parr correlation functional) method, ～60% too small compared with experiment. However, using MP2, MP3, and MP4 we obtained values around 200% too large. The MP series turned out to converge far too slowly to the experimental barrier value, showing no sign of convergence even at MP4, while higher orders are out of our reach for such a system. Obviously, of all methods used, DFT worked best despite some shortcomings. The barrier corresponds to 77 K; thus, there should be rapid interconversion over the barrier at room temperature, a phenomenon actually observed at room temperature, the measured barrier corresponding to 201 K. Thus, we decided to use the DFT/6‐311+G** calculations to predict reasonable vibrational spectra and assignments of the lines found. The ring puckering mode is found at 80 cm^?1 in DFT in good agreement with the experimental value of 78.3 cm^?1 for this vibration. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Engaging Aldehydes in CuH‐Catalyzed Reductive Coupling Reactions: Stereoselective Allylation with Unactivated 1,3‐Diene Pronucleophiles

Recently, CuH‐catalyzed reductive coupling processes involving carbonyl compounds and imines have become attractive alternatives to traditional methods for stereoselective addition because of their ability to use readily accessible and stable olefins as surrogates for organometallic nucleophiles. However, the inability to use aldehydes, which usually reduce too rapidly in the presence of copper hydride complexes to be viable substrates, has been a major limitation. Shown here is that by exploiting relative concentration effects through kinetic control, this intrinsic reactivity can be inverted and the reductive coupling of 1,3‐dienes with aldehydes achieved. Using this method, both aromatic and aliphatic aldehydes can be transformed into synthetically valuable homoallylic alcohols with high levels of diastereo‐ and enantioselectivities, and in the presence of many useful functional groups. Furthermore, using a combination of theoretical (DFT) and experimental methods, important mechanistic features of this reaction related to stereo‐ and chemoselectivities were uncovered.     

The microwave spectrum of a two-top peptide mimetic: the N-acetyl alanine methyl ester molecule

The rotational spectrum of N-acetyl alanine methyl ester, a derivative of the biomimetic, N-acetyl alanine N'-methyl amide or alanine dipeptide, has been measured using a mini Fourier transform spectrometer between 9 and 25 GHz as part of a project undertaken to determine the conformational structures of various peptide mimetics from the torsion-rotation parameters of low-barrier methyl tops. Torsion-rotation splittings from two of the three methyl tops capping the acetyl end of the -NH-C(=O)- and the methoxy end of -C(=O)-O- groups account for most of the observed lines. In addition to the AA state, two E states have been assigned and include an AE state having a torsional barrier of 396.45(7) cm(-1) (methoxy rotor) and an EA state having a barrier of 64.96(4) cm(-1) (acetyl rotor). The observed torsional barriers and rotational constants of alanine dipeptide and its methyl ester are compared with predictions from M?ller-Plesset second-order perturbation theory (MP2) and density functional theory (DFT) in an effort to explore systematic errors at the two levels of theory. After accounting for zero-point energy differences, the torsional barriers at the MP2/cc-pVTZ level are in excellent agreement with experiment for the acetyl and methoxy groups while DFT predictions range from 8% to 80% too high or low. DFT is found to consistently overestimate the overall molecular size while MP2 methods give structures that are undersized. Structural discrepancies of similar magnitude are evident in previous DFT results of crystalline peptides.     

On the achievement of high fidelity and scalability for large‐scale diagonalizations in grid‐based DFT simulations

Recent advance in high performance computing (HPC) resources has opened the possibility to expand the scope of density functional theory (DFT) simulations toward large and complex molecular systems. This work proposes a numerically robust method that enables scalable diagonalizations of large DFT Hamiltonian matrices, particularly with thousands of computing CPUs (cores) that are usual these days in terms of sizes of HPC resources. The well‐known Lanczos method is extensively refactorized to overcome its weakness for evaluation of multiple degenerate eigenpairs that is the substance of DFT simulations, where a multilevel parallelization is adopted for scalable simulations in as many cores as possible. With solid benchmark tests for realistic molecular systems, the fidelity of our method are validated against the locally optimal block preconditioned conjugated gradient (LOBPCG) method that is widely used to simulate electronic structures. Our method may waste computing resources for simulations of molecules whose degeneracy cannot be reasonably estimated. But, compared to LOBPCG method, it is fairly excellent in perspectives of both speed and scalability, and particularly has remarkably less (< 10%) sensitivity of performance to the random nature of initial basis vectors. As a promising candidate for solving electronic structures of highly degenerate systems, the proposed method can make a meaningful contribution to migrating DFT simulations toward extremely large computing environments that normally have more than several tens of thousands of computing cores.     

