Reference Wave Function Research Articles

Electronic Structure of Thienylene Vinylene Oligomers: Singlet Excited States, Triplet Excited States, Cations, and Dications

This paper describes a quantum chemical study of the electronic structure of thienylene vinylene oligomers ranging in size from two thienylene rings (2TV) to 12TV. The geometries of the TV oligomers in the ground state, the lowest triplet state, and the singly and doubly oxidized states were optimized using density functional theory calculations. The electronic absorption spectra were obtained from configuration interaction calculations with an INDO/s reference wave function. Comparison with experimental data shows that the agreement is satisfactory, except for the triplet−triplet absorption spectra. For closed shell systems (ground state and doubly occupied state), the spectra were also calculated by time dependent density functional theory (TDDFT). TDDFT considerably underestimates the neutral singlet−singlet excitation energies for longer chains. The nature of the excited states for the TV radical cations was found to be more similar to that of thiophenes than to that of phenylene vinylenes, indicating...

Geminal model chemistry II. Perturbative corrections.

We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein-Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, with dispersion interactions between the geminals being the dominant effect missing in the reference wave functions.

The diazocarbene (CNN) molecule: characterization of the X 3Sigma- and A 3Pi electronic states.

The ground (X (3)Sigma(-)) and first excited triplet (A (3)Pi) electronic states of diazocarbene (CNN) have been investigated systematically starting from the self-consistent-field theory and proceeding to the coupled cluster with single, double, and full triple excitations (CCSDT) method with a wide range of basis sets. While the linear X (3)Sigma(-) ground state of CNN has a real degenerate bending vibrational frequency, the A (3)Pi state of CNN is subject to the Renner-Teller effect and presents two distinct real vibrational frequencies along the bending coordinate. The bending vibrational frequencies of the A (3)Pi state were evaluated via the equation-of-motion coupled cluster (EOM-CC) techniques. The significant sensitivity to level of theory in predicting the ground-state geometry, harmonic vibrational frequencies, and associated infrared intensities has been attributed to the fact that the reference wave function is strongly perturbed by the excitations of 1pi-->3pi followed by a spin flip. At the highest level of theory with the largest basis set, correlation-consistent polarized valence quadruple zeta (cc-pVQZ) CCSDT, the classical X-A splitting (T(e) value) was predicted to be 68.5 kcal/mol (2.97 eV, 24 000 cm(-1)) and the quantum mechanical splitting (T(0) value) to be 69.7 kcal/mol (3.02 eV, 24 400 cm(-1)), which are in excellent agreement with the experimental T(0) values, 67.5-68.2 kcal/mol (2.93-2.96 eV, 23 600-23 900 cm(-1)). With the EOM-CCSD method the Renner parameter (epsilon) and averaged bending vibrational frequency (omega(2)) for the A (3)Pi state were evaluated to be epsilon=-0.118 and omega(2)=615 cm(-1), respectively. They are in fair agreement with the experimental values of epsilon=-0.07 and nu(2)=525 cm(-1).

Putting error bars on the ab initio theoretical estimates of the magnetic coupling constants: the parent compounds of superconducting cuprates as a case study.

The influence of the basis set size and computational method in the calculation of the magnetic coupling constant J is evaluated using a series of cuprate superconductor parent compounds as a case study. The variational DDCI method and an iterative modification, the IDDCI method, are tested, as well as the perturbative CASPT2 method, with two different reference wave functions. Results show that the DDCI magnetic coupling constant is in rather good agreement with the experiment, although it shows a moderate basis set dependency. The IDDCI results are less dependent on the size of the basis set, but slightly overestimate the magnetic coupling constant. CASPT2 results are nearly independent of the chosen basis set. With a minimal active space values are obtained that are about 20% smaller than the DDCI results. The experimental coupling constant can be reproduced when an extended reference wave function is used.

