Single Double Configuration Interaction Research Articles

First principles electron-correlated calculations of optical absorption in magnesium clusters

In this paper, we report large-scale configuration interaction (CI) calculations of linear optical absorption spectra of various isomers of magnesium clusters Mg$_{n}$ (n=2--5), corresponding to valence transitions. Geometry optimization of several low-lying isomers of each cluster was carried out using coupled-cluster singles doubles (CCSD) approach, and these geometries were subsequently employed to perform ground and excited state calculations using either the full-CI (FCI) or the multi-reference singles-doubles configuration interaction (MRSDCI) approach, within the frozen-core approximation. Our calculated photoabsorption spectrum of magnesium dimer (Mg$_{2}$) isomer is in excellent agreement with the experiments both for peak positions, and intensities. Owing to the sufficiently inclusive electron-correlation effects, these results can serve as benchmarks against which future experiments, as well as calculations performed using other theoretical approaches, can be tested.

Pariser–Parr–Pople Model Based Investigation of Ground and Low-Lying Excited States of Long Acenes

Several years ago, Angliker et al. [ Chem. Phys. Lett. 1982 , 87 , 208 ] predicted nonacene to be the first linear acene with the triplet state 1(3)B2u as the ground state, instead of the singlet 1(1)Ag state. However, contrary to that prediction, in a recent experimental work, Tönshoff and Bettinger [ Angew. Chem. Int. Ed. 2010 , 49 , 4125 ] demonstrated that nonacene has a singlet ground state. Motivated by this experimental finding, we decided to perform a systematic theoretical investigation of the nature of the ground and the low-lying excited states of long acenes, with an emphasis on the singlet-triplet gap, starting from naphthalene, all the way up to decacene. The methodology adopted in our work is based upon the Pariser-Parr-Pople model (PPP) Hamiltonian, along with the large-scale multireference singles-doubles configuration interaction (MRSDCI) approach. Our results predict that even though the singlet-triplet gap decreases with the increasing conjugation length, nevertheless, it remains finite till decacene, thus providing no evidence of the predicted singlet-triplet crossover. We also analyze the nature of many-particle wave function of the correlated singlet ground state and find that the longer acenes exhibit a tendency toward an open-shell singlet ground state. Moreover, when we compare the experimental absorption spectra of octacene and nonacene with their calculated singlet and triplet absorption spectra, we observe excellent agreement for the singlet case. Hence, the optical absorption results also confirm the singlet nature of the ground state for longer acenes. Calculated triplet absorption spectra of acenes predict two well-separated intense long-axis polarized absorptions, against one such peak observed for the singlet case. This is an important prediction regarding the triplet optics of acenes, which can be tested in future experiments on oriented samples.

Correlated theory of linear optical absorption of octacene and nonacene

The technological importance of higher acenes has led to resurgence of interest in synthesizing higher acenes such as octacene, nonacene etc. Recently, Tönshoff and Bettinger [2010 Angew. Chem. Int. Ed. 49 4125] have synthesized octacene and nonacene. Motivated by their work, we have performed large-scale calculations of linear optical absorption of octacene and nonacene. Methodology adopted in our work is based upon Pariser-Parr-Pople model (PPP) Hamiltonian, along with large-scale multi-reference singles-doubles configuration interaction (MRSDCI) approach.

LARGE-SCALE FIRST PRINCIPLES CONFIGURATION INTERACTION CALCULATIONS OF OPTICAL ABSORPTION IN BORON CLUSTERS

We have performed systematic large-scale all-electron correlated calculations on boron clusters B n(n = 2 - 5), to study their linear optical absorption spectra. Several possible isomers of each cluster were considered, and their geometries were optimized at the coupled-cluster singles doubles (CCSD) level of theory. Using the optimized ground-state geometries, the excited states of different clusters were computed using the multi-reference singles-doubles configuration–interaction (MRSDCI) approach, which includes electron correlation effects at a sophisticated level. These CI wave functions were used to compute the transition dipole matrix elements connecting the ground and various excited states of different clusters, eventually leading to their linear absorption spectra. The convergence of our results with respect to the basis sets, and the size of the CI expansion were carefully examined. The contribution of configurations to many body wave-function of various excited states suggests that the excitations involved are collective, plasmonic type.

