Simple estimation of electron correlation energy for multi-atomic strong ionic compounds KX and (KX)2 (X=OH, NC)

On the basis of the calculations and analyses of the intrapair and interpair correlation energy of KX (X = OH, NC) molecules and the results of the transferability of both the innermost intrapair correlation energy and the inner core effect of K and X in KX molecules, we defined and calculated the K^δ+ and X^δ-correlation contributions to the total correlation energy of KX molecules. With the comparison of the pair correlation energy of K⁺, X^- and KX systems, we present a simple estimation method to estimate the electron correlation energy of strong ionic compound by summarizing the correlation energy of its constituent ion and ionic group. By using this simple method, the reasonable estimation results of the correlation energy of (KOH)₂ and (KNC)₂ have been obtained at mp2/6-311++G(d) level with Gaussian98 program, and the deviations are very small. Applying the scheme of “Separate Large System into Smaller Ones” to the calculation of electron correlation energy of large ionic compounds, it can not only save lot of computation work but also reach the chemical accuracy.     

Simple estimation of electron correlation energy for multi-atomic strong ionic compounds KX and (KX)2 (X=OH, NC)

On the basis of the calculations and analyses of the intrapair and interpair correlation energy of KX (X = OH, NC) molecules and the results of the transferability of both the innermost intrapair correlation energy and the inner core effect of K and X in KX molecules, we defined and calculated the K^δ+ and X^δ-correlation contributions to the total correlation energy of KX molecules. With the comparison of the pair correlation energy of K⁺, X^- and KX systems, we present a simple estimation method to estimate the electron correlation energy of strong ionic compound by summarizing the correlation energy of its constituent ion and ionic group. By using this simple method, the reasonable estimation results of the correlation energy of (KOH)₂ and (KNC)₂ have been obtained at mp2/6-311++G(d) level with Gaussian98 program, and the deviations are very small. Applying the scheme of “Separate Large System into Smaller Ones” to the calculation of electron correlation energy of large ionic compounds, it can not only save lot of computation work but also reach the chemical accuracy.     

Rules on intrapair and interpair correlation energy for Cl, Cl~(-) and MCI (M=H, Li, Na, K)

According to the calculation results of the intrapair and interpair correlation energy for the title systems, it has been found that the intrapair correlation energy of K shell of Cl is almost a constant and both the intrashell and intershell correlation energy of K and L shell changes little. It has also been found that in MCI series compounds the value of Cl correlation energy contribution depends on the ionicity of MCI compounds, i.e., the Cl correlation energy contribution increases with the increase of the ionic bond strength of the compound and this value is always less than the correlation energy of Cl" anion but always larger than that of Cl atom. These rules are helpful for the estimation of the correlation energy of ionic compounds and the energy changes of chemical reactions.     

NHn(n=1～3)体系电子对内对间相关能的变化规律

众所周知,电子相关能问题是量子化学的瓶颈问题‘’‘．为了更深人地了解和认识电子相关能的轨道本质,建立P。St－HF理论校正模型,JS等”－”应用电子对内对间电子相关模式,指出国际著名量子     

Rules on intrapair and interpair correlation energy for Cl, Cl?and MCl (M=H, Li, Na, K)

According to the calculation results of the intrapair and interpair correlation energy for the title systems, it has been found that the intrapair correlation energy of K shell of Cl is almost a constant and both the intrashell and intershell correlation energy of K and L shell changes little. It has also been found that in MCl series compounds the value of Cl correlation energy contribution depends on the ionicity of MCl compounds, i.e., the Cl correlation energy contribution increases with the increase of the ionic bond strength of the compound and this value is always less than the correlation energy of Cl^- anion but always larger than that of Cl atom. These rules are helpful for the estimation of the correlation energy of ionic compounds and the energy changes of chemical reactions.     