Valence ab initio calculation of the potential-energy curves for the Ca 2 dimer

The electronic structure of the Ca2 molecule has been investigated by use of a two-valence-electron semiempirical pseudopotential and applying the internally contracted multireference configuration interaction method with complete-active-space self-consistent-field reference wave functions. Core–valence correlation effects have been accounted for by adding a core-polarization potential to the Hamiltonian. The ground-state properties of the Ca2 and Ca2 + dimers have also been studied at the single-reference coupled-cluster level with single and double excitations including a perturbative treatment of triple excitations. Good agreement with experiment has been obtained for the ground-state potential curve and the only experimentally known A1Σ u + excited state of Ca2. The spectroscopic parameters D e and R e deduced from the calculated potential curves for other states are also reported. In addition, spin–orbit coupling between the singlet and triplet molecular states correlating, respectively, with the (4p)1P and (4p)3P Ca terms has been investigated using a semi-empirical two-electron spin–orbit pseudopotential.

Valence ab initio calculation of the potential energy curves for the Sr 2 dimer

The ground and excited states of the Sr 2 molecule has been investigated by use of a two-valence-electron semi-empirical pseudopotential (PP(2)) and applying the internally contracted multireference CI method (ICMRCI) and complete active space SCF (CAS SCF) reference wavefunctions. In the calculations, core polarization and core-valence correlation have been accounted for by adding a core-polarization potential (CPP) to the hamiltonian. Moreover, the single-reference coupled-cluster approach with single and double excitations including a perturbative treatment of triple excitations (CCSD(T)) has been used in ground-state calculations for Sr 2 and Sr 2 + to yield more accurate potential curves. Spin–orbit (SO) coupling between the singlet and triplet states correlating, respectively, with the (5p) 1P and (5p) 3P Sr terms has been investigated using a semi-empirical two-electron SO pseudopotential.

Combining two-body density functionals with multiconfigurational wavefunctions: diatomic molecules

The MCSCF method provides a correct zero-order wavefunction for all regions of molecular potential energy surfaces. To obtain quantitative accuracy a proper treatment of the dynamic correlation problem must be implemented. Traditionally this has been achieved through multireference variants of perturbation theory, configuration interaction and coupled cluster theory. The computational cost of such techniques makes them prohibitive for all but the smallest molecular problems. Reported here is an investigation into the efficacy of two-body density functionals in providing the dynamic correlation energy for MCSCF reference states. Tests were made on the two-body density functionals of Colle and Salvetti (CS), Moscardó and San-Fabán (MSF), and Moscardó and Pérez-Jiménez (MPJS) in predicting the equilibrium bond lengths, harmonic frequencies and dissociation eneries of fifteen diatomic molecules (3B2, 3BN, 2BS, 1C2, 2CN, 1CO, 1F2, 1FC1, 1N2, 3NCl, 3O2, 1PN, 3Si2, 1SiO, 3SO) using full valence-shell CASSCF reference wavefunctions. Also studied were modifications of these functionals recently suggested by Miehlich, Stoll and Savin (MSS) and Gráfenstein and Cremer (GC). The results obtained show accuracy comparable with and typically superior to the popular Kohn-Sham BLW and B3LW methods. However, the latter methods are not applicable in all regions of a potential energy surface, and even predict incorrect ground states for some systems. The use of two-body density functionals with MCSCF reference states does not share this shortcoming.

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

AbstractA recently proposed perturbational approach to the electron correlation cusp problem Sirbu, I.; King, H. F. J Chem Phys 2002, 117, 6411–6416 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Theoretical and experimental studies of the opto-electronic properties of positively charged oligo(phenylene vinylene)s: Effects of chain length and alkoxy substitution

In this paper a combined experimental and quantum chemical study of the geometry and opto-electronic properties of unsubstituted and dialkoxy-sustituted phenylene–vinylene oligomers (PV’s) is presented. The optical absorption spectra for PV cations with different chain lengths and substitution patterns were measured using pulse radiolysis with time-resolved spectrophotometric detection from 1380 to 500 nm (0.9 to 2.5 eV). The geometries of the PV’s studied were optimized using density functional theory (DFT) for both the neutral and singly charged molecule. The spectra for the PV radical cations were then calculated using singly excited configuration interaction with an intermediate neglect of differential overlap reference wave function method together with the DFT geometry. The agreement between experimental and theoretical absorption energies is excellent; most of the calculated radical cation absorption energies are within 0.15 eV of the experimental values. The pattern of dialkoxy-substitution is found to have a large effect on the optical absorption spectrum of the cation. Using the calculated charge distribution it is shown that the degree of delocalization of the charge correlates with the energy of the lowest absorption band. If alkoxy side chains are present on some of the rings the positive charge tends to localize at those sites.

