Multireference Moller Plesset Perturbation Research Articles

New benzene dimers: a benchmark theoretical investigation

A wide variety of methods have been used to study the retro-dimerization reactions of one cis-fused (1) and four new trans-fused benzene dimers (2–5). These methods, which included both single-reference and multi-reference approaches, were benchmarked against multi-reference Moller-Plesset perturbation theory of the second order (MRMP2) based on CASSCF(12,12) wavefunctions. Each of the single-reference approaches was found to be overestimating the activation barrier for retro-dimerization process. Interestingly, N-electron valence perturbation theory (NEVPT2) energies also diverged for these reactions from MRMP2 values. Canonical MP2 barriers were in better agreement with MRMP2 results than the NEVPT2 numbers, with mean unsigned deviations (MUD) of 5.4 kcal/mol and 6.6 kcal/mol, respectively. The behavior of each of the methods is discussed and compared with the application of the same methods to the standard pericyclic reaction set proposed by Houk et al. (J Phys Chem A 107:11445, 2003). The comparison between NEVPT2 and MRMP2 reaction barriers, when applied to the cycloadditions in the Houk set and the synchronous symmetry-allowed retro-dimerization of the benzene dimer 1, showed that these two methods give almost identical results for these reaction types (MUD of 0.5 kcal/mol).

New benzene dimers: an MRMP2 study

The reaction energies of one cis-fused and four new trans-fused benzene dimers have been studied with state-specific multi-reference Moller-Plesset perturbation theory of the second order (MRMP2) based on reference CASSCF(12,12) wavefunctions. The cis-fused dimer 1, the product of symmetry-allowed [4 + 2] cycloaddition process, has been previously characterized experimentally and theoretically and, in this study, was used as reference. Dimer 1 lies 45 kcal/mol above two isolated benzene molecules, and its retro-dimerization activation energy is ~ 8 kcal/mol. In contrast, the [4 + 2] formation of trans-fused dimer 2 is symmetry-forbidden with an energetic driving force (Erel) of 57.6 kcal/mol. An activation barrier for corresponding retro-dimerization calculated to be 31.0 kcal/mol. The thermal [2 + 2] formation of dimers 3 and 4 are also symmetry-forbidden. They have been calculated to be 79.0 kcal/mol and 105.1 kcal/mol higher in energy than two isolated benzene molecules, respectively. However, the activation energies of 23.2 and 20.5 kcal/mol could allow for kinetic persistence of these compounds. Dimer 5 is the only symmetry-allowed [2 + 2] cycloaddition product. With Erel of 67.5 kcal/mol and Ea for retro-dimerization reaction of 19.2 kcal/mol, it shows high similarity with the symmetry-forbidden dimers. The wave function for each of the dimers at their local minimum geometry contains greater than 80% of the configuration $$\sigma^{4} \pi^{8} \sigma^{*0} \pi^{*0}$$. The transition state for the retro-dimerization of 1 (1TS) also contains more than 80% of the closed-shell configuration $$\sigma^{4} \pi^{8} \sigma^{*0} \pi^{*0}$$. For 2TS–5TS systems, the wavefunctions exhibit significant biradical character (20%, 20%, 14% and 26%, respectively).

L-SHELL DIELECTRONIC SATELLITE TRANSITIONS OF Fe XVII

We have used the relativistic multi-reference Moller-Plesset perturbation theory to calculate the positions of the dielectronic satellite transitions involving doubly excited 3l3l' configurations that are associated with the X-ray spectrum of Fe XVII. A comparison of these positions with the wavelengths employed in astrophysical modeling codes shows discrepancies of up to 36 mA. Inspection of the spectrum of Capella recorded with the high energy transmission grating on the Chandra X-Ray Observatory reveals several features enhanced by Fe XVI lines formed by dielectronic recombination, one of which may be of future diagnostic use as it is fairly well isolated and in large part formed by dielectronic recombination.

