Multireference perturbation CI I. Extrapolation procedures with CAS or selected zero-order spaces

We discuss the “three class” approximation to full multireference perturbation CI, which greatly reduces the computational effort by restricting the summation of diagrams to determinants belonging to a subspace of the zero-order space. In the framework of the CIPSI algorithm, we propose a new extrapolation procedure allowing recovery of the full “two class” results. The new procedure is applied to complete active spaces (CAS) and to individually selected zero-order spaces. Comparison with a full two class calculation on a CAS shows a reduction of computer time of one or two orders of magnitude in the tests presented here, with an accuracy in the order of 0.1 kcal/mol. Our procedure can thus compete with the CASPT2 algorithm, specifically conceived to deal with CAS. In the case of selected zero-order spaces, the speed-up is less dramatic but the method still retains its advantages. Received: 12 June 1997 / Accepted: 31 July 1997     

硝基取代亚酞菁衍生物的电子光谱和非线性光学性质的理论研究

在AM₁方法优化的几何结构基础上,用INDO/CI-SOS方法深入探讨亚酞菁(C₂₄H₁₂B₁Cl₁N₆)的硝基取代对体系的电子光谱和二阶非线性光学性质的影响.结果表明,吸电子取代基和取代基的共轭链的增长对亚酞菁的分子结构和电子光谱的最大吸收峰影响很小,但对非线性光学性质都有较大影响,随着共轭链的增长,二阶非线性光学系数大幅度增强.未被取代的亚酞菁的β₀计算值与实验值十分相符,分别为-0.73×10^-28和-0.70×10^-28esu,共轭链最长的硝基取代化合物β₀值增大到-1.47×10^-28esu,增加约近1倍.     

Multireference perturbation CI IV. Selection procedure for one-electron properties

We present in this paper a modification of the selection procedure, within the CIPSI algorithm, specifically intended for the calculation of one-electron properties. In this new procedure the determinants are selected following their contribution to a certain one-electron property. As test cases we report the calculation of the electric dipole of carbon monoxide and of the hyperfine coupling constants of the CH₃ radical. Received: 20 August 2000 / Accepted: 2 October 2000 / Published online: 21 December 2000     

A Simple Approximate Perturbation Approach to Quasi-degenerate Systems

In this paper a simple approximate approach for the study of quasi-degenerate systems is presented in the frame of multireference perturbation theory. The formulation can be considered as an approximation of the quasi-degenerate perturbation theory (QDPT) with the simplification that only the state specific (diagonal) perturbation corrections to the energy have to be computed. The new approach is discussed and compared with previous QDPT formulations using the weakly avoided crossing model (for which new properties are here presented) and applied to the case of the neutral/ionic energy crossing in the LiF molecule.     

Analysis of coupled cluster methods

Summary A procedure is developed that leads from CI to size-extensive CI (ECI) by stepwise cancellation of disconnected terms in the CI equations. The ECI methods thus obtained are identical with the corresponding coupled cluster (CC) methods with the exception of CISD and CISDT, which convert to size-extensive quadratic CI (QCISD) and ECISDT. The latter method has similar properties as CCSDT, but does not offer any significant time-savings as compared to CCSDT. Therefore, the idea of extending CI methods to size-extensive CI methods does not lead to a hierarchy of independent CC methods. However, the procedure of obtaining ECI methods lays the basis for deriving QCI methods that are truly size-extensive. This is accomplished by (a) deleting the first linear term of thep-fold CI excitation equations (p 3) since this term always represents a disconnected term and (b) including just the connected part of appropriate quadratic correction terms in all but the energy equation. In this way, size-extensive QCISDT and QCISDTQ are obtained and their properties are discussed in comparison with QCISD(T) and CCSDT.This paper is dedicated to Prof. Werner Kutzelnigg on the occasion of his sixtieth birthday     

Full CI benchmark calculations for molecular properties

Full CI calculations of first- and second-order properties are presented to provide benchmark results for comparisons with other methods, such as multireference CI(MRCI). The full CI(FCI) polarizability of F^– is computed using a double zeta plus polarization plus diffuse basis set. These FCI results are compared to those obtained at other levels of theory; the CASSCF/MRCI with Davidson correction results are in excellent agreement with the FCI. Differences between the polarizability results computed as a (numerical) second derivative of the energy or as an induced dipole moment are also discussed. FCI calculations are presented for the dipole moment and polarizability of HF, CH₂ and SiH₂ using a DZP basis set. Again, the CASSCF/MRCI values are in excellent agreement with the FCI results, whereas SDCI values, whether computed as an expectation value or as an energy derivative, are much worse. The results obtained using the CPF approach are in considerably better agreement with the FCI results than SDCI, and are similar in quality to the SDCI energy derivative results with the inclusion of Davidson's correction.     

