Self-consistent Field Wave Functions Research Articles

The predicted infrared spectrum of the hypermetallic molecule CaOCa in its lowest two electronic states [formula omitted] and [formula omitted

This study of CaOCa is our third paper in a series on Group 2 alkaline-earth M2O hypermetallic oxides. As with our previous calculations for BeOBe and MgOMg, the ab initio calculations we report here show that CaOCa has a linear 1Σg+ ground electronic state and a very low lying linear a˜3Σu+ first excited triplet electronic state. For CaOCa we determine that the singlet–triplet splitting Te(a˜)=386cm-1. We calculate the three-dimensional potential energy surface, and the electric dipole moment surfaces, of each of the two states using a multireference configuration interaction (MRCISD) approach in combination with internally contracted multireference perturbation theory (RS2C) based on full-valence complete active space self-consistent field (FV-CASSCF) wavefunctions with a cc-pwCVQZ-DK basis set for Ca and a cc-pCVQZ basis set for O. We simulate the infrared absorption spectra of 40Ca16O40Ca in each of these electronic states in order to aid in its eventual spectroscopic characterization.

Toward Accurate Theoretical Thermochemistry of First Row Transition Metal Complexes

The recently developed correlation consistent Composite Approach for transition metals (ccCA-TM) was utilized to compute the thermochemical properties for a collection of 225 inorganic molecules containing first row (3d) transition metals, ranging from the monohydrides to larger organometallics such as Sc(C(5)H(5))(3) and clusters such as (CrO(3))(3). Ostentatiously large deviations of ccCA-TM predictions stem mainly from aging and unreliable experimental data. For a subset of 70 molecules with reported experimental uncertainties less than or equal to 2.0 kcal mol(-1), regardless of the presence of moderate multireference character in some molecules, ccCA-TM achieves transition metal chemical accuracy of ±3.0 kcal mol(-1) as defined in our earlier work [J. Phys. Chem. A2007, 111, 11269-11277] by giving a mean absolute deviation of 2.90 kcal mol(-1) and a root-mean-square deviation of 3.91 kcal mol(-1). As subsets are constructed with decreasing upper limits of reported experimental uncertainties (5.0, 4.0, 3.0, 2.0, and 1.0 kcal mol(-1)), the ccCA-TM mean absolute deviations were observed to monotonically drop off from 4.35 to 2.37 kcal mol(-1). In contrast, such a trend is missing for DFT methods as exemplified by B3LYP and M06 with mean absolute deviations in the range 12.9-14.1 and 10.5-11.0 kcal mol(-1), respectively. Salient multireference character, as demonstrated by the T(1)/D(1) diagnostics and the weights (C(0)(2)) of leading electron configuration in the complete active self-consistent field wave function, was found in a significant amount of molecules, which can still be accurately described by the single reference ccCA-TM. The ccCA-TM algorithm has been demonstrated as an accurate, robust, and widely applicable model chemistry for 3d transition metal-containing species with versatile bonding features.

Accurate predictions of the energetics of silicon compounds using the multireference correlation consistent composite approach

Theoretical studies, using the multireference correlation consistent composite approach (MR-ccCA), have been carried out on the ground and lowest lying spin-forbidden excited states of a series of silicon-containing systems. The MR-ccCA method is the multireference equivalent of the successful single reference ccCA method that has been shown to produce chemically accurate (within ±1.0 kcal mol(-1) of reliable, well-established experiment) results. The percentage contributions of the SCF configurations to complete active space self-consistent field wave functions together with the Frobenius norm of the t(1) vectors and related D(1) diagnostics of the coupled-cluster single double wave function with the cc-pVTZ basis set have been utilized to illustrate the multi-configurational characteristics of the compounds considered. MR-ccCA incorporates additive terms to account for relativistic effects, atomic spin-orbit coupling, scalar relativistic effects, and core-valence correlation. MR-ccCA has been utilized to predict the atomization energies, enthalpies of formation, and the lowest energy spin-forbidden transitions for Si(n)X(m) (2 ≤ n + m ≥ 3 where n ≠ 0 and X = B, C, N, Al, P), silicon hydrides, and analogous compounds of carbon. The energetics of small silicon aluminides and phosphorides are predicted for the first time.