Comparison of Multireference Møller−Plesset Theory and Time-Dependent Methods for the Calculation of Vertical Excitation Energies of Molecules

The vertical singlet−singlet excitation energies for a benchmark set of 14 medium and large molecules have been investigated with three quantum chemical methods. Calculations for electronic states with very different character in organic and inorganic systems are used to assess the accuracy and applicability of a simplified multireference Møller−Plesset (MR-MP2) approach, time-dependent density functional theory (TDDFT), and an approximate coupled cluster method with single and double excitations (CC2). In the pure ab initio approaches the resolution of the identity (RI) method for the calculation of the two-electron integrals is used to improve computational efficiency. It is shown that independently of the complexity of the electronic states involved, only the MR-MP2 method yields high accuracy (mean absolute deviation of 0.14 eV for 22 states). This finding is of particular importance because our scheme avoids computationally demanding orbital optimization steps and employs very compact reference wave functions. The TDDFT results are significantly poorer (mean absolute deviation of 0.26 eV), and systematic deviations for some π → π* states, Rydberg states, and systems with unusual electronic structure are obtained. It is concluded that TDDFT has a potential for exploratory investigations or for very large molecules due to its computational efficiency. The CC2 method shows a tendency to overestimate excitation energies and is also limited to systems where the ground state is well described by a single determinant.

On triplet tetraoxygen: ab initio study along minimum energy path and global modelling

MRCI calculations are reported for O4(3A) using two distinct CASSCF reference wave functions, and the results compared with previous ab initio calculations. By combining the force field of the best ab initio CASSCF surface at the saddle point with the recommended estimate for the barrier height, a four-body analytic term is obtained which added to the popular double many-body expansion potential energy surface for the title system makes it fit well such properties.

Basis set limit extrapolation of ACPF and CCSD(T) results for the third and fourth lanthanide ionization potentials

Theoretical values for the third and fourth ionization potentials of the lanthanide elements from La to Lu are presented. The results are based on large-scale multi-reference averaged coupled-pair functional calculations starting from a complete active space reference wavefunction and single-reference coupled-cluster calculations. Relativistic effects were accounted for by small-core energy-consistent ab initio pseudopotentials. The results obtained for optimized uncontracted valence basis sets including up to i functions were extrapolated to the basis set limit. The importance of higher angular momentum basis functions in ab initio calculations for energy differences between configurations with different 4f occupation numbers is discussed.

Multiconfigurational Perturbation Theory: An Efficient Tool to Predict Magnetic Coupling Parameters in Biradicals, Molecular Complexes, and Ionic Insulators

The performance of the complete active space second-order perturbation theory (CASPT2) to accurately predict magnetic coupling in a wide series of molecules and solid state compounds has been established. It is shown that CASPT2, based on a reference wave function that only includes the effects described by the Anderson or Hay−Thibeault−Hoffmann model, correctly reproduces all experimental trends. For a complete quantitative agreement with experiment (or with accurate results arising from the difference dedicated configuration interaction method), it is necessary to include effects that go beyond the Anderson model in the reference wave function. The CASPT2 method is computationally less demanding than CI based methods and, hence, allows us to extend the study of magnetic coupling parameters to larger molecules or systems with elevated spin moments. Moreover, CASPT2 provides a reliable and accurate alternative to density functional based methods that require the use of a broken symmetry approach.

