post-HF Levels Research Articles

TWOE Code: An Efficient Tool for Explicit Partition of Coupled Cluster and Configuration Interaction Energies into Atomic and Diatomic Contributions

The efficient implementation of the TWOE program for evaluating the atomic and interatomic energy components at post-HF level was developed. The systematic convergence of these terms up to a near full-CI limit was performed for the first time for a series of coupled cluster methods: CCSD → CCSDT → CCSDTQ → CCSDTQP. A comparison with corresponding CI approaches (up to fifth excitation level) is additionally discussed. For a set of diatomic systems, it was demonstrated that, along with a full molecular energy convergence, all its components are also converged but with different patterns. It was found that not all components are decreased in their values at increasing computational rank. For instance, atomic energy parts are decreased while interatomic (interaction) energies are increased as the limiting level is approached. Two schemes were employed for atomic partition of molecules: the Baders approach and planes dissection. Influence of dynamical correlation effects on atomic energy components was analyzed in detail. Current TWOE implementation allows one, in principle, to work with any ab initio method providing the two-particle density matrix. It is believed that the developed program will be a useful tool for a real space energy decomposition that helps to reveal the most peculiar points in the structure of the total and correlation energies of a molecule.

Intramolecular photo-induced charge transfer in visual retinal chromophore mimics: electron density-based indices at the TD-DFT and post-HF levels

The first bright transition of a series of ten retinal-based dyes was simulated using TD-DFT, with several hybrid functionals, and with several post-Hartree–Fock methods. The CASPT2 results were used as reference to compare the results. The comparisons were not only based on the transitions energies, that is generally the case for such works, but were also based on the variation of the electron density from the ground to the excited along with several density-based indices recently developed. Among all the results obtained, it clearly appears that the PT2 correction to the CASSCF wavefunction is increasing with the increase in the charge transfer character of the transition. As already highlighted in the literature, TD-DFT poorly reproduces transition energies of this family of molecules whatever the functional. This work also confirms this observation for the variation of the electron density that is different between TD-DFT and CASPT2. Nevertheless, some functionals give better results than others. It appears that functionals having a fraction of 40–50 % of exact exchange give a better description of the electron density variation than the other functionals. Moreover, the best functional to compute the transition energies is not the best to simulate excited electron density that confirms an observation done in the literature on a different family of molecules.

广义化的电荷分解分析(GCDA)方法

电荷分解分析(CDA)是一种重要的深入研究电荷转移问题的方法。本文对CDA进行了介绍，阐述了计算中需要注意的问题，并提出了一种新的CDA形式，称为广义化的电荷分解分析(GCDA)。在HF、DFT级别GCDA与CDA等价，但GCDA能更好地用于后HF计算，而且还明确考虑了开壳层时的计算形式。通过以OC-BH3和顺式二氯二胺合铂体系作为测试实例，我们发现各种理论级别下GCDA的结果都较为合理且定性相符，但在定量上有所区别，特别是d项存在大体趋势：低HF成份的泛函 > 高HF成份的泛函 > HF ≥ MP2 > CCSD。文中还对GCDA计算时基组的选择进行了讨论。 Charge decomposition analysis (CDA) is an important method to study charge transfer problems in depths. In this paper, we introduced CDA method, elucidated the issues that needed attention in the calculation, and presented a new form of CDA, which was called GCDA. At HF and DFT levels, GCDA is equivalent to CDA, while GCDA is more applicable at post-HF level, and meantime its open-shell form is explicitly considered. By taking OC-BH3 and cis-dichlorodiamine as test cases, we find the GCDA results at various theoretical levels are reasonable and qualitatively consistent, but differ quantitatively; in particular, a rough trend exists in the d term: Functional with low HF composition > Functional with high HF composition > HF ≥ MP2 > CCSD. The paper also discussed the choice of basis-set in GCDA calculation.