Ab initio study of hydrated potassium halides KX(H2O)1-6 (X=F,Cl,Br,I)

The ionic dissociation of salts was examined with a theoretical study of KX (X=F,Cl,Br,I) hydrated by up to six water molecules KX(H2O)n (n=1-6). Calculations were done using the density functional theory and second order M?ller-Plesset (MP2) perturbational theory. To provide more conclusive results, single point energy calculations using the coupled cluster theory with single, double, and perturbative triple excitations were performed on the MP2 optimized geometries. The dissociation feature of the salts was examined in terms of K-X bond lengths and K-X stretch frequencies. In general, the successive incorporation of water molecules to the cluster lengthens the K-X distance, and consequently the corresponding frequency decreases. Near 0 K, the KX salt ion pairs can be partly separated by more than five water molecules. The pentahydrated KX salt is partly dissociated, though these partly dissociated structures are almost isoenergetic to the undissociated ones for KFKCl. For the hexahydrated complexes, KF is undissociated, KClKBr is partly dissociated, and KI is dissociated (though this dissociated structure is nearly isoenergetic to a partly dissociated one). On the other hand, at room temperature, the penta- and hexahydrated undissociated structures which have less hydrogen bonds are likely to be more stable than the partly dissociated ones because of the entropy effect. Therefore, the dissociation at room temperature could take place for higher clusters than the hexahydrated ones.     

HX体系电子对内、对间相关研究

在6-311+G^*基组水平上用CISD（configurationinteractionwithsinglyanddoublyexcitedconfigurations)方法研究HX(X=Li-F,HBe)体系电子对内、对间的相关能。计算结果表明不同元素形成的HX(X=Li-F,HBe^+,HBe)体系,其价层电子对内、对间相关能的变化较大,它们之间存在着轨道差别,不宜将其相关贡献归为简单的常数。在使用相同理论方法和相同质量基组的前提下,电子数将直接影响到电子对间相关能的大小。对于多电子体系,电子对间相关在总相关中占有优势,若将其忽略会引起较大误差。     

Rules on intrapair and interpair correlation energy for Cl, Cl−and MCl (M=H, Li, Na, K)

According to the calculation results of the intrapair and interpair correlation energy for the title systems, it has been found that the intrapair correlation energy of K shell of Cl is almost a constant and both the intrashell and intershell correlation energy of K and L shell changes little. It has also been found that in MCl series compounds the value of Cl correlation energy contribution depends on the ionicity of MCl compounds, i.e., the Cl correlation energy contribution increases with the increase of the ionic bond strength of the compound and this value is always less than the correlation energy of Cl^- anion but always larger than that of Cl atom. These rules are helpful for the estimation of the correlation energy of ionic compounds and the energy changes of chemical reactions.     

Rules on pair electron correlation in MOH (M=H,Li, Na)

In this article, the transferable property of pair correlation energies of OH components is discussed for a series of OH containing compounds MOH (M=H, Li, Na). In this series of compounds, from OH free radicals through HOH, LiOH, NaOH to OH^?, both the intra‐ and interpair correlation energies and intra‐ and intershell correlation energies of the inner orbital electrons change little. The 1s$_{\mathrm{O}}^{2}$ is very much alike in all the above OH containing systems and such a pair correlation is transferable. But the interpair correlation and intrashell correlation energies of the valence electrons are large and change a lot in all systems. In MOH molecules, the OH correlation energy contribution increases with the increase of the ionic bond strength of the compound and this contribution is always between the correlation energy values of OH free radicals and OH^? atomic groups. For strong ionic compounds, we present a very simple method to estimate the correlation energy by adding the correlation energies of its component ions within the chemical accuracy (2 kcal/mol). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 311–317, 2001     

强离子键体系电子相关能简捷计算方案的应用

The calculation results of electron correlation energies of KF and （KF）2 were reported. The transferability of 1s^2 K , 1s^2 F and the inner core correlation effects of K and F in both K, K^＋, KF and F, F^-, KF systems were investigated respectively. The correlation energy contributions of K and F component to KF system were calculated. By applying the simple estimation scheme to the calculation of the correlation energy of the strong ionic compound KF and （KF）2, it was shown that such a powerful scheme could not only reach the chemical accuracy but also need little computational work.     