NEW IDENTIFICATIONS OF Fe IX, Fe X, Fe XI, Fe XII, AND Fe XIII LINES IN THE SPECTRUM OF PROCYON OBSERVED WITH THE CHANDRA X-RAY OBSERVATORY

We have analyzed 280 ks of co-added observations performed with Chandra's Low Energy Transmission Grating Spectrometer using theoretical spectra of Fe VIII through Fe XVII. The model spectral data were produced by combining collisional excitation data generated with the Flexible Atomic Code and transition energies generated with a relativistic code based on the multi-reference Moller-Plesset perturbation theory. The spectroscopic accuracy of the theoretical Fe IX wavelengths was ascertained in a comparison with existing laboratory measurements. We find several new Fe IX lines in the 100-140 A region and confirm two previous identifications. We also have identified a new line from Fe X near 111 A; several weak features near 102 A may also be ascribed to Fe X. A line near 100.5 A is identified as originating from Fe XI; a neighboring feature near 101 A may also be from Fe XI. A cluster of three weak lines between 117 and 118 A may be ascribed to Fe XII. Two lines near 104 and 106 A, respectively, have been assigned to Fe XIII. In addition, we confirmed the presence of two out of four Fe VIII lines that were thought to exist in the spectrum. These two lines are located near 131 A. The Fe IX emission is weakly sensitive to the assumed electron density, while the Fe XIII is strongly dependent on density. We find that a density between 109 and 1010 cm–3 provides the best fit to the Procyon spectrum. We note that several of the new identifications have come at the expense of prior assignments to magnesium or calcium lines, removing evidence for the presence of these elements in this spectral region. No evidence for Fe XVIII, Fe XIX, or Fe XX was found.

HIGH-ACCURACY MR-MP PERTURBATION THEORY ENERGY AND RADIATIVE RATES CALCULATIONS FOR CORE-EXCITED TRANSITIONS IN Fe XVI

Accurate theoretical energy level, lifetime, and transition probability calculations of core-excited Fe XVI were performed employing the relativistic Multireference Moller-Plesset perturbation theory. In these computations the term energies of the highly excited n ≤ 5 states arising from the configuration 1s 22sk 2pm 3l p nl' q , where k + m + p + q = 9, l ≤ 3 and p + q ≤ 2 are considered, including those of the autoionizing levels with a hole-state in the L-shell. All even and odd parity states of sodium-like iron ion were included for a total of 1784 levels. Comparison of the calculated L-shell transition wavelengths with those from laboratory measurements shows excellent agreement. Therefore, our calculation may be used to predict the wavelengths of as of yet unobserved Fe XVI, such as the second strongest 2p-3d Fe XVI line, which has not been directly observed in the laboratory and which blends with one of the prominent Fe XVII lines.

Benchmark Ab Initio Calculations of the Barrier Height and Transition-State Geometry for Hydrogen Abstraction from a Phenolic Antioxidant by a Peroxy Radical and Its Use to Assess the Performance of Density Functionals

This Letter presents benchmark results for the transition-state geometry and classical barrier height for the hydrogen atom abstraction from phenol by an organic peroxyl radical. We use multireference Moller–Plesset perturbation theory (MRMP2) based on a complete active space self-consistent field (CASSCF) wave function with a previously defined well-balanced nom-CPO+π active space and a triple-ζ one-electron basis set for the benchmark calculations, including full geometry optimization of the saddle point at the MRMP2 level. The classical barrier height for the abstraction reaction by the methylperoxyl radical is found to be 7.4 kcal/mol. A variety of density functionals are tested for their ability to reproduce the benchmark calculations for this reaction to provide guidance for selecting a reliable density functional in future calculations of larger systems involving phenolic antioxidants. The best-performing density functional is M05, and other functionals with above-average performance (for both tran...

State-specific complete active space multireference Møller–Plesset perturbation approach for multireference situations: illustrating the bond breaking in hydrogen halides

Assessment of the complete active space-based state-specific multireference Moller–Plesset perturbation theory, SS-MRMPPT, has been performed on the ground states of HX (X = F, Cl, and Br) systems through the computation of potential energy surface (PES) and spectroscopic constants (such as equilibrium bond lengths, rotational constants, centrifugal distortion constants, vibrational frequencies, anharmonicity constants, and dissociation energies that are closely related to the shape and accuracy of the energy surfaces) extracted from the computed PES. The SS-MRMPPT (involves multiple amplitude sets to parametrize the exact wavefunction) approach isolates one of the several states provided by an effective Hamiltonian in an attempt to avert intruder states in size-extensive manner and hence it forms the basis of a robust approach to the electron correlation problem in cases where a multireference formalism is required. The absence of intruder problem makes SS-MRMPPT an interesting choice for the calculation of the dissociation energy surface(s). The performance of the method has been judged by comparing the results with calculations provided by current generation ab initio methods (multireference or single-reference methods) and we found, in general, a very good accordance between them which clearly demonstrates the usefulness of the SS-MRMPPT method.

