New perspectives in multireference perturbation theory: the n-electron valence state approach

The n-electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory which is based on a zero order reference wavefunction of CAS-CI type (complete active space configuration interaction) and which is characterized by the utilization of correction functions (zero order wavefunctions external to the CAS) of multireference nature, obtained through the diagonalization of a suitable two-electron model Hamiltonian (Dyall’s Hamiltonian) in some well defined determinant spaces. A review of the NEVPT approach is presented, starting from the original second order state-specific formulation, going through the quasidegenerate multi-state extension and arriving at the recent implementations of the third order in the energy and of the internally contracted configuration interaction. The chief properties of NEVPT—size consistence and absence of intruder states—are analyzed. Finally, an application concerning the calculation of the vertical spectrum of the biologically important free base porphin molecule, is presented.     

Generalization of coupled-cluster response theory to multireference expansion spaces: application of the coupled-cluster singles and doubles effective Hamiltonian

Employing separate cluster ansatz in time-independent and time-dependent wave-operators, coupled-cluster (CC) response theory is generalized to multireference (MR) expansion spaces. For state energies, this corresponds to the MR secular problem with an arbitrary similarity-transformed effective Hamiltonian, H˜=Ω⁻¹ HΩ. The effective Hamiltonian can be generated via size-extensive CC methods. Thus the states in MR linear response theory (MRLRT) maintain the usual CC core-extensive properties. We have used the Gelfand unitary group basis of the spin-adapted configurations to construct the matrix of H˜ in the MR excitation space. As a preliminary application, the CC singles and doubles effective Hamiltonian is applied to excitation and photoionization energies of the CH⁺ and N₂ molecules, and is compared with experimental results and results from other numerical procedures including conventional CC linear response theory (CC-LRT), MR and full configuration interaction (MRCI and FCI) methods. The numerical results indicate that MRLRT reproduces valence and external excited states quantitatively, combining the best features of CC-LRT and MRCI. Received: 2 July 1998 / Accepted: 28 August 1998 / Published online: 11 November 1998     

An ab initio study of the ground and excited states of p-benzoquinone

The results of anab initio SCF calculation for the ground state and CI calculations for the excited states of p-benzoquinone are presented and discussed. A minimum basis set of Slater type orbitals was employed and the CI calculations were performed by considering single excitations from valence to virtual SCF molecular orbitals. The convergence of the calculated excitation energies is studied as a function of the number of orbitals used in the CI calculations. These calculations explain quite well the experimental results.     

Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores

Almost all time-dependent density-functional theory (TDDFT) calculations of excited states make use of the adiabatic approximation, which implies a frequency-independent exchange-correlation kernel that limits applications to one-hole/one-particle states. To remedy this problem, Maitra et al. [N.T. Maitra, F. Zhang, R.J. Cave, K. Burke, Double excitations within time-dependent density functional theory linear response theory, J. Chem. Phys. 120 (2004) 5932 ] proposed dressed TDDFT (D-TDDFT), which includes explicit two-hole/two-particle states by adding a frequency-dependent term to adiabatic TDDFT. This paper offers the first extensive test of D-TDDFT, and its ability to represent excitation energies in a general fashion. We present D-TDDFT excited states for 28 chromophores and compare them with the benchmark results of Schreiber et al. [M. Schreiber, M.R. Silva-Junior, S.P.A. Sauer, W. Thiel, Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3, J. Chem. Phys. 128 (2008) 134110]. We find the choice of functional used for the A-TDDFT step to be critical for positioning the 1h1p states with respect to the 2h2p states. We observe that D-TDDFT without HF exchange increases the error in excitations already underestimated by A-TDDFT. This problem is largely remedied by implementation of D-TDDFT including Hartree-Fock exchange.     

Theoretical investigation of excited states of molecules. An application on the nitrogen molecule

Diverse existing lines for the calculation of excited states are exposed, with an emphasis on those methods that consider both types of correlation energy: the dynamic and the non-dynamic one. We analyze the possibility of to calculate the dynamic correlation energy using a correlation energy density functional applied to a multi-determinantal wavefunction, which would include the non-dynamic correlation energy, versus the use of mono-determinantal wavefunctions, which are not able to include the long-range correlation energy, and versus the use of variational or perturbative calculations from multi-determinantal wavefunctions, with their excessive computational cost. The results obtained with several methods are compared. Contribution to the Serafin Fraga Memorial Issue.     

Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A²Σ⁺,B²Π,E²Π,3²Π, and 1²Δ states of HeH. For the C²Σ⁺ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space. Received: 3 June 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

An ab initio CI study of the ground and excited states of p-quinodimethane

Configuration interaction (CI) studies of the ground, electronically excited singlet and triplet states and of the ionized states (cations) are reported for p- quinodimethane (p-xylylene). The calculated ionization potentials are compared with the experimental photoelectron spectrum for the low-energy ionization region. The two high-energy low-intensity flanks of the second and third band observed in the photoelectron spectrum are assigned to be due to the two non-Koopmans' cation states, ascribing to shake-up ionizations.The calculated singlet-singlet and singlet-triplet excitation energies are compared with previous semiempirical MO results and experimental data.     

Ab initio computation of the interaction energy curves for some low-lying states of CO which dissociate to ground-state3 P O and3 P C atoms

Summary We investigate the molecular electronic structure of the quintet states of CO which correspond to the C(³ P)+O(³ P) interaction at several levels of theory. We find the 1⁵⁺ state to be relatively deeply bound (D _e ca. 587 cm^–1) while the other quintets have relatively shallow potential wells (D _e<40 cm^–1) according to our multireference configuration interaction calculations which are counterpoise corrected for basis set superposition effects. Our results are in qualitative accord with the recent semiempirical estimates of Bussery and co-workers [(1989) Chem. Phys. 134:7].National Academy of Sciences, National Research Council, Air Force Astronautics Laboratory, Resident Research Associate 1987–89     

Excess energy and equation of state of fluids with hard-core potential models from a second-order Monte Carlo perturbation theory

Monte Carlo simulations in the NVT ensemble of the reference hard-sphere fluid have been performed to obtain the “exact” first- and second-order terms in the inverse temperature expansion of the free energy of fluids with hard-core potentials. The results have been used to obtain parametrizations of the free energy of fluids with Sutherland potentials with variable range as well as for a fluid with a hard-core Lennard–Jones potential. The results for the excess energy and the equation of state are compared with simulation data available in the literature for these fluids.     

CEPA calculations on open-shell molecules. III. Potential curves for the six lowest excited states of He2 in the vicinity of their equilibrium distances

CEPA-PNO and PNO-CI calculations have been performed for the potential energy curves of the He ₂ ⁺ ground state and the six lowest excited states of He₂ in the range of 1.4 a₀ ≤R ≤ 3.5 a₀. The calculated equilibrium distances as well as the spectroscopic constants are in very good agreement with molecular constants as derived experimentally from the rotation-vibration spectrum of He₂ by Ginter, except for thec ³∑ _g ⁺ state. This latter discrepancy is probably due to an “obligatory” hump in thec ³∑ _g ⁺ state occurring at 3.5 a₀ which cannot be properly treated in our calculation. The relative energetic positions of the six lowest states and their ionization energies are reproduced by our calculations with an accuracy of 0–400 cm⁻¹. Extrapolation of our results to infinite basis sets leads to estimates of the dissociation energies of He₂ excited states which cannot be measured spectroscopically because of the humps in all these states.     

An application of mean-field perturbation theory for the adsorption of polar molecules in nanoslit-pores

In the present research study, we present the development of a model for characterizing and predicting the adsorption of polar molecules between two parallel plates based on mean-field perturbation theory. The electrostatic forces between fluid–fluid molecules in the slit shaped pore are modeled by considering permanent dipole–dipole interactions and permanent dipole-induced dipole moment interactions. The intermolecular potential for the electrostatic interactions was obtained by considering statistical averages over all possible orientations of the molecules. The proposed model is then used to study the sorption of water molecules in the slit shaped pore and an explicit equation for the Helmholtz free energy of the pore phase fluid is derived. Adsorption isotherms for different pore sizes are simulated and the relative contributions of fluid–wall and fluid–fluid interactions to the Helmholtz free energy are calculated as an illustration and compared with the results of existing models in the literature.AMS subject classification: 82B03, 82B05, 82B26, 82B30, 82D15, 31B10, 41A25     

An application of RPA theory to conjugated systems in the excited states

In order to obtain a relationship between the molecular dimension and the correlation effect, RPA method has been applied to the calculation of electronic transition energies of linear polyenes. It has been found that the effect of electron correlation on the excitation energy decreases with increasing the size of molecule. The calculated oscillator strengths are remarkably improved by RPA calculation.     