ChemInform Abstract: Nonlinear Optical Processes in Short Polyenes: Configuration Interaction Description of Two-Photon Absorption and Third-Harmonic Generation.

We use a multireference determinant single–double configuration interaction approach within a Pariser–Parr–Pople Hamiltonian (based on long‐range hopping integrals and the use of the Ohno formula) to investigate linear polyenes containing from four to sixteen carbons. We calculate the low‐lying excited states, the two‐photon absorption spectrum, and the third‐harmonic generation (THG) response. The mAg state, essential to the cubic nonlinear optical response, is found to saturate as the 6Ag state when chain length increases; for the longer polyenes, another high‐lying Ag state also becomes important. We analyze the length dependence of the static third‐order susceptibility χ(3); indication of the beginning of saturation behavior is found. Focusing our attention to the two‐photon resonance peak present in the free‐electron laser THG measurements on polyacetylene, we conclude that the experimental data can be explained within the strongly correlated electron one‐dimensional model used in this work, in addit...

The role of orbital transformations in coupled-pair functionals

The replacement of single excitations by orbital transformations in coupled-pair functionals derived from a single double configuration interaction approach is discussed. It is demonstrated that this modification leads to considerably improved density matrices and better agreement with results from coupled cluster singles doubles calculations taken as a reference. A comparison between the variationally optimized orbitals and the Brueckner orbitals shows that these two sets of orbitals are different.

The electronic spectroscopy of transition metal carbonyls: The tough case of Cr(CO) 6

The electronic spectroscopy of Cr(CO) 6, representative molecule for transition metal carbonyls is revisited by various quantum chemical methods from self consistent size consistent single double configuration interaction, equation of motion coupled cluster single double, multi state complete active space second-order perturbation, MS-CASPT2, and time-dependent density functional theory (TD-DFT). Comparison is done with previous CASPT2 and TD-DFT studies. Compared to experiment, most methods (except MS-CASPT2) do not give completely satisfactory quantitative results, which emphasizes the difficulty to perform highly accurate spectroscopy calculations. However, the results allow to clearly assign the nature of the different states, compared to experiment.

Correlated theory of triplet photoinduced absorption in phenylene-vinylene chains

In this paper we present results of large-scale correlated calculations of triplet photoinduced absorption (PA) spectrum of oligomers of poly-(para)phenylenevinylene (PPV) containing up to five phenyl rings. In particular, the high-energy features in the triplet PA spectrum of oligo-PPVs are the focus of this study, which, so far, have not been investigated theoretically, or experimentally. The calculations were performed using the Pariser-Parr-Pople (PPP) model Hamiltonian, and many-body effects were taken into account by means of multi-reference singles-doubles configuration interaction procedure (MRSDCI), without neglecting any molecular orbitals. The computed triplet PA spectrum of oligo-PPVs exhibits rich structure consisting of alternating peaks of high and low intensities. The predicted higher energy features of the triplet spectrum can be tested in future experiments. Additionally, theoretical estimates of exciton binding energy are also presented.

Theoretical study on the photoisomerization of azobenzene

Ab initio calculations are performed to elucidate the mechanism of the photoisomerization of azobenzene. We obtain the excitation energies of the S1(n→π*), S2(π→π*), and S3(n2→π*2) states by complete active space self-consistent field (CASSCF) and multireference single double configuration interaction (MRSDCI) calculations. Two-dimensional potential surfaces of the ground- and excited states are obtained at the CASSCF level in order to investigate the isomerization pathways. A conical intersection between the ground state and the S1 state is found near the midpoint of the rotation pathway, and causes a radiationless transition. On the other hand, the S2 state has local minima at the cis and trans structures, so that the isomerization proceeds at the S2 surface following the deexcitation.

