A natural linear scaling coupled-cluster method

It is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupled-cluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupled-cluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation. (c) 2004 American Institute of Physics.     

含三重键有机小分子定域分子轨道的理论研究

为了能够应用定域分子轨道(LMO)模型计算链状有机大分子的光电子能谱,我们已做了一系列工作。本文是用STO-3G基组和Foster-Boys LMO程序,采用文中的计算方法,对含H、C、N和O原子及单,双和叁键的近20个有机小分子进行研究,得到了它们     

Intermolecular interactions of formic acid with benzene: Energy decomposition analyses with ab initio MP2 and double‐hybrid density functional computations

The intermolecular interactions of formic acid (HCOOH) with benzene (C₆H₆) have been investigated using localized molecular orbital energy decomposition analyses (LMO‐EDA) with ab initio MP2 and several double‐hybrid density functionals. The molecular geometries of five HCOOH…C₆H₆ complexes and corresponding benchmark total interaction energies at the CCSD(T)/CBS level are taken from literature (Zhao et al., J. Chem. Theory Comput. 2009, 5, 2726). According to the results of LMO‐EDA with the MP2 method, the dispersion energies are found to be as important as the electrostatic energies for the total interaction energies of the five HCOOH…C₆H₆ complexes. Based on LMO‐EDA with the double‐hybrid density functionals of B2PLYP, B2K‐PLYP, B2T‐PLYP, and B2GP‐PLYP computations, two new parameters for the framework of B2PLYP are extrapolated. These two new parameters are tested with other 10 complexes involving C₆H₆ (Crittenden, J. Phys. Chem. A 2009, 113, 1663), and they perform well on predicting the corresponding total interaction energies. Interestingly, these two new parameters for the framework of B2PLYP also perform well on the noncovalent complexation energies database (NCCE31/05) developed by Truhlar's group (Zhao and Truhlar, J. Phys. Chem. A 2005, 109, 5656). Therefore, these two new parameters appear to be suitable for investigating the noncovalent interactions, and they are denoted as B2N‐PLYP, where N stands for the noncovalent interaction. This study is expected to provide new insight into the derivation of double‐hybrid density functionals for studying the noncovalent interactions. © 2013 Wiley Periodicals, Inc.     

含双键有机小分子的定域分子轨道的研究

选择22种具有双键的有机小分子(含C、H、O和N原子)作模型分子,应用ab initioSTO-3G和Foster-Boys定域化分子轨道程序,对它们的定域分子轨道进行了研究,得到了定域分子轨道能量,确定了相应分子轨道间的相互作用。对烯类分子的光电子能谱进行了分析,结果较为满意。     

Relativistic Density Functional NMR Tensors Analyzed with Spin-free Localized Molecular Orbitals

The implementation of fast relativistic methods based on density functional theory, in conjunction with localized molecular orbital (LMO) based analysis, allows straightforward interpretations of NMR parameters in terms of contributions from core shells, lone pairs, and bonds, for compounds containing elements from across the periodic table. We present a conceptual review of a frequently used LMO analysis of NMR parameters calculated in the presence of spin-orbit interactions and other relativistic effects. An accompanying example focuses on the ¹⁵N shielding in a heavy metal complex.     

A relationship between the sizes and energies of localized molecular orbitals. I. A study of selected first-row hydrides

Ab initio calculations have been performed on selected first-row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMO 'S ) were computed and analysed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with an MO , and the relationship between the sizes and energies of such orbitals was examined. It was found that a simple energy–size relationship exists for core LMO 'S but only approximately holds for bond LMO 'S .     

有机链状分子的定域分子轨道的研究

利用Foster-Boys定域化程序和STO-3G ab initio方法,对含有C、H、O、N原子的100多个有机链状分子进行了研究,得到定域分子轨道能量及其相互作用参数。应用这些参数和定域分子轨道模型,对于众多的含有C、H、O、N原子的有机链状分子,可得到相应的正则分子轨道能量及其与定域分子轨道的关系。以此预测它们的电离能,结果与实验值符合较好。     

Research in the method of large molecular calculations utilizing transferability of LMO

The localized molecular orbitals of some saturated hydrocarbons and their derivatives have been formed using ab initio method and M. P. [1–2] localization procedure. Two models, SLMO and ELMO , a set of parameters of LMO Fock matrix elements, and a technique called “Group Effect” are proposed. Based on these, we developed a procedure to simulate the ab initio calculations on large molecules. Some test calculations have been done. The results are compared with those of the ab initio method. In general, absolute errors of orbital energies are about 10^?3 a.u., and the relative errors of total energies are about 10^?4. For the original applications, we applied this procedure to some large systems of alkane and their derivatives as well as three Crown-ether compounds. Satisfactory results are obtained.     