Two Typical Examples of Scaling Ionic Partition Scheme for Estimating Correlation Energy of A2 Type Molecules

Based on the calculation results of pair correlation energy contributions of the various electron pairs in Na2 and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the total correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of error, however, in this way, more than 90% of computational work can be saved. The most attractive result in present paper is that, in these two molecules the coefficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A^- to that of A^ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 molecules would be very useful to estimate the correlation energies of large symmetrical molecules.     

Changing Rules of Bonding Electron Pair Correlation Energies of CH3X （X = F, OH, NH2） Systems

1 INTRODUCTION It has been known that the electron correlation energy of molecular systems was, and still is, one of the most serious bottleneck problems to the chemis- try accuracy of computational quantum chemistry. Since L鰓din[1] gave the definition …     

硼、钾改性KX沸石上甲苯和甲醇的侧链烷基化反应

研究了硼、钾改性ＫＸ沸石催化剂的甲苯侧链烷基化反应性能。结果表明,硼和钾同时改性可显著地提高甲苯侧链烷基化反应活性,Ｈ３ＢＯ３和ＫＯＨ在催化剂样品浸渍过程中形成了不同化学计量比的碱金属硼酸盐,该硼酸盐在沸石上作为新的碱性中心而有利于醇的催化脱氢。实验发现,各样品的甲苯侧链反应产物收率与异丙醇分解产物丙酮选择性之间有较好的关联。此外,酸碱中毒试验也进一步证实碱性位在反应中起主要作用     

Dissociative photoionization of N(2)O in the region of the N(2)O(+)(B (2)Pi) state studied by ion-electron velocity vector correlation

Dissociative direct photoionization of the N2O(X 1Sigma+) linear molecule via the N2O+(B 2Pi) ionic state induced by linearly polarized synchrotron radiation P in the 18-22 eV photon energy range is investigated using the (VA+,Ve,P) vector correlation method, where VA+ is the nascent velocity vector of the NO+, N2+, or O+ ionic fragment and Ve that of the photoelectron. The DPI processes are identified by the ion-electron kinetic energy correlation, and the IchiA+(thetae,phie) molecular frame photoelectron angular distributions (MFPADs) are reported for the dominant reaction leading to NO+ (X 1Sigma+,v) + N(2D)+ e. The measured MFPADs are found in satisfactory agreement with the reported multichannel Schwinger configuration interaction calculations, when bending of the N2O+(B 2Pi) molecular ion prior to dissociation is taken into account. A significant evolution of the electron scattering anisotropies is observed, in particular in the azimuthal dependence of the MFPADs, characteristic of a photoionization transition between a neutral state of Sigma symmetry and an ionic state of Pi symmetry. This interpretation is supported by a simple model describing the photoionization transition by the coherent superposition of two ssigma and ddelta partial waves and the associated Coulomb phases.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Ionic hydrates,M(p)X(q).nH(2)O: lattice energy and standard enthalpy of formation estimation

This paper is one of a series (see: Inorg. Chem. 1999, 38, 3609; J. Am. Chem. Soc. 2000, 122, 632; Inorg. Chem. 2002, 41, 2364) exploring simple approaches for the estimation of lattice energies of ionic materials, avoiding elaborate computation. Knowledge of lattice energy can lead, via thermochemical cycles, to the evaluation of the underlying thermodynamics involving the preparation and subsequent reactions of inorganic materials. A simple and easy to use equation for the estimation of the lattice energy of hydrate salts, U(POT)(M(p)X(q).nH(2)O) (and therefore for solvated salts, M(p)X(q).nS, in general), using either the density or volume of the hydrate, or of another hydrate, or of the parent anhydrous salt or the volumes of the individual ions, is derived from first principles. The equation effectively determines the hydrate lattice energy, U(POT)(M(p)X(q).nH(2)O), from a knowledge of the (estimated) lattice energy, U(POT)(M(p)X(q)), of the parent salt by the addition of ntheta(U) where theta(U)(H(2)O)/kJ mol(-1) = 54.3 and n is the number of water molecules. The average volume of the water molecule of hydration, V(m)(H(2)O)/nm(3) = 0.0245, has been determined from data on a large series of hydrates by plotting hydrate/parent salt volume differences against n. The enthalpy of incorporation of a gaseous water molecule into the structure of an ionic hydrate, [Delta(f)H degrees (M(p)X(q).nH(2)O,s) - Delta(f)H degrees (M(p)X(q),s) - nDelta(f)H degrees (H(2)O,g)], is shown to be a constant, -56.8 kJ (mol of H(2)O)(-1). The physical implications with regard to incorporation of the water into various types of solid-state structures are considered. Examples are given of the use of the derived hydrate lattice energy equation. Standard enthalpies of formation of a number of hydrates are thereby predicted.     