Evaluation of the contribution from triply excited intermediates to the fourth-order perturbation theory energy on Intel distributed memory supercomputers

Summary Three previously reported algorithms for the evaluation of the fourth-order triple excitation energy component in many-body perturbation theory have been compared. Their implementation on current Intel distributed memory parallel computers has been investigated. None of the algorithms, which were developed for shared memory computer architectures, performed well since they lead to prohibitive IO demands. A new algorithm suitable for distributed memory machines is suggested and its implementation on two Intel i860 supercomputers is described. A high level of parallelism is obtained.     

Perturbative solution of the RPA equation. An application to the calculation of rotational strengths

The RPA equation is solved by perturbation in Møller-Plesset (MP) and Epstein-Nesbet (EN) partitions, which are first compared on a specific example. To still accelerate the faster one (EN), a third scheme is proposed, which involves preliminary diagonalization within a limited subset , followed by usual EN perturbation between and the rest of the whole configuration space. Criteria for the choice of are given.     

Theory of spin triplet ground states ind 6 transition metal compounds and the effect of high-energy states on the nature of the ground state

The formation of spin triplet, quintet, and singlet ground states within the 3d ⁶ electron configuration is investigated inD _4h , andD _3d symmetries employing irreducible tensor operator methods. Significant differences in the possible ground states are encountered between a complete CI and spin-orbit interaction treatment and an approximate calculation within the cubic⁵ T ₂,¹A₁,³ T ₁, and³ T ₂ parents.     

Discrete contributions to static dipole polarizabilities of excited bound states of non-relativistic hydrogen-like atoms

The static dipole polarizability α _{d, i} for an arbitrary bound state i of the non-relativistic hydrogen-like atom has been known for a long time from, e.g; the second-order perturbation theory treatment of the Stark effect. A reliable result for the ground state requires both summation over the discrete spectrum and inclusion of the continuum contribution. This continuum contribution is known to decrease for excited states, but a systematic study of this decrease has not been available so far. We present here representative results from a systematic study of α _{d, i} , which was performed as a first test of a new algorithm for the radial integrals involved. Partial sum approximations of the discrete contribution yield the total α _{d, i} with a relative error of less than 1% for all states i with principal quantum number n≥5. Corresponding results for the relativistic case, for which the radial integral algorithm was developed, will be presented elsewhere. Dedicated to Professor Hermann Stoll on the occasion of his 60th birthday An erratum to this article is available at .     

Application of open-shell coupled cluster theory to the ground state of GaAs

Summary Theoretical calculations at the coupled cluster level of theory including all single, double and perturbative triple excitations, CCSD(T), are carried out for the^3– ground state of GaAs. Employing a (7s5p3d1f) basis set, the theoretical predictions forr _e (2.560 Å), _e (217 cm^–1),D _e (1.84 eV), and IP (7.80 eV), are in good agreement with recent experimental results. The importance of includingf-type polarization functions in the basis set and the effect of correlating 3d electrons are discussed in detail.     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li2H

A 285-point multi-reference configuration-interaction involving single and double excitations (MRS-DCI) potential energy surface for the electronic ground state of Li₂H is determined by using 6-311G (2df, 2pd) basis set. A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a X² of 4.64 × 10^-6. The equilibrium geometry occurs at R_e =0.172 nm and <LiHLi =94.10. The dissociation energy for reaction Li₂H(²A)⇑ Li₂(¹⌆_g)+H(²S) is 243.910 kJ/mol. and that for reaction Li₂H(²A)⇑HLi(¹be)+Li(²S) is 106.445 kJ/mol. The inversion barrier height is 50.388 kJ/mol. The vibrational energy levels are calculated using the discrete variable representation (DVR) method. Project supported by the National Natural Science Foundation of China (grant No. 29673029) and by the Special Doctoral Research Foundation of the State Education Commission of China.