Exploiting regularity in systematic sequences of wavefunctions which approach the full CI limit

Summary The ground state total energy and related 1-electron properties are computed for three small molecules (N₂, H₂O, and H₂CN) using several systematic sequences of wavefunctions which approach the full CI. These sequences include multireference CI, averaged coupled pair functional and quasidegenerate variational perturbation theory wavefunctions. It is demonstrated that sufficient regularity exists in the sequence of variationally computed energies to permit extrapolation to the full CI limit using simple analytic expressions. It is furthermore demonstrated that a subset of the original list of configurations employed in the normal singles and doubles CI procedure can be selected using second order perturbation theory without adversely affecting the extrapolation to the full CI limit. This significantly broadens the range of applicability of the method. Along these lines, a scheme is proposed for the extrapolation of the selected CI results to the zero threshold (i.e. unselected) values in cases where the numbers of configurations associated with the latter would render the calculations intractable. Due to the vast reduction in the number of configurations which are handled variationally, the proposed scheme makes it possible to derive estimates of the full CI limit in cases where explicit full CI is either very difficult or currently impossible.Dedicated to Prof. Klaus RuedenbergThe Pacific Northwest Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under contract DE-AC06-76RLO 1830     

New implementations of MRCI in semiempirical frameworks

Multireference configuration interaction with single and double excitations (MRCISD) as well as its analytic CI gradients has been implemented in the semiempirical framework. The hole‐particle symmetry and a mixed driven model for computing coupling coefficients have been used in the new code that allows us to perform MRCI and gradient calculations with higher efficiency and less storage requirements. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Full configuration interaction benchmark calculations for transition moments

Full configuration-interaction (FCI) calculations have been performed for the ã ¹A₁–b¹B₁and ã ¹A₁–(2)¹A₁transitions in CH₂ and for selected dipole and quadrupole transitions in BeO. The FCI transition moments are compared to those obtained from correlation treatments that truncate the n-particle expansion. The state-averaged MCSCF/SOCI and FCI results agree well, even for BeO, where the CASSCF level nonorthogonal transition moment differs from the state-averaged CASSCF transition moment.     

Generalization of analytic energy derivatives for configuration interaction wave functions

This paper takes the form of a review including some original contributions. A fresh derivation of analytic energy derivative expressions for configuration interaction (CI) wave functions is presented. In this method the CI energy is described by _IJC_IC_J(H _IJ-_IJE) so that the orthonormality condition is explicitly included therein. In the sequence of differentiations up to fourth order it will be demonstrated that each derivative may be expressed in terms of (H _IJ-_IJE) and its derivatives in a symmetric way with respect to the interchange of differential variables. In a similar manner, the CI variational condition may be described in an equation which explicitly includes the normalization condition. It is shown that the differentiation of the modified variational condition produces the coupled perturbed configuration interaction (CPCI) equations in directly soluble and compact forms. The necessary formulae for the energy derivatives up to fourth order and the CPCI equations up to second order are explicitly given.     

Adding the linked contributions of Triples and Quadruples to a size-consistent Singles and Doubles CI

Summary A convenient procedure has been proposed recently to insure the size-consistence of Singles and Doubles CI; the method goes through a self-consistent dressing of the energies of the excited determinants which incorporates the unlinked effects of the Triples and Quadruples. Two strategies are proposed here to add thelinked contributions of the Triples and Quadruples, either by an perturbative MP-type calculation of these effects, or by a redefinition of the dressing of the SD-CI matrix. Test calculations on Be₂, FH, NH₃ and F₂ molecules show that both methods efficiently approach the Full CI results (error 1 kcal mol^–1). The second one satisfactorily treats the single-bonds breaking. It is finally shown that the effect of the T-Q linked effects may be efficiently approximated by truncating the MO basis set to the most occupied virtual quasi-natural MOs.On leave from Departament de Quimica Fisica. Facultat de Quimica. Universitat de Valencia. Dr. Moliner 50, E-46100, Burjasot (Valencia), Spain     