Towards multireference equivalents of the G2 and G3 methods

The effect of replacing the standard single-determinant reference wave functions in variants of G2 and G3 theory by multireference (MR) wave functions based on a full-valence complete active space has been investigated. Twelve methods of this type have been introduced and comparisons, based on a slightly reduced G2-1 test set, are made both internally and with the equivalent single-reference methods. We use CASPT2 as the standard MR-MP2 method and MRCl+Q as the higher correlation procedure in these calculations. We find that MR-G2(MP2,SVP), MR-G2(MP2), and MR-G3(MP2) perform comparably with their single-reference analogs, G2(MP2,SVP), G2(MP2), and G3(MP2), with mean absolute deviations (MADs) from the experimental data of 1.41, 1.54, and 1.23 kcal mol−1, compared with 1.60, 1.59, and 1.19 kcal mol−1, respectively. The additivity assumptions in the MR-Gn methods have been tested by carrying out MR-G2/MRCI+Q and MR-G3/MRCI+Q calculations, which correspond to large-basis-set MRCI+Q+ZPVE+HLC calculations. These give MADs of 1.84 and 1.58 kcal mol−1, respectively, i.e., the agreement with experiment is somewhat worse than that obtained with the MR-G2(MP2) and MR-G3(MP2) methods. In a third series of calculations, we have examined pure MP2 and MR-MP2 analogs of the G2 and G3 procedures by carrying out large-basis-set MP2 and CASPT2(+ZPVE+HLC) calculations. The resultant methods, which we denote G2/MP2, G3/MP2, MR-G2/MP2, and MR-G3/MP2, give MADs of 4.19, 3.36, 2.01, and 1.66 kcal mol−1, respectively. Finally, we have examined the effect of using MCQDPT2 in place of CASPT2 in five of our MR-Gn procedures, and find that there is a small but consistent deterioration in performance. Our calculations suggest that the MR-G3(MP2) and MR-G3/MP2 procedures may be useful in situations where a multireference approach is desirable.

Theoretical study of spin-orbit coupling constants for O2+ (A 2Π3/2,1/2u, v+=0–17 and a 4Π5/2,3/2,1/2,−1/2u, v+=0–25)

The spin-orbit coupling constants (Av+) for O2+(A 2Πu,v+=0–17) and O2+(a 4Πu,v+=0–25) were computed based on the Pauli–Breit Hamiltonian with one and two electron terms for comparison with experimental measurements. In the present theoretical study, the vibrational wave functions are obtained using the potential energy curve calculated at the multireference configuration interaction (MRCI) level of theory, with single and double excitations from the complete active space self-consistent field (CASSCF) reference wave function. The electronic wave functions and spin-orbit coupling constants are obtained at the CASSCF and restricted MRCI levels. The effect on Av+ for O2+(A 2Πu,v+) and O2+(a 4Πu,v+) due to interactions of the O2+(A 2Πu,v+), O2+(a 4Πu,v+), and O2+(2Σu+) states is examined. The theoretical Av+ predictions for O2+(A 2Πu,v+) are found to be consistent with the experimental finding that O2+(A 2Πu) is an inverted spin-orbit state at low v+ levels and becomes a regular spin-orbit state at higher v+ levels. Good accord between theoretical predictions and experimental results for O2+(A 2Πu,v+=0–12) is observed with discrepancies in the range of 2–10 cm−1. In the case of O2+(a 4Πu,v+), excellent agreement between theoretical ab initio and experimental results is found with a discrepancy of 2–5 cm−1. Our effort to theoretically reproduce experimental fine structure in the Av+ curve for O2+(a 4Πu,v+) based on interstate vibrational interactions has met with limited success.

Simultaneous calculation of Rydberg and valence excited states of formaldehyde

The presence of low-lying Rydberg states interspersed among valence states constitutes a substantial challenge for the accurate quantum chemical calculation of electronically excited states because of the need to treat a relatively large number of states simultaneously. We present a general and efficient scheme that allows the treatment of a large number of Rydberg and valence states at the MR-CISD, MR-CISD+Q and MR-AQCC levels while using only a fraction of the size of the configuration space as compared to a full complete-active-space reference wave function. This scheme is applied to the calculation of vertical excitations and various avoided crossings between ten Rydberg and five valence singlet states of formaldehyde including transition dipole moments and oscillator strengths. Basis set effects, choice of configuration space and size-extensivity corrections have been considered. It is found that size-extensivity effects as computed by MR-CISD+Q and MR-AQCC play an important role especially for the description of the ππ* state and for avoided crossings in which this state is involved.