C_4S_4~(m-)(m=0,1,2,3,4)的从头算研究2.成键状况、电离势和振动频率

在ＲＨＦ（基离子在ＵＨＦ）／６－３１Ｇ,６－３１Ｇ＊和６－３１＋Ｇ水平用从头算和Ｂｏｙｓ定域化方法计算了Ｃ４Ｓ４ｍ－（ｍ＝０,１,２,３,４）的电子结构、电离势和定域化分子轨道。讨论了其成键特征和电离势与ΔＥＳＣＦ的关系。在６－３１Ｇ水平用ａｂｉｎｉｔｉｏ解析方法计算它们的谐振动频率。电子结构计算结果和Ｂｏｙｓ定域化分子轨道及振动分析结果与优化的平衡几何和相对稳定性相一致     

Investigation of the resonance‐assisted hydrogen bond in model β‐diketones through localized molecular orbital analysis of the spin–spin coupling constants related to the O–H · · · O hydrogen bond

The resonance‐assisted hydrogen bond (HB) phenomenon has been studied theoretically by a localized molecular orbital (LMO) decomposition of the spin–spin coupling constants between atoms either involved or close to the O–H · · · O system of some β‐diketones and their saturated counterparts. The analysis, carried out at the level of the second‐order polarization propagator approximation, shows that the contributions in terms of LMO to the paramagnetic spin orbital and the spin dipolar Ramsey terms proof the importance of the delocalized π‐electron structure supporting the idea of the existence of the resonance‐assisted HB phenomenon phenomenon. The LMO contributions to the Fermi contact term indicate mainly the presence of the HB that may or not be linked to the π‐electrons. Copyright © 2014 John Wiley & Sons, Ltd.     

On Koopmans' theorem in density functional theory

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.     

Excitation energies expressed as orbital energies of Kohn–Sham density functional theory with long-range corrected functionals

A new simple and conceptual theoretical scheme is proposed for estimating one-electron excitation energies using Kohn–Sham (KS) solutions. One-electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two-step process, ionization, and electron attachment. KS with long-range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one-electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies.     

Evaluating the Free Energies of Solvation and Electronic Structures of Lithium‐Ion Battery Electrolytes

Adaptive biasing force molecular dynamics simulations and density functional theory calculations were performed to understand the interaction of Li⁺ with pure carbonates and ethylene carbonate (EC)‐based binary mixtures. The most favorable Li carbonate cluster configurations obtained from molecular dynamics simulations were subjected to detailed structural and thermochemistry calculations on the basis of the M06‐2X/6‐311++G(d,p) level of theory. We report the ranking of these electrolytes on the basis of the free energies of Li‐ion solvation in carbonates and EC‐based mixtures. A strong local tetrahedral order involving four carbonates around the Li⁺ was seen in the first solvation shell. Thermochemistry calculations revealed that the enthalpy of solvation and the Gibbs free energy of solvation of the Li⁺ ion with carbonates are negative and suggested the ion–carbonate complexation process to be exothermic and spontaneous. Natural bond orbital analysis indicated that Li⁺ interacts with the lone pairs of electrons on the carbonyl oxygen atom in the primary solvation sphere. These interactions lead to an increase in the carbonyl (C=O) bond lengths, as evidenced by a redshift in the vibrational frequencies [ν(C=O)] and a decrease in the electron density values at the C=O bond critical points in the primary solvation sphere. Quantum theory of atoms in molecules, localized molecular orbital energy decomposition analysis (LMO‐EDA), and noncovalent interaction plots revealed the electrostatic nature of the Li⁺ ion interactions with the carbonyl oxygen atoms in these complexes. On the basis of LMO‐EDA, the strongest attractive interaction in these complexes was found to be the electrostatic interaction followed by polarization, dispersion, and exchange interactions. Overall, our calculations predicted EC and a binary mixture of EC/dimethyl carbonate to be appropriate electrolytes for Li‐ion batteries, which complies with experiments and other theoretical results.     

Low energy (e,2e) studies from CH4: results from symmetric coplanar experiments and molecular three-body distorted wave theory

Low energy experimental and theoretical triply differential cross sections are presented for electron impact ionization of methane (CH(4)) for both the highest occupied molecular orbital (HOMO) and next highest occupied molecular orbital (NHOMO). The HOMO is a predominantly p-type orbital which is labeled 1t(2) and the NHOMO is predominantly s-type labeled 2a(1). Coplanar symmetric (symmetric both in final state electron energies and observation angles) are presented for final state electron energies ranging from 2.5 to 20 eV. The theoretical M3DW (molecular three-body distorted wave) results are in surprisingly good agreement with experiment for the HOMO state and less satisfactory agreement for the NHOMO state. The molecular NHOMO results are also compared with the ionization of the 2s shell of neon which is the isoelectronic atom.     