Ab initio investigation of the vertical and adiabatic excitation spectrum of NO3

The ground and excited electronic states up to approximately 100 000 cm−1 of the nitrate free radical (NO3) are investigated by complete active space self-consistent-field (CASSCF) and mulitreference–singles doubles configuration interaction calculations. Extended basis sets, containing polarization and diffuse functions, and an active space consisting of 13 orbitals and 17 electrons are used. A total of 28 electronic states is obtained within the D3h framework which split into 44 states in C2v. All calculated states are valence states and their character is discussed in detail. Oscillator strength and radiative lifetimes are determined from the CASSCF wave functions and give evidence for a strong transition that was not yet known experimentally. For the experimentally observed E″2 and E′2 states equilibrium geometries, harmonic frequencies, and adiabatic excitation energies are calculated in excellent agreement with experimental data. Important new insight is gained about the role of the low-lying electronic states in the photodissociation and the mechanism of this process is discussed.

A detailed study on the symmetry breaking and its effect on the potential surface of NO3

The tenacious symmetry breaking of the electronic wave function of the nitrate radical (NO3) and its effect on the ground-state potential energy surface is investigated in detail. The symmetry breaking of Hartree–Fock wave functions results from a dominance of the orbital localization effect over the resonance effect and leads to three different solutions, one symmetrical and two distorted ones, for the same electronic state. The respective equilibrium geometries of these solutions are points on different potential surfaces, making their comparison meaningless. The resonance effect is promoted by dynamic as well as static electron correlation. However, the dynamic correlation methods [e.g., many-body perturbation theory (MBPT) and coupled-cluster single double (CCSD)] cannot overcome the symmetry breaking of the reference function and the problem of multiple solutions persists. The symmetry breaking can be avoided by the complete active space self-consistent field (CASSCF) approach that yields unique, single-valued surfaces for all electronic states. However, a sufficiently large and appropriately selected active space has to be used to avoid unphysical distortion of the wave function. Still the orbital localization effect leads to equilibrium geometries of C2v symmetry which strongly depend on the state-averaging of the CASSCF wave function. Multireference single double configuration interaction (MR-SDCI) wave functions are also free of symmetry breaking, if the reference orbitals are and if the configuration space is invariant under the symmetry operations. MRCI geometry optimizations only result in D3h symmetric structures with bond lengths and harmonic frequencies in close agreement with experimental data.

Contracted Schrödinger equation: Determining quantum energies and two-particle density matrices without wave functions

The contracted Schr\odinger equation (CSE) technique through its direct determination of the two-particle reduced density matrix (2RDM) without the wave function may offer a fresh alternative to traditional many-body quantum calculations. Without additional information the CSE, also known as the density equation, cannot be solved for the 2RDM because it also requires a knowledge of the 4RDM. We provide theoretical foundations through a reconstruction theorem for recent attempts at generating higher RDMs from the 2RDM to remove the indeterminacy of the CSE. With Grassmann algebra a more concise representation for Valdemoro's reconstruction functionals [F. Colmenero, C. Perez del Valle, and C. Valdemoro, Phys. Rev. A 47, 971 (1993)] is presented. From the perspective of the particle-hole equivalence we obtain Nakatsuji and Yasuda's correction for the 4RDM formula [H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996)] as well as a corrective approach for the 3RDM functional. A different reconstruction strategy, the ensemble representability method (ERM), is introduced to build the 3- and 4-RDMs by enforcing four-ensemble representability and contraction conditions. We derive the CSE in second quantization without Valdemoro's matrix contraction mapping and offer the first proof of Nakatsuji's theorem for the second-quantized CSE. Both the functional and ERM reconstruction strategies are employed with the CSE to solve for the energies and the 2RDMs of a quasispin model without wave functions. We elucidate the iterative solution of the CSE through an analogy with the power method for eigenvalue equations. Resulting energies of the CSE methods are comparable to single-double configuration-interaction (SDCI) energies, and the 2RDMs are more accurate by an order of magnitude than those from SDCI. While the CSE has been applied to systems with 14 electrons, we present results for as many as 40 particles. Results indicate that the 2RDM remains accurate as the number of particles increases. We also report a direct determination of excited-state 2RDMs through the CSE. By circumventing the wave function, the CSE presents new possibilities for treating electron correlation.