Quasi-degenerate second-order perturbation theory for occupation restricted multiple active space self-consistent field reference functions

A multi-configuration quasi-degenerate second-order perturbation method based on the occupation restricted multiple active space (ORMAS-PT/ORMAS) reference wavefunction is presented. ORMAS gives one the ability to approximate a complete active space self-consistent field (CASSCF) wavefunction using only a subset of the configurations from the CASSCF space. The essential idea behind ORMAS-PT is to use the multi-reference Møller-Plesset formalism to correct the ORMAS reference energy. A computational scheme employing direct CI methodology is presented. Several tests are presented to demonstrate the performance of the ORMAS-PT method.

Detailed Ab Initio First-Principles Study of the Magnetic Anisotropy in a Family of Trigonal Pyramidal Iron(II) Pyrrolide Complexes

A theoretical, computational, and conceptual framework for the interpretation and prediction of the magnetic anisotropy of transition metal complexes with orbitally degenerate or orbitally nearly degenerate ground states is explored. The treatment is based on complete active space self-consistent field (CASSCF) wave functions in conjunction with N-electron valence perturbation theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for treatment of magnetic field- and spin-dependent relativistic effects. The methodology is applied to a series of Fe(II) complexes in ligand fields of almost trigonal pyramidal symmetry as provided by several variants of the tris-pyrrolylmethyl amine ligand (tpa). These systems have recently attracted much attention as mononuclear single-molecule magnet (SMM) complexes. This study aims to establish how the ligand field can be fine tuned in order to maximize the magnetic anisotropy barrier. In trigonal ligand fields high-spin Fe(II) complexes adopt an orbitally degenerate (5)E ground state with strong in-state spin-orbit coupling (SOC). We study the competing effects of SOC and the (5)E⊗ε multimode Jahn-Teller effect as a function of the peripheral substituents on the tpa ligand. These subtle distortions were found to have a significant effect on the magnetic anisotropy. Using a rigorous treatment of all spin multiplets arising from the triplet and quintet states in the d(6) configuration the parameters of the effective spin-Hamiltonian (SH) approach were predicted from first principles. Being based on a nonperturbative approach we investigate under which conditions the SH approach is valid and what terms need to be retained. It is demonstrated that already tiny geometric distortions observed in the crystal structures of four structurally and magnetically well-documented systems, reported recently, i.e., [Fe(tpa(R))](-) (R = tert-butyl, Tbu (1), mesityl, Mes (2), phenyl, Ph (3), and 2,6-difluorophenyl, Dfp (4), are enough to lead to five lowest and thermally accessible spin sublevels described sufficiently well by S = 2 SH provided that it is extended with one fourth order anisotropy term. Using this most elementary parametrization that is consistent with the actual physics, the reported magnetization data for the target systems were reinterpreted and found to be in good agreement with the ab initio results. The multiplet energies from the ab initio calculations have been fitted with remarkable consistency using a ligand field (angular overlap) model (ab initio ligand field, AILFT). This allows for determination of bonding parameters and quantitatively demonstrates the correlation between increasingly negative D values and changes in the σ-bond strength induced by the peripheral ligands. In fact, the sigma-bonding capacity (and hence the Lewis basicity) of the ligand decreases along the series 1 > 2 > 3 > 4.

The predicted spectrum of the hypermetallic molecule MgOMg

The present study of MgOMg is a continuation of our theoretical work on Group 2 M(2)O hypermetallic oxides. Previous ab initio calculations have shown that MgOMg has a linear (1)Σ(g)+ ground electronic state and a very low lying first excited triplet electronic state that is also linear; the triplet state has (3)Σ(u)+ symmetry. No gas phase spectrum of this molecule has been assigned, and here we simulate the infrared absorption spectrum for both states. We calculate the three-dimensional potential energy surface, and the electric dipole moment surfaces, of each of the two states using a multireference configuration interaction (MRCISD) approach based on full-valence complete active space self-consistent field (FV-CASSCF) wavefunctions with a cc-pCVQZ basis set. A variational MORBID calculation using our potential energy and dipole moment surfaces is performed to determine rovibrational term values and to simulate the infrared absorption spectrum of the two states. We also calculate the dipole polarizability of both states at their equilibrium geometry in order to assist in the interpretation of future beam deflection experiments. Finally, in order to assist in the analysis of the electronic spectrum, we calculate the vertical excitation energies, and electric dipole transition matrix elements, for six excited singlet states and five excited triplet states using the state-average full valence CASSCF-MRCISD/aug-cc-pCVQZ procedure.

Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field

To reduce the basis set incompleteness of the complete-active-space self-consistent field (CASSCF) wave function and energy we develop a second-order perturbation correction due to single excitations to complete set of unoccupied states. Other than the one- and two-electron integrals, only one- and two-particle reduced density matrices are required to compute the correction, denoted as [2](S). Benchmark calculations on prototypical ground-state bond-breaking problems show that only the aug-cc-pVXZ basis is needed with the [2](S) correction to match the accuracy of CASSCF energies of the aug-cc-pV(X+1)Z quality.

Communication: Rotational g-factor and spin-rotation constant of CH+

The rotational g-factor and spin-rotation constants of the methylidynium ion CH(+) have been calculated for the first time with a large multiconfigurational self-consistent field wave function and at the coupled-cluster singles and doubles level augmented by a perturbative triples correction. The results for an equilibrium internuclear distance as well as for the v=0, J=1 vibration-rotational state are presented.

The predicted infrared spectrum of the hyperberyllium molecule BeOBe in its [formula omitted] and [formula omitted] electronic states

Hypermetallation is a concept that applies to molecules having metal stoichiometries that exceed normal valence, and BeOBe is just one example of such a molecule. Previous ab initio calculations and spectroscopic studies have shown that BeOBe has a linear 1 Σ g + ground electronic state and a very low lying 3 Σ u + first excited electronic state. As the gas phase infrared spectrum of this molecule is unknown, we simulate such absorption spectra for both of these electronic states. To this end, we calculate the three-dimensional potential energy surfaces and the electric dipole moment surfaces of each of the two states using a multireference configuration interaction (MRCISD) approach based on full-valence complete active space self-consistent field (FV-CASSCF) wavefunctions. This is followed by variational MORBID calculations, using our potential energy and dipole moment surfaces, in order to determine rovibrational term values and to simulate the infrared absorption spectrum of both the singlet and triplet states. We also calculate the dipole polarizability for both states at their equilibrium geometry, as this is of interest for probing the molecule in future beam deflection experiments.

Excited-state polarizabilities of solvated molecules using cubic response theory and the polarizable continuum model

The theory and an implementation of the solvent contribution to the cubic response function for the polarizable continuum model for multiconfigurational self-consistent field wave functions is presented. The excited-state polarizability of benzene, para-nitroaniline, and nitrobenzene has been obtained from the double residue of the cubic response function calculated in the presence of an acetonitrile and dioxane solvent. The calculated excited-state polarizabilities are compared to results obtained from the linear response function of the explicitly optimized excited states.

Exact quantum scattering study of the Ne+H2+ reaction on a new ab initio potential energy surface

We present a new potential energy surface (PES) for the ground state (1(2)A(')) of the chemical reaction Ne+H(2) (+) from a set of accurate ab initio data, which were computed using highly correlated complete active space self-consistent field and multireference configuration interaction wave functions with a basis set of aug-cc-pV5Z. The quantum reactive scattering dynamics calculation was carried out over the collision energy (E(col)) range of 0.5-1.5 eV based on the new PES. In this work we have taken the Coriolis coupling (CC) effect into account. The importance of including the CC quantum scattering calculation has been revealed by the comparison between the CC and the centrifugal sudden approximation calculation. The magnitude and profile of the CC total cross sections for v=0 and j=1 over the collision energy range of 0.5-1.5 eV are found to be in good agreement with the available experimental measurements obtained recently by Zhang et al. [J. Chem. Phys. 119, 10175 (2003)] after taking into account the experimental uncertainties.

Structural and optical properties of a neutral Nickel bisdithiolene complex: density functional versus ab initio methods

Density functional theory (DFT) and ab initio computations are applied to examine different properties of diamagnetic, square planar neutral nickel complexes that contain two bidentate ligands derived from bis ((ethylene)-1,2-dithiolato) ligands. Geometry, vibrational spectra (IR and Raman) are well reproduced in the density functional framework whereas TD-DFT methods are clearly insufficient to reproduce absorption properties. Multiconfigurational perturbation theory based on a complete active space self-consistent field wave function, i.e. MRPT2 and MRPT4 methods, reveal the pronounced multiconfigurational character of the ground state wave function. The singlet–triplet energy gap, the energy gained from symmetry breaking and the singlet diradical character are discussed in the DFT and ab initio frameworks. The complex of interest does not display a strong singlet diradical character. This molecule having a peculiar electronic structure; strong delocalization as shown by a new electron pair localization function analysis (EPLF); exemplifies the fragility of the TD-DFT method and thus, caution should be taken in the determination of the energetic properties of such compounds.