A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two-Particle Density-Matrices of MP4SDQ and CCSD

Within the quantum topological energy partitioning method called Interacting Quantum Atoms (IQA) we transition from Møller-Plesset (MP4SDQ) to CCSD in calculating intra- and interatomic electron correlation energies for a set of hydrides, diatomics, a few simple molecules and non-covalently bonded complexes, using the uncontracted basis set 6-31++G(2d,2p). CCSD-IQA allows a more rigorous analysis of atomic electron correlation than that offered by Møller-Plesset, which returns IQA contributions that are identical to Hartree–Fock counterparts except for two-electron terms. The CCSD-IQA analysis returns bond and other interatomic correlation energies that are typically much larger in magnitude than the MP4SDQ values. Crisp patterns of energy transferability are detected in water clusters, both for intra-atomic and interatomic correlation energies. CCSD determines that the intra-atomic correlation energy of an oxygen drops by 15 kJ · mol^–1 for donating a hydrogen and by 25 kJ · mol^–1 for accepting a hydrogen.     

Rules of electron correlation energies of van der Waals' complexes RgX (Rg = Ar,Kr, X = F,Cl, Br)

First, the intrapair and interpair correlation energies of the Rg atom, X atom, and the optimized RgX (Rg = Ar, Kr, X = F, Cl, Br) complexes are calculated by the MELD program at the 6‐311++g(d), 6‐311++g(3df, 3pd), and cc‐pvqz basis sets (denoted by basis sets a, b, and c, respectively). It is found that the relationship E_corr(RgX) ≈ E_corr(Rg) + E_corr(X) is correct for all the above systems but introducing an unsound absolute error for some RgX systems. Second, the same calculations are selectively carried out for ArF (the smallest system) and KrBr (the largest system) at their increasing interatomic distance. It was found that both the correlation energies of ArF and those of KrBr will decrease whenever the interatomic distance of them become larger. On the basis of our results, we provided an approach to quickly estimate the correlation energies of RgX complexes by which not only the absolute error becomes smaller but more computation work is saved than the direct calculation. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

簇合物Mo_2X_8~(4-)(X=Cl,Br)低能态电子光谱

应用间略微分重叠自洽场和组态作用(INDO/S-CI)方法,计算双核簇合物Mo_2X_8~(4-)(X=Cl,Br)基态~1A_(1g)至不同低能态的d电子自旋允许的跃迁能,得出Mo—Mo四重键均裂时所需的能量大小依次为键σ>π>>δ。对于Mo_2Cl_8~(4-)簇合物态~1A_(1g)→1~1A_(2u)(δ→δ~*)和~1A_(1g)→2~1E_g(π→δ~*)的电子跃迁能,理论值(15584和22587cm~(-1))与低温时测得光谱实验值(18083和22000cm~(-1))较为接近。此外,本文还提出了簇合物Mo_2X_8~(4-)的态相同而X不同时,电子跃迁能变化,主要决定于参与电子转移过程的分子轨道组成成份的看法。     

Pseudopotential investigation of some alkali metal molecules

The effect of electron correlation on the results of pseudopotential calculations was examined using a simple analytical semiempirical pseudopotential and a correlated floating-type one-center wave function. Investigations were performed for the XH alkali metal hydride molecules (X ? Na, K, Rb, Cs). The inclusion of the electron correlation in the ground state proved important for the calculation of the dissociation and ionization energies, but it is less significant for the determination of the equilibrium nuclear distances. The ground state potential energy curves are also determined.