密度泛函理论及其数值方法新进展

综述了密度泛函理论及其数值方法的最新进展.密度泛函理论的发展以寻找合适 的交换相关近似为主线,从最初的局域密度近似、广义梯度近似到现在的非局域泛函、自相 互作用修正,多种泛函形式的相继出现使得密度泛函理论可以提供越来越精确的计算结果. 除了交换相关近似的发展,近年来密度泛函理论向含时理论、相对论等方面的扩展也很活跃 .另外,在密度泛函理论体系发展的同时,相应的数值计算方法的发展也非常迅速.从古老 的有限差分、有限元到新兴的小波分析都被用来实现密度泛函理论的数值计算.与此同时, 线性标度的密度泛函理论算法日趋成熟,使得通过密度泛函理论研究诸如生物大分子之类的 体系成为可能.随着密度泛函理论本身及其数值方法的发展,它的应用也越来越广泛,一些新的应用领域和研究方向不断涌现.     

The devil in the details: A tutorial review on some undervalued aspects of density functional theory calculations

Density functional theory (DFT) has become ubiquitous for chemical applications in research and in education. The exact functional at the foundation of DFT is unfortunately unknown, and issues arise when choosing an approximation for a specific application. With this tutorial review, we tackle the selection problem and many related ones, such as the choices of a basis set and of an integration grid, that are often overlooked by occasional practitioners and by more experienced users as well. We offer a practical approach in the form of a commented notebook containing 12 experiences that can be run on a simple computer in just a few hours. We propose this review as a primary source for those who are willing to include DFT in their everyday research or teaching activities in a way that reflects the research advances of the field in the last couple of decades.     

The computation of the potential energy surface for H2 + OH → H2O + H using ab initio and density functional theory methods

The reaction energy profile for H₂ + OH → H + H₂O was computed using HF, MP2, MP4, QCISD, G1, G2, and G2MP2 ab initio methods. In addition, the B3LYP, B3P86, B3PW91, BLYP, BP291, and SVWN density functional theory (DFT) methods were also used. All the ab initio methods, with the exception of the G series, produced much higher activation barriers and heats of reaction than the experimental values. On the other hand, the DFT methods produced negative forward and reverse barriers which were too low, with the exception of the hybrid DFT methods. The G2 ab initio method generated energies which deviated from the experimental values by ∼ 1 kcal/mol and therefore should be considered a very accurate computational method. The hybrid DFT methods produced positive forward reaction barriers with energies that were 2–4 kcal/mol lower than the experimental values. The geometries of the transition state and energies computed by the ab initio and DFT methods were compared. These results suggest that, in the hybrid exchange functional, the portion of the Slater exchange term should be increased. This may be the reason why the computed energies were too low. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 639–644, 1997     

Atropisomers of hindered triarylisocyanurates: structure, conformation, stereodynamics, and absolute configuration

The syn and anti diastereoisomers of some 1,3,5-triarylisocyanurate derivatives were isolated and their configuration assigned by NOE experiments and by X-ray diffraction. The kinetics of the syn/anti interconversion were determined, and the experimental activation energies matched satisfactorily the values predicted by DFT computations. Low-temperature NMR spectra were employed to determine the rotation barrier of N-bonded unhindered aryl substituents: these barriers, too, are satisfactorily reproduced by DFT computations. In the case of racemic diastereoisomers, the two expected enantiomers (atropisomers) were isolated by enantioselective HPLC and the absolute configuration established by DFT simulation of the electronic and vibrational circular dichroism spectra.     

Toward an accurate and efficient theory of physisorption. I. Development of an augmented density-functional theory model

Currently available density functionals cannot describe the dispersion component of the interaction energy present in weakly bound complexes. Moreover, the exchange energy as obtained from the density-functional theory is often incorrect. Examples of problematic cases include clusters of van der Waals-bound rare-gas atoms and most hydrogen-bonded molecular systems. Thus, accurate ab initio methods to treat intermolecular forces should be used in such systems. These methods are, however, too slow to be applicable to the large systems needed to model adsorption. This is why DFT continues to be used, where, in addition, a quite common compensation of errors sometimes produces some sort of agreement with the corresponding experimental data. In this paper, we analyze in detail the inadequacy of standard DFT for describing the weak binding present in a few rare gas-rare gas, metal atom-rare gas, and metal atom-metal atom dimers.Inspired by the success of the Hartree-Fock plus (damped) dispersion (HFD) method, we test the use of an improved hybrid model in which to a density-functional interaction energy (with corrected exchange and avoidance of double-counting of dispersion), a (damped) dispersion expansion is added in the usual way.Comparisons with accurate theoretical or experimental benchmarks show that our DFdD method using the revPBEx or revPBEx+VWNc functionals and accurate dispersion coefficients is found to recover the interaction energy curves very well for many of the tested systems. The sec and paper in this series will describe the use of the DFdD method for physisorption for the previously well-studied (but not solved) case of Xe/Cu(111).     