Relations between DFT and CI approximation

Relations between the two quantum chemical methods density functional theory (DFT) and configuration interaction (CI) are studied. As a result a new expression of the density functional based on CI approximation is presented. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 55–58, 1999     

双核铁原子簇体系的CI计算

用ＩＮＤＯ／ＣＩ方法研究了含有Ｆｅ－Ｆｅ键的原子簇体系［Ｆｅ２Ｓ２Ｘ４］＾２－（Ｘ＝Ｃｌ，Ｂｒ，Ｉ）的电子光谱及电子结构，对于这些多谱带体系，谱带波数计算值与实验值符合，在谱带的指认分析中，发现了πｄ＾１→πｄ等新的跃迁方式，对跃迁方式作了解释和分类，并讨论了谱带的电荷转移性质，此外，还对体系的化学键等性质进行了分析。     

Theoretical Studies on Electronic Spectra and Second-order Nonlinear Optical Properties of Barbituric Acid Derivatives Substituted with Schiff Base

Barbituric acid (BA) is a very important kind of compound in biological chemistry and medicine. It can be applied in abirritative medicine and antioxidants.1 It is an important sort of raw material for organic synthe-sis.2 It predicts the important reactive mechanism for organic synthesis.3 Some investigations for NLO prop-erties of a series of BA derivatives have been reported by Feng and coworkers in the view of theory.4,5 The Schiff base has extensive application in the fields of organi…     

酉群组态相互作用方法及其应用

在处理电子激发、反应途径(势能面)和分子解离等问题时,必须考虑电子相关能,组态相互作用是考虑电子相关作用的常规方法。为处理涉及电子相关的分子体系问题,本文将UGCI方法与自行改编后的限制性CNDO程序连接,形成CNDO-UGCI程序。该程序对苯及吡啶等体系的计算结果很好,表明了该方法的可靠性,也表明UGCI方法的有效性。     

Cluster expansion of the wavefunction

Numerical examples illustrate the SAC and SAC-CI results for correlatioin energies compared to those from full CI calculations of Bauschlicher and Taylor.     

Ni 3s-hole states in NiO by non-orthogonal configuration interaction

The origin of the features in the Ni 3s X-ray photoelectron spectrum of NiO is investigated using a non-orthogonal configuration interaction approach for an embedded [NiO₆] cluster. We study the interplay of inter-atomic screening with the metal core hole and intra-atomic exchange and electron correlation effects. We show that the spectrum can be described in terms of only few key configurations, provided that orbital relaxation effects are explicitly taken into account for the excited charge transfer configurations. The strength of this approach has been demonstrated earlier for those final states that have a high-spin coupling. In the present contribution the analysis is extended to include low-spin coupled 3s-hole states. The effects of enlarging the embedded cluster and of an improved representation of the nearest cluster surroundings were studied for the high-spin final states. We found only minor effects on the computed peak separations.     

Full‐CI quantum chemistry using the density matrix renormalization group

We describe how density matrix renormalization group (DMRG) can be used to solve the full configuration interaction problem in quantum chemistry. As an illustration of the potential of this method, we apply it to a paramagnetic molecule. In particular, we show the effect of various basis set, the scaling as the fourth power of the size of the problem, and compare the DMRG with other methods. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 331–342, 2000     

A CASSCF-CI study of the coordination of ethylene with iron

Summary Complete active space SCF, CASSCF, and contracted CI calculations have been performed on the -bonded complex between ethylene and an iron atom. An extended basis set of the ANO type was used, which included polarization functions on all centers. The results indicate an attractive interaction between Fe ⁵ F(d⁷s) and ethylene, with an estimated binding energy of 14 kcal/mol. The low spin complex arising from Fe ³ F(d⁷s) was found to be bound with 18 kcal/mol. Both these potential minima are, however, above the ground state of the iron atom. It is concluded that the interaction between atomic ground state iron and ethylene is not of the normal -bonded type, but is dominated by dispersion forces. A preliminary study showed this interaction to be almost isotropic, with no preferred site for the iron atom.