Contraction of completeness-optimized basis sets: Application to ground-state electron momentum densities

Completeness-optimization is a novel method for the formation of one-electron basis sets. Contrary to conventional methods of basis set generation that optimize the basis set with respect to ground-state energy, completeness-optimization is a completely general, black-box method that can be used to form cost-effective basis sets for any wanted property at any level of theory. In our recent work [J. Lehtola, P. Manninen, M. Hakala, and K. Hämäläinen, J. Chem. Phys. 137, 104105 (2012)] we applied the completeness-optimization approach to forming primitive basis sets tuned for calculations of the electron momentum density at the Hartree-Fock (HF) level of theory. The current work extends the discussion to contracted basis sets and to the post-HF level of theory. Contractions are found to yield significant reductions in the amount of functions without compromising the accuracy. We suggest polarization-consistent and correlation-consistent basis sets for the first three rows of the periodic table, which are completeness-optimized for electron momentum density calculations.

Theoretical Study on the 3D Aromaticity in Cationic X44+ (X=O, S, Se, and Te) Clusters

The stable structures and 3D aromatic characters for four cationic X44+(X=O, S, Se, and Te) clusters are investigated at the DFT and post HF level of theory with the extended 6-311+G* basis set used for O, S, Se atoms and correlation consistent, effective-core potential (ECP) basis set ECP46MWB_AVTZ for the heavier Te atom. Two optimized structures of tetrahedron (Td) and rhombus (D2h) for four X44+ species have been obtained. The calculated results show that the tetrahedral (Td) structures are stable and correspond to energy minima, whereas the rhombic (D2h) ones are unstable and have one or more saddle points on the potential energy surfaces. The calculated NICS values show that four tetrahedral X44+ isomers have higher degree of 3D aromaticities. Whereas four rhombic X44+ isomers can be regarded to possess 3D antiaromaticities. The molecular orbital analyses reveal that the tetrahedral X44+ cations possess two-fold (σ and π) 3D aromaticity, conforming to the 2(N+1)2 electron counting rule for 3D aromaticity

Linear-scaling electronic structure calculation program based on divide-and-conquer method

Abstract In 2009, the authors implemented the linear-scaling divide-and-conquer (DC) methods into the GAMESS quantum chemistry package. This program enabled fast energy calculations of closed-shell large molecules with high accuracy in Hartree-Fock (HF), density functional theory, and post-HF levels of theory. After the first implementation, we extended the applicability of the DC scheme into several directions. In this Paper, we summarized recent and future developments in the DC code in GAMESS, namely, the energy gradient methods and open-shell treatments.

Theoretical study on the aromaticity from d-AOs in cationic X 3 + (X = Sc, Y, La) clusters

The stable structures and aromatic characters for three cationic X(3)(+) (X = Sc, Y, and La) and three relevant neutral X(3)Cl (X = Sc, Y, La) clusters are investigated at the DFT and post HF level of theory. The calculated results show that the X(3)(+) cations each has two stable structures: the regular trigon (D(3h)) and the line (D∞h) with the regular trigon (D(3h)) being the ground state, while for three neutral X(3)Cl clusters, Sc(3)Cl has three stable isomers: the trigon-pyramidal (C(3v)), bidentate (C(2v)-1), and C(2v)-2 structures, Y(3)Cl and La(3)Cl each has only two stable isomers: the trigon-pyramidal (C(3v)) and bidentate (C(2v)-1) structures. The ground states for three X(3)Cl species are all the bidentate (C(2v)-1) isomers. The calculations of the resonance energy (RE) and NICS show that trigonal X(3)(+) isomers exhibit higher degree of aromaticity. The detailed molecular orbital analyzes reveal that the isolated trigonal Sc(3)(+) and Y(3)(+) cations each has one delocalized π-type MO and shows single π-aromaticity, while the isolated trigonal La(3)(+) cation has one delocalized σ-type MO and shows single σ-aromaticity. The single π- or σ-aromaticity for X(3)(+) are attributed to the contributions mainly from the d AOs of the corresponding transition metal X atoms. However, when a singly negatively charged counterion Cl(-) is added to Sc(3)(+), Y(3)(+), and La(3)(+) cations respectively, the aromatic type for the two Sc(3)(+), Y(3)(+) units in the corresponding neutral Sc(3)Cl, Y(3)Cl complexes are changed from π-aromaticity into σ-aromaticity, whereas the σ-aromaticity of the La(3)(+) units in the La(3)Cl complex keeps unchanged in this process. Thus three Sc(3)(+), Y(3)(+), La(3)(+) units in the corresponding X(3)Cl complexes all have only one σ-type MO and exhibit single σ-aromaticity.