On the size extensivity of second-order Møller–Plesset perturbation theory based on a perfectly-paired generalized valence bond reference wavefunction

This paper examines the size extensivity property of second-order Møller–Plesset perturbation theory based on a spin-zero, perfectly-paired generalized valence bond reference wavefunction (GVB-MP2). Size extensivity is a desirable property of any approximate method. The GVB-MP2 energy can be evaluated using a contracted formulation or by using the uncontracted formulation. This paper shows that the contracted formulation of GVB-MP2 is size extensive, while the uncontracted implementation of the perturbation theory is not size extensive. The paper also shows that the uncontracted formulation of GVB-MP2 yields results in agreement with expectations based on the cluster expansion of the energy.

Problematic p-benzyne: Orbital instabilities, biradical character, and broken symmetry

The equilibrium geometry, harmonic vibrational frequencies, and infrared transition intensities of p-benzyne were calculated at the MBPT(2), SDQ-MBPT(4), CCSD, and CCSD(T) levels of theory using different reference wave functions obtained from restricted and unrestricted Hartree-Fock (RHF and UHF), restricted Brueckner (RB) orbital, and Generalized Valence Bond (GVB) theory. RHF erroneously describes p-benzyne as a closed-shell singlet rather than a singlet biradical, which leads to orbital near-instabilities in connection with the mixing of orbital pairs b1u-ag (HOMO–LUMO), b2g-ag (HOMO-1-LUMO), and b1g-ag (HOMO-2-LUMO). Vibrational modes of the corresponding symmetries cause method-dependent anomalous increases (unreasonable force constants and infrared intensities) or decreases in the energy (breaking of the D2h symmetry of the molecular framework of p-benzyne). This basic failure of the RHF starting function is reduced by adding dynamic electron correlation. However RHF-MBPT(2), RHF-SDQ-MBPT(4), RHF-CCSD, RB-CCD, and RHF-CCSD(T) descriptions of p-benzyne are still unreliable as best documented by the properties of the b1u-, b2g-, and b1g-symmetrical vibrational modes. The first reliable spin-restricted description is provided when using Brueckner orbitals at the RB-CCD(T) level. GVB leads to exaggerated biradical character that is reduced at the GVB-MP2 level of theory. The best results are obtained with a UHF reference wave function, provided a sufficient account of dynamic electron correlation is included. At the UHF-CCSD level, the triplet contaminant is completely annihilated. UHF-CCSD(T) gives a reliable account of the infrared spectrum apart from a CCH bending vibrational mode, which is still in disagreement with experiment.

Calculations using generalized valence bond based Møller–Plesset perturbation theory

This work presents calculations on small molecules using second-order Møller–Plesset perturbation theory with a generalized valence bond reference wave function. Møller–Plesset perturbation theory applied to a generalized valence bond reference (GVB-MP2) currently provides the best tradeoff between accuracy and computational feasibility among the methodologies of electronic structure. Frienser and co-workers have shown that the computational effort required for the GVB-MP2 methodology scales as no more than the third power of the size of the system, while that for the coupled-cluster and complete-active space methods scales as the seventh or worse power of system size. The GVB wave function is a qualitative wave function. Spectroscopic parameters and energetics at the GVB level are in qualitative agreement with experimentally determined values. The calculations presented in this work demonstrate that spectroscopic parameters computed using GVB-MP2 are in better agreement with experiment than those computed at the GVB level, and in close agreement with those obtained from the coupled-cluster plus singles and doubles with triples substitutions, which requires significantly more effort.

The dispersion of the polarizability of C60: A confirmation of recent experimental results through theoretical calculations

We present frequency-dependent linear response calculations of the polarizability of C60 using a Hartree–Fock reference wave function. The results indicate that the apparent dispersion of the polarizability as extracted from two recent, independent experiments are slightly too large, although our results are consistent with both experiments to within experimental uncertainty.