Silacyclopropenylidene and Its Most Important SiC2H2 Isomers

In pioneering matrix isolation experiments, Maier and Reisenauer reported and identified infrared spectra for 1-silacyclopropenylidene and three of its isomers. These experiments were followed by microwave spectroscopy identification of two of the structures. Seven low-lying isomers of SiC2H2 are systematically investigated here using ab initio restricted Hartree−Fock (RHF), coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triple excitations [CCSD(T)] methods and the correlation-consistent polarized valence cc-pVXZ/cc-pV(X+d)Z (X = D, T, and Q) basis sets. Full valence complete active space self-consistent field (CASSCF) wave functions are used for interpretation. All levels of theory employed in this study confirm the global minimum of the SiC2H2 potential energy surface (PES) to be 1-silacyclopropenylidene (1S). Among the seven singlet stationary points, six isomers are found to be minima, whereas one structure (6S) is a second-order saddle point. For the lowest-lyin...

Calculation of MP2 and Coupled-Cluster Molecular Properties Using the q-Integral Method

The main purpose of this paper is to report results of quantum mechanical calculation of the H(2) system using the q-Integral method with correlation corrections to the SCF (Self Consistent Field) wave functions included through the Møller-Plesset second-order perturbation (MP(2)) and Coupled-Cluster (CC) theory. Using the q-Integral method, we evaluated potential energy curves, rovibrational spectroscopy constants, rovibrational spectra, interatomic equilibrium distance and longitudinal static hyper(polarizability). All calculations were carried out through the STO-3G, STO-6G, and double-zeta (DZV) atomic basis set. The q-Integral method was implemented in the source code of the general ab initio quantum chemistry package GAMESS.

Structures and Energetics of H6+ Clusters

Theoretical investigations of the equilibrium structures and associated isomerization reactions of the hydrogen clusters H(6)(+) have been carried out. Three equilibrium structures and three isomerization transition states were located on the electronic doublet and quartet states of the respective potential energy surfaces. The research employed ab initio self-consistent-field (SCF), coupled cluster (CC) with single and double excitations (CCSD), CCSD with perturbative triple excitations (CCSD(T)), and full triple excitations (CCSDT) wave functions and a wide variety of correlation-consistent polarized valence cc-pVXZ and aug-cc-pVXZ (where X = D, T, Q) basis sets. For each structure the geometry, energy, dipole moment, harmonic vibrational frequencies, and infrared intensities are predicted. Complete active space SCF (CASSCF) and multireference configuration interaction (MRCI) wave functions are used to analyze the effect of correlation on physical properties and energetics. Extensive focal point analyses (including CCSDTQ and full CI energies and basis sets up to sextuple zeta) are used to obtain complete basis set (CBS) limit energies. The H(2)(+)-core H(6)(+) cluster with D(2d) symmetry is the global minimum, lying 3.9 (4.2) +/- 0.1 kcal mol(-1) below the H(3)(+)-core H(6)(+) cluster with C(s) symmetry, where zero-point vibrational energy (ZPVE) corrected value are shown in parentheses. The barrier of the isomerization reaction between these two structures is 7.4 (5.2) +/- 0.1 kcal mol(-1). The dissociation energies for the H(2)(+)-core H(6)(+) isomer [H(6)(+) (D(2d)) --> 2H(2) + H(2)(+)] and the H(3)(+)-core H(6)(+) isomer [H(6)(+) (C(s)) --> H(3)(+) + H(2) + H] are 57.5 (50.9) +/- 0.1 and 12.3 (8.3) +/- 0.1 kcal mol(-1), respectively.

Is the Photoinduced Isomerization in Retinal Protonated Schiff Bases a Single- or Double-Torsional Process?