Computation of molecular vibrational frequencies using anomalous harmoniclike potentials

The instabilities of Hartree-Fock (HF) solutions at or near the equilibrium geometry of symmetric molecular species imply the existence of broken-symmetry solutions having a lower energy than the corresponding symmetry-adapted ones. Moreover, the distortion of the nuclear framework along the normal modes that are implied by such broken-symmetry solutions results in an anomalous or even singular behavior in the corresponding cuts of the potential energy surface (PES). Using such HF solutions as a reference, these anomalies propagate to a post-HF level and make it impossible to determine reliable harmonic or fundamental vibrational frequencies for such modes by relying on either numerical or analytical differentiation of the PES, requiring instead a numerical integration of the Schrodinger equation for the nuclear motion. This, in turn, requires a detailed knowledge on the PES in a wide range of geometries, necessitating a computation of the potential energy function in a large number of points. We present an alternative approach to this problem, referred to as the integral averaging method (IAM), which facilitates this task by significantly reducing the number of geometries for which one has to compute the potential energy while yielding results of practically the same accuracy as the solution of the Schrodinger equation. The IAM is applied to several ABA-type triatomics and to the allyl radical, whose asymmetric stretching mode potential suffers from an anomalous behavior due to the spin-preserving instabilities in restricted open-shell HF solutions.

A Computational Study on Some Viable Targets for Gas-Phase Synthesis of Metal Complexes of the Cyclic (B6C)−2and Their Bonding Pattern

In this account, a detailed computational study is conducted to verify the geometric, energetic, and electronic properties of the planar cyclic (B 6C) (-2) (as the simplest carrier of hexacoordinate carbon) within some metal complexes. The [M(B 6C)] ((-)) (M = Li, Na, K) and [M(B 6C)] (M = Be, Mg, Ca) series are employed for this purpose. Relevant ab initio calculations at both DFT and post-HF levels vividly demonstrate that this dianion is stabilized considerably in the electric field generated by cations, whereas the geometrical and electronic properties of this ring remain almost intact in these complexes. The complementary topological analysis of charge densities confirms that cyclic (B 6C) (-2) within these complexes exhibits the same topological patterns as the naked dianion, thus confirming the presence of an unusual charge density distribution in this dianion. An electrostatic model is proposed that not only qualitatively but also quantitatively explains the observed computational trends in these complexes. This model successfully traces the polarization of the central carbon atom of the ring in the presence of a hard, multiply charged cation. To facilitate experimental detection, the photoelectron spectra of the [M(B 6C)] ((-)) (M = Li, Na, K) series are computed and the dominant features are extracted. Although considered species are not global minima on their potential energy hypersurfaces, their kinetic stabilities are verified and demonstrated unequivocally.

An ab initio study of geometry and vibrational spectrum of cyclic (B 6C) −2: The out-of-plane bending problem

In this Letter, a comprehensive ab initio post-HF study was conducted on the geometry and vibrational spectrum of cyclic, hypercoordinate carbon containing (B 6C) −2 dianion. The analysis reveals extraordinary sensitivity of out-of-plane bending mode of this molecule to the diffuse functions of Pople-type basis sets. Accordingly, this molecule seems to be another example of the set of recently described planar molecules that exhibit spurious (but artificial) ‘imaginary’ out-of-plane bending frequencies at post-HF levels. The analysis eventually comes to the conclusion that this anion is indeed stable with regard to nuclear distortions, but unstable in regard to electron auto-detachment.