THEORETICAL WAVELENGTHS OF Fe XVI L-SHELL TRANSITIONS AND COMPARISON WITH LABORATORY MEASUREMENTS ANDCHANDRAOBSERVATIONS OF CAPELLA

We have used the relativistic multi-reference Moller-Plesset perturbation theory to calculate the energy levels of Fe XVI, including those of the autoionizing levels with a hole state in the L shell. Comparison of the resulting L-shell transition wavelengths with those from recent laboratory measurements shows remarkable agreement, i.e., agreement within the experimental uncertainties. Our calculation allows us to predict the wavelength of the second strongest 2p-3d Fe XVI line, which has not yet been directly observed in the laboratory, to be 15.266 A. This wavelength is within 0.0042 A of the strong Fe XVII line commonly labeled 3D. Relying on the high accuracy of our calculations, we have reassigned two previously identified lines and predict a different location than previously thought for the strongest Fe XVI magnetic quadrupole transition. Inspection of the spectra of Capella recorded with the transmission grating spectrometers on the Chandra X-ray Observatory yields features corresponding to the predicted location of the innershell excited Fe XVI lines. These features have not been identified before. Our analysis shows that these features are most likely from Fe XVI.

Ab initio study of the excited singlet states of all-trans α,ω-diphenylpolyenes with one to seven polyene double bonds: Simulation of the spectral data within Franck–Condon approximation

Computational simulations of the electronic spectra with ab initio electronic structure calculations are presented for all-trans alpha,omega-diphenylpolyenes with the polyene double bond number (N) from 1 to 7. A direct comparison of the fluorescence spectra of diphenylpolyenes was made between the results of highly accurate calculations and the experimental data for the systems with various chain lengths. For the realistic simulation of the emission, the total vibrational wave function was described approximately as a direct product of one-dimensional (1D) vibrational wave functions along the normal coordinates that are determined from the vibrational analysis of the ground state. The observed spectra can be reproduced in a computationally efficient way by selecting effective C-C and C=C stretching modes for the constructions of the 1D vibrational Hamiltonians. The electronic structure calculations were performed using the multireference Moller-Plesset perturbation theory with complete active space configuration interaction reference functions. Based on the vertical excitation energies computed, the lowest singlet excited state of diphenylbutadiene is shown to be the optically forbidden 2 (1)A(g) state. The simulations of fluorescence spectra involving vibronic coupling effects reveal that the observed strong single C=C band consists of two major degenerate vibrational C=C modes for the shorter diphenylpolyenes with N=3 and 5. Further, the relative intensities of the C-C stretching modes in the fluorescence spectra tend to be larger than those of the C=C stretching modes for the systems with N over 5. This indicates that the geometric differences of the energy minima between the ground (1 (1)A(g)) and 2 (1)A(g) states grow larger towards the direction of the C-C stretching mode with increasing N.

Theoretical Study on the Photochemical Behavior of 4-Dimethylamino-4′-cyanodiphenylacetylene

The photochemical behavior of 4-dimethylamino-4'-cyanodiphenylacetylene (DCDPA) has been examined by ab initio complete active space self-consistent field (CASSCF) and its second-order multireference Moller-Plesset perturbation (MRMP2) methods. DCDPA is mainly excited into an internal charge-transfer (ICT) state where the charge transfers from the dimethylanilino group into the benzonitrile part. In S(1), there are two stable geometries. One is an ICT state where DCDPA is skeletally relaxed from the stable geometry in S(0) upon electronic excitation. The other is a diradical state where DCDPA takes a trans-bent form and the acetylenic C identical withC triple bond turns to be an ethylenic C horizontal lineC double bond, as already confirmed in the case of parent diphenylacetylene. On the way to the globally stable trans-bent form in S(1), a conical intersection between the charge-transfer and the diradical state is located. The photochemical behavior of DCDPA in polar solvent has been also examined by CASSCF combined with the polarized continuum model. Thereby, it was found that a twisted ICT (TICT) state where the dimethylanilino group is perpendicularly twisted against the remaining part is formed in polar solvent.