Theoretical studies on the role of pi-electron delocalization in determining the conformation of N-benzylideneaniline with three types of LMO basis sets

To understand the role of pi-electron delocalization in determining the conformation of the NBA (Ph-N==CH-Ph) molecule, the following three LMO (localized molecular orbital) basis sets are constructed: a LFMO (highly localized fragment molecular orbital), an NBO (natural bond orbital), and a special NBO (NBO-II) basis sets, and their localization degrees are evaluated with our suggesting index D(L). Afterward, the vertical resonance energy DeltaE(V) is obtained from the Morokuma's energy partition over each of three LMO basis sets. DeltaE(V) = DeltaE(H) (one electron energy) + DeltaE(two) (two electron energy), and DeltaE(two) = DeltaE(Cou) (Coulomb) + DeltaE(ex) (exchange) + DeltaE(ec) (or SigmaDeltaE(n)) (electron correction). DeltaE(H) is always stabilizing, and DeltaE(Cou) is destabilizing for all time. In the case of the LFMO basis set, DeltaE(Cou) is so great that DeltaE(two) > |DeltaE(H)|. Therefore, DeltaE(V) is always destabilizing, and is least destabilizing at about the theta = 90 degrees geometry. Of the three calculation methods such as HF, DFT, and MPn (n = 2, 3, and 4), the MPn method provides DeltaE(V) with the greatest value. In the case of the NBO basis set, on the contrary, DeltaE(V) is stabilizing due to DeltaE(Cou) being less destabilizing, and it is most stabilizing at a planar geometry. The LFMO basis set has the highest localization degree, and it is most appropriate for the energy partition. In the NBA molecule, pi-electron delocalization is destabilization, and it has a tendency to distort the NBA molecular away from its planar geometry as far as possible.     

H3PO→H2POH异构化反应的LMO研究

The localized molecular orbital (LMO) theory is used to study the reaction mechanism of the isomerization reaction: H_3PO→H_2POH. The energy transition state (TS) of the reaction is also obtained by Powell's mehtod using 6-31G basis set. The resluts show that the lone pair electrons of oxygen atom play an forortant role in this reaction.     

Maximum overlap symmetry molecular orbitals in conjugated systems

The application of the maximum overlap symmetry orbital (MOSO) method to conjugated systems is discussed briefly. The MOSO method can be employed to construct not only the symmetry orbitals and the molecular orbitais in alternant conjugated systems, but also the symmetry orbitais in non-alternant systems. It is shown that under the Hückel approximation the matrix MM⁺ can be written out directly from the molecular skeleton and may be treated by using chemical graph theory. Because the matrix MM⁺ of a system can be regarded as the Huckel matrix of a smaller system, the maximum overlap symmetry molecular orbital (MOSMO) calculation results can be easily obtained from those of the smaller systems. For homonuclear conjugated systems and for systems in which two kinds of atom appear altemantly, the MOSMOs and the corresponding molecular orbital (MO) energies obtained by the MOSMO calculation are the same as the MOs and the MO energies calculated by the Hückel molecular orbital method.     

Effect of hyperconjugation on ionization energies of hydroxyalkyl radicals

On the basis of electronic structure calculations and molecular orbital analysis, we offer a physical explanation of the observed large decrease (0.9 eV) in ionization energies (IE) in going from hydroxymethyl to hydroxyethyl radical. The effect is attributed to hyperconjugative interactions between the sigma CH orbitals of the methyl group in hydroxyethyl, the singly occupied p orbital of carbon, and the lone pair p orbital of oxygen. Analyses of vertical and adiabatic IEs and hyperconjugation energies computed by the natural bond orbital (NBO) procedure reveal that the decrease is due to the destabilization of the singly occupied molecular orbital in hydroxyethyl radical as well as structural relaxation of the cation maximizing the hyperconjugative interactions. The stabilization is achieved due to the contraction of the CO and CC bonds, whereas large changes in torsional angles bear little effect on the total hyperconjugation energies and, consequently, IEs.     

Theoretical Study on the Hydrogen Bonding Interactions in Complexes of 5‐Hydroxytryptamine with Water

The energies, geometries and harmonic vibrational frequencies of 1:1 5‐hydroxytryptamine‐water (5‐HT‐H₂O) complexes are studied at the MP2/6‐311++G(d,p) level. Natural bond orbital (NBO), quantum theory of atoms in molecules (QTAIM) analyses and the localized molecular orbital energy decomposition analysis (LMO‐EDA) were performed to explore the nature of the hydrogen‐bonding interactions in these complexes. Various types of hydrogen bonds (H‐bonds) are formed in these 5‐HT‐H₂O complexes. The intermolecular C4H5^5‐HT···O^w H‐bond in HTW3 is strengthened due to the cooperativity, whereas no such cooperativity is found in the other 5‐HT‐H₂O complexes. H‐bond in which nitrogen atom of amino in 5‐HT acted as proton donors was stronger than other H‐bonds. Our researches show that the hydrogen bonding interaction plays a vital role on the relative stabilities of 5‐HT‐H₂O complexes.     

定域分子轨道模型——含H、C、N、O有机小分子的研究

应用STO_(-3)G从头算方法和Fostre-Boys定域化分子轨道程序, 我们研究了20多个有机小分子(含H、C、N,O)的定域化分子轨道, 获得了它们的能量和相互作用参数。采用定域分子轨道模型和统一的参数, 对正醇类分子进行了计算, 与光电子能谱数据比较, 得到的电离能的计算结果是相当令人满意的。