An Efficient Fragment-Based Approach for Predicting the Ground-State Energies and Structures of Large Molecules

An efficient fragment-based approach for predicting the ground-state energies and structures of large molecules at the Hartree-Fock (HF) and post-HF levels is described. The physical foundation of this approach is attributed to the "quantum locality" of the electron correlation energy and the HF total energy, which is revealed by a new energy decomposition analysis of the HF total energy proposed in this work. This approach is based on the molecular fractionation with conjugated caps (MFCC) scheme (Zhang, D. W.; Zhang, J. Z. H. J. Chem. Phys. 2003, 119, 3599), by which a macromolecule is partitioned into various capped fragments and conjugated caps formed by two adjacent caps. We find that the MFCC scheme, if corrected by the interaction between non-neighboring fragments, can be used to predict the total energy of large molecules only from energy calculations on a series of small subsystems. The approach, named as energy-corrected MFCC (EC-MFCC), computationally achieves linear scaling with the molecular size. Our test calculations on a broad range of medium- and large molecules demonstrate that this approach is able to reproduce the conventional HF and second-order Moller-Plesset perturbation theory (MP2) energies within a few millihartree in most cases. With the EC-MFCC optimization algorithm described in this work, we have obtained the optimized structures of long oligomers of trans-polyacetylene and BN nanotubes with up to about 400 atoms, which are beyond the reach of traditional computational methods. In addition, the EC-MFCC approach is also applied to estimate the heats of formation for a series of organic compounds. This approach provides an appealing approach alternative to the traditional additivity rules based on either bond or group contributions for the estimation of thermochemical properties.

Theoretical study of low-lying electronic states and emission spectra of the excimer ions NaHe + and NaNe +

Ab initio CASSCF calculations using the Gaussian basis set aug_cc_pVTZ developed by Dunning et al. specifically for calculations at the post-HF level was carried out for excimer NaHe + and NaNe + ions in order to determine spectroscopic characteristics and radiation lifetimes of their low-lying excited electronic states. The computed emission spectra of these were shown to be in good agreement with the experimental ones observed recently by Hammer et al. (Hyperfine Interactions 88 (1994) 151). Contrary to the earlier popular opinion, all excited electronic states of these ions, correlating with the limit Rg ++Na, and not just the radiating singlet states turn out to be bound. It was shown that under the conditions of an experiment similar to the one performed by Hammer et al., the excited triplet NaHe +(1 3Σ +) states can decay as a result of their interactions with a high-energy Ar + beam. This decay has to be accompanied with the formation of the ions He +, which in turn can interact with sodium atoms to yield the radiating NaHe +(2 1Σ +) states again and, thus to maintain the emission observed in the experiment.

The Ability of the Semiempirical PM3 Method to Model Proton Transfer Reactions in Symmetric Hydrogen Bonded Systems

Geometries and energies of small proton-bound symmetric dimers and minimum energy pathways for the proton transfer from one subunit to the other were calculated both at the semiempirical MNDO/PM3 and at ab initio HF and post HF levels. Except for systems, in which carbon atoms are involved or oxygen atoms are part of acceptor molecules, PM3 can be used for a good quantitative description of hydrogen bonds near the equilibrium geometry. If the subunits are separated by more than 2.5 Å, attractive forces will be lost quickly. Proton transfer reactions are modeled in a qualitative acceptable manner. The global barrier of proton transfer rises as well as the calculated association enthalpy of the hydrogen bonded dimer rises. If proton transfer occurs between nitrogen acid/base pairs, PM3 barriers of activation are about 5 - 10 kcal/mol higher than corrected ab initio results. Two dimensional slices through the potential energy hypersurfaces of proton transfer of two systems described in the paper. Energy values are in kcal/mol relative to the grid point with the lowest energy. Points signed with M represent equilibrium structures, those signed with S are saddle points of first order.