3,5-contracted Schr�dinger equation: Determining quantum energies and reduced density matrices without wave functions

Through the 3,5-contracted Schrödinger equation (3,5-CSchE) quantum energies and 3-particle reduced density matrices (3-RDMs) are determined directly without wave functions. Since the 3,5-CSchE involves the 5-RDM, its solution is indeterminate without N-representability conditions. However, the indeterminacy of the 3,5-CSchE may be removed through a reconstruction strategy for building the 4- and 5-RDMs from the 3-RDM. We present a systematic procedure for obtaining corrections for Valdemoro's reconstruction functionals from two complementary approaches, the particle–hole duality and the theory of cumulants. With the cumulants we are able to demonstrate that we have obtained all terms in the reconstruction functionals which may be written as antisymmetric products of the lower rdms. The cumulants allow us to understand the reconstruction functionals in terms of a renormalized many-body perturbation theory. The reconstruction functionals also lead to a natural generalization of Wick's theorem for evaluating expectation values of fermionic annihilation and creation operators with respect to correlated reference states. Previous work [Phys. Rev. A 57, 4219 (1998)] has explored the determination of correlation energy and 2-RDMs through the 2,4-CSchE, also known as the density equation. Because the reconstruction functionals employed with the 3,5-CSchE depend only on the antisymmetric products of lower RDMs in constrast to those used with the 2,4-CSchE, the 3,5-CSchE method presented here does not require the solution of systems of linear equations during reconstruction or the storage of the reconstructed RDMs. Application of the 3,5-CSchE technique to a quasi-spin model generates ground-state energies and 2-RDMs similar in accuracy to single–double configuration interaction (SDCI). We employ a simple iterative procedure for the solution of the 3,5-CSchE without traditional diagonalization. The CSchE techniques offer an approximate solution of the N-representability problem and a new approach to electron correlation. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 557–570, 1998

3,5‐contracted Schrödinger equation: Determining quantum energies and reduced density matrices without wave functions

Through the 3,5-contracted Schrödinger equation (3,5-CSchE) quantum energies and 3-particle reduced density matrices (3-RDMs) are determined directly without wave functions. Since the 3,5-CSchE involves the 5-RDM, its solution is indeterminate without N-representability conditions. However, the indeterminacy of the 3,5-CSchE may be removed through a reconstruction strategy for building the 4- and 5-RDMs from the 3-RDM. We present a systematic procedure for obtaining corrections for Valdemoro's reconstruction functionals from two complementary approaches, the particle–hole duality and the theory of cumulants. With the cumulants we are able to demonstrate that we have obtained all terms in the reconstruction functionals which may be written as antisymmetric products of the lower rdms. The cumulants allow us to understand the reconstruction functionals in terms of a renormalized many-body perturbation theory. The reconstruction functionals also lead to a natural generalization of Wick's theorem for evaluating expectation values of fermionic annihilation and creation operators with respect to correlated reference states. Previous work [Phys. Rev. A 57, 4219 (1998)] has explored the determination of correlation energy and 2-RDMs through the 2,4-CSchE, also known as the density equation. Because the reconstruction functionals employed with the 3,5-CSchE depend only on the antisymmetric products of lower RDMs in constrast to those used with the 2,4-CSchE, the 3,5-CSchE method presented here does not require the solution of systems of linear equations during reconstruction or the storage of the reconstructed RDMs. Application of the 3,5-CSchE technique to a quasi-spin model generates ground-state energies and 2-RDMs similar in accuracy to single–double configuration interaction (SDCI). We employ a simple iterative procedure for the solution of the 3,5-CSchE without traditional diagonalization. The CSchE techniques offer an approximate solution of the N-representability problem and a new approach to electron correlation. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 557–570, 1998