Modeling and computations of the intramolecular electron transfer process in the two-heme protein cytochrome c(4)

The di-heme protein Pseudomonas stutzeri cytochrome c(4) (cyt c(4)) has emerged as a useful model for studying long-range protein electron transfer (ET). Recent experimental observations have shown a dramatically different pattern of intramolecular ET between the two heme groups in different local environments. Intramolecular ET in homogeneous solution is too slow (>10 s) to be detected but fast (ms-μs) intramolecular ET in an electrochemical environment has recently been achieved by controlling the molecular orientation of the protein assembled on a gold electrode surface. In this work we have performed computational modeling of the intramolecular ET process by a combination of density functional theory (DFT) and quantum mechanical charge transfer theory to disclose reasons for this difference. We first address the electronic structures of the model heme core with histidine and methionine axial ligands in both low- and high-spin states by structure-optimized DFT. The computations enable estimating the intramolecular reorganization energy of the ET process for different combinations of low- and high-spin heme couples. Environmental reorganization free energies, work terms ("gating") and driving force were determined using dielectric continuum models. We then calculated the electronic transmission coefficient of the intramolecular ET rate using perturbation theory combined with the electronic wave functions determined by the DFT calculations for different heme group orientations and Fe-Fe separations. The reactivity of low- and high-spin heme groups was notably different. The ET rate is exceedingly low for the crystallographic equilibrium orientation but increases by several orders of magnitude for thermally accessible non-equilibrium configurations. Deprotonation of the propionate carboxyl group was also found to enhance the ET rate significantly. The results are discussed in relation to the observed surface immobilization effect and support the notion of conformationally gated ET.     

Theory of electrocatalysis: hydrogen evolution and more

Density functional theory (DFT) by itself is insufficient to model electrochemical reactions, because the interface is too large, and there is no satisfactory way to incorporate the electrode potential. In our group we have developed a theory of electrocatalysis, which combines DFT with our model for electrochemical electron transfer, and thereby avoids these difficulties. Our theory explains how a metal d band situated near the Fermi level can lower the energy of activation for a charge transfer reaction. An explicit application to the hydrogen evolution reaction gives results that agree very well with experimental data obtained both on plain and on nanostructured electrodes. Finally, we outline how our method can be extended to other reactions and present first results for the adsorption of OH on Pt(111).     

Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry

Improving the accuracy and thus broadening the applicability of electronic density functional theory (DFT) is crucial to many research areas, from material science, to theoretical chemistry, biophysics and biochemistry. In the last three years, the mathematical structure of the strong-interaction limit of density functional theory has been uncovered, and exact information on this limit has started to become available. The aim of this paper is to give a perspective on how this new piece of exact information can be used to treat situations that are problematic for standard Kohn-Sham DFT. One way to use the strong-interaction limit, more relevant for solid-state physical devices, is to define a new framework to do practical, non-conventional, DFT calculations in which a strong-interacting reference system is used instead of the traditional non-interacting one of Kohn and Sham. Another way to proceed, more related to chemical applications, is to include the exact treatment of the strong-interaction limit into approximate exchange-correlation energy density functionals in order to describe difficult situations such as the breaking of the chemical bond.     

An examination of density functionals on aldol, Mannich and ��-aminoxylation reaction enthalpy calculations

The reaction enthalpies of aldol, Mannich and ??-aminoxylation reactions were calculated by density functional theory (DFT) using long-range-corrected (LC), hybrid B3LYP and other up-to-date functionals to show why conventional DFT including B3LYP has given poor enthalpies for these reactions. As a result, we found that long-range exchange interactions significantly affect the reaction enthalpies. We therefore proposed that the poor enthalpies of B3LYP are due to its insufficient long-range exchange effect. On the other hand, LC functionals accurately reproduce reaction enthalpies for these reactions. However, we noticed that even LC functionals present poor reaction enthalpies for specific reactions, in which many branches are produced or very small molecules such as methane molecule participate.