Nonadiabatic photodynamical simulations are presented for the all-trans and 5-cis isomers of the hepta-3,5,7-trieniminium cation (PSB4) with the goal of characterizing the types of torsional modes occurring in the cis-trans isomerization processes in retinal protonated Schiff base (RPSB), the rhodopsin and bacteriorhodopsin chropomhore. Steric hindrance of these processes due to environmental effects have been modeled by imposing different sets of mechanical restrictions on PSB4 and studying its response in the photodynamics. Both the mechanism toward the conical intersection and the initial phase of the hot ground state dynamics has been studied in detail. A total of 600 trajectories have been computed using a complete active space self-consistent field wave function. Careful comparison with higher level methods has been made in order to verify the accuracy of the results. The most important mechanism driving restricted PSB4 isomerization in the excited state is characterized by two concerted twist motions (bipedal and closely related to it nonrigid bipedal) from which only one torsion tends to be continued during the relaxation into the ground state. The one-bond-flip is found to be important for the trans isomer as well. The main isomerization trend is a torsion around C(5)C(6) (equivalent to C(11)C(12) in RPSB) in the case of the cis isomer and around C(3)C(4) (C(13)C(14) in RPSB) in the case of the trans isomer. The simulations show an initial 70 fs relaxation into twisted regions and give an average internal conversion time of 130-140 fs, timings that are fully compatible with the general picture described by femtosecond transient absorption spectroscopic studies.

Localized orbitals in the coupled cluster singles and doubles model

In the vast majority of many-body perturbation theory and coupled-cluster method (MBPT/CCM) calculations, the self-consistent field (SCF) wavefunction is employed as the zeroth-order wave-function, and its associated canonical orbitals as the molecular orbital basis. The recent development of the coupled-cluster singles and doubles (CCSD) formalism provides an opportunity to explore alternative reference function and orbital choices, on a consistent basis. Here we examine, specifically, sets of orbitals that are more “localized” than the SCF orbitals. In particular, the bonding orbitals are selected to resemble traditional chemical bonds. CCSD calculations in the localized basis on methane employing a better than double-zeta basis set are performed and compared with conventional SCF basis results.

Some applications of atomic analytical wave functions

Calculations of certain atomic quantities were carried out, using our accurate analytical self-consistent-field (SCF) wave functions for the ground and excited states. The total weighted electric dipole oscillator strength for certain optical multiplets of Al, Cr3+, Cr, and Mn3+, and Fe3+, was calculated with the determinantal wave functions, while comparing various approximations. Orientational calculations of the electric quadrupole multiplet strength were carried out for some transitions in Cr3+, Cr, and Fe3+. Our SCF wave functions were also used for the calculation of the estimates of the electronic density at the nucleus, considered in the Mossbauer isomer shift studies.

An improved MCSCF method

An improved scheme for calculating multiconfiguration self-consistent field wavefunctions has been developed. This scheme is powerful in its algebraic formulation and quadratic in its convergence behavior. Shell and wavefunction replacement operators are introduced to make equation manipulation more transparent and less tedious. The configuration state function coefficients as well as the orbital expansion coefficients are improved in each iteration by exponential unitary transformations. The symmetry properties of the wavefunctions are fully exploited. The present scheme should be convergent for a wider range of applications than currently available schemes.

Theoretical investigation of anthracene‐9,10‐endoperoxide vertical singlet and triplet excitation spectra

The electronic absorption spectrum of anthracene-9,10-endoperoxide (APO) has been investigated by means of multiconfigurational multi-state second order perturbation theory on complete active space self-consistent field wavefunctions (MS-CASPT2/CASSCF) and two single reference methods: time-dependent density functional theory (TD-DFT) and coupled cluster of second order (CC2). After testing several active spaces and basis sets, a CAS (14,12) active space together with an ANO-S basis set was found an appropriate choice to describe the vertical singlet and triplet electronic states of APO. Unfortunately, TD-DFT and CC2 methods cannot reproduce the MS-CASPT2 and experimental spectrum. Our MS-CASPT2//CASSCF(14,12)/ANO-S calculations predict a predominant pi*(OO)sigma*(OO) character for the lowest singlet excited state S(1) at 3.85 eV. Accordingly, the lowest singlet state of APO should be responsible for homolysis of the endoperoxide group. The next two absorbing excited states, experimentally proposed to be responsible for singlet oxygen production and therefore connected to the biological interest of APO, have been computed vertically at 4.34 and 4.59 eV and assigned to pi(CC)pi*(CC) and pi*(OO)pi*(CC) transitions, respectively. The vertical triplet electronic spectrum follows the singlet vertical spectrum ordering. The high density of triplet and singlet excited states of different nature within few eV points to the possibility of intersystem crossings between potential energy surfaces of different multiplicity.