Full configuration–interaction and state of the art correlation calculations on water in a valence double-zeta basis with polarization functions

Using a valence double-zeta polarization basis, full configuration–interaction (FCI) calculations are carried out on water at its equilibrium geometry and at geometries where the OH bond lengths are stretched until dissociation. At the same geometries and with the same basis set configuration interaction calculations at excitation levels up to hextuples, multireference singles doubles configuration interaction calculations, coupled cluster calculations at excitation levels up to quadruples, Mo/ller–Plesset perturbation theory calculations through order fifteen, and complete active space second-order perturbation theory calculations are also carried out. The static correlation contribution increase with increasing bond length. The calculations show that the coupled cluster approach has a remarkable ability to describe even relatively large static correlation contributions. The single reference perturbation expansion breaks down for larger OH bond length, while the multireference approach preserves the accuracy for the whole potential curve. At the equilibrium geometry, FCI calculations have also been carried out for the lowest state of 2A1, 2B1, and 2B2 symmetry of H2O+, and the results compared with state of the art correlation results for total energies and ionization potentials (IP’s). Differential energies (IP’s) are obtained more accurately than absolute (total) energies in the size extensive coupled cluster and perturbation approaches. For the nonsize extensive configuration interaction method errors are obtained of the same size for differential and absolute energies.

Rate coefficients for the N+O2 reaction computed on an ab initio potential energy surface

Accurate calculations of the potential energy surface of the N+O2 reaction have been performed at complete active space self-consistent field (CASSCF) and multireference single–double configuration interaction (MR-SDCI) levels. Features of the calculated potential energy values are analyzed and compared with those of previous ab initio calculations and experimental data. The comparison has been extended to kinetic properties of the reaction.

Theoretical investigation of the nonlinear optical properties of oligomers of polythienylenemethylidene, a low band-gap material

We present a theoretical investigation by the sum-over-states formalism of the static first- and third-order polarizabilities of thienylenemethylidene oligomers; following the incorporation of a single conjugated carbon between the rings, these compounds present a partially quinoid geometry. We use a multireference determinant single–double configuration interaction approach to calculate excited-state energies, state dipole moments, and transition dipole moments which are introduced in the sum-over-states expressions. All the results are discussed in comparison to those obtained in thiophene oligomers of similar sizes; they indicate that the third-order polarizabilities are smaller for the methine-bridged compounds than for the corresponding thiophene oligomers. This feature is rationalized by analyzing the main optical (virtual excitation) channels that contribute to the nonlinear response.

Nonlinear optical processes in short polyenes: Configuration interaction description of two-photon absorption and third-harmonic generation

We use a multireference determinant single–double configuration interaction approach within a Pariser–Parr–Pople Hamiltonian (based on long-range hopping integrals and the use of the Ohno formula) to investigate linear polyenes containing from four to sixteen carbons. We calculate the low-lying excited states, the two-photon absorption spectrum, and the third-harmonic generation (THG) response. The mAg state, essential to the cubic nonlinear optical response, is found to saturate as the 6Ag state when chain length increases; for the longer polyenes, another high-lying Ag state also becomes important. We analyze the length dependence of the static third-order susceptibility χ(3); indication of the beginning of saturation behavior is found. Focusing our attention to the two-photon resonance peak present in the free-electron laser THG measurements on polyacetylene, we conclude that the experimental data can be explained within the strongly correlated electron one-dimensional model used in this work, in addition to the weakly interacting model successfully exploited in a previous study.

Theoretical enthalpies of formation for small silicon hydrides

Enthalpies of formation (Δ f H ○- 298 ) and Gibbs functions of formation (Δ f G ○- 298 ) for 27 molecular systems with up to three silicon atoms were calculated with high-quality electronic structure methods (multiconfigurational reference wave functions, singles-doubles configuration interaction) in combination with empirical bond enthalpy corrections