Improved virtual orbital multireference Møller–Plesset study of the ground and excited electronic states of protonated acetylene, C2H3+

The ground state geometries and associated normal mode frequencies of the classical and nonclassical protonated acetylene ion, i.e., the vinyl cation C(2)H(3) (+), are computed using the complete active space self-consistent field and improved virtual orbital (IVO) complete active space configuration interaction methods. In addition, the minimum-energy reaction path for the classical to nonclassical interconversion is determined (as are excitation energies) using the IVO modification of multireference Moller-Plesset (MRMP) perturbation theory. The IVO-MRMP treatment predicts the nonclassical structure to be 4.8 kcalmol more stable than the classical one, which is consistent with other high level theoretical estimates. The proton affinity of acetylene from the IVO-MRMP treatment (154.8 kcalmol) also agrees well with experiment (153.3 kcalmol) and with earlier CASPT2 calculations (154.8 kcalmol). We further report geometries and vibrational frequencies of low lying excited states of C(2)H(3) (+), which have not been observed and/or studied before. Comparisons with previous highly correlated calculations further demonstrate the computational efficiency of the IVO-MRPT methods.

Tetra-hydrides of the third-row transition elements: spin–orbit coupling effects on geometrical deformation in WH4 and OsH4

The dissociation energies of MH4 (M = La, Hf–Hg) were computed using full optimized reaction space (FORS) multi-configuration self-consistent field (MCSCF) and second-order multi-reference Moller–Plesset perturbation methods with the SBKJC basis sets augmented by a set of polarization functions (SBKJC(f,p)). It was shown that of the molecules examined, only four tetra-hydrides HfH4, TaH4, WH4, and OsH4 with Td symmetry are lower in energy than the corresponding dissociation limits. For WH4 and OsH4, the potential energy surfaces from the D4h to the Td structure were explored from both theoretical calculations and symmetry arguments based on the pseudo-Jahn- Teller effect. As for WH4, it is found that the ground state could be 3Eg, 3A2g, or 3B2g at the D4h structure. The present calculations suggest that the ground state is 3Eg, and that this state is stabilized by the eu deformation into a C2v structure (3B1) and then sequentially to the most stable Td structure (3A2). If the molecular system is promoted to the lowest 3B2g state, the D4h structure can directly deform into the most stable Td structure along the b2u vibrational mode. For OsH4, the ground state (5B1g) at the D4h structure deforms into a D2d structure and the resulting 5B2 state strongly interacts with the lowest 3E and 1A1 states due to the spin-orbit couplings (SOCs). As a result, it was shown that the relativistic potential energy of the lowest spin-mixed state (ground state) monotonically decreases along the D2d deformation path from the D4h to the Td structure.

Accurate calculation of core-electron binding energies: multireference perturbation treatment.

Multireference perturbation theory (MRPT) with multiconfigurational self-consistent field (MCSCF) reference functions is applied to the calculations of core-electron binding energies (CEBEs) of atoms and molecules. Orbital relaxations in a core-ionized state and electron correlation are both taken into account in a conventional MCSCF-MRPT procedure. In the MCSCF calculation, the target core ionized state is directly optimized as an excited state and this treatment can completely prevent a variational collapse. Multireference Moller-Plesset perturbation theory and multiconfigurational self-consistent field reference quasidegenerated perturbation theory were used to treat electron correlation. The present method quite accurately reproduced the 1s CEBEs of CH4, NH3, H2O, and FH; the average deviation from the experimental data is 0.11 eV using Ahlrichs' VTZ basis set. The C 1s and O 1s CEBEs of formic acid and acetic acid were calculated and the results are consistent with the bonding characters of the atoms in these molecules. The present procedure can also be applied to CEBEs of higher angular momentum orbitals by including spin-orbit coupling. The calculated CEBEs of Ar 2p, HCl 2p, Kr 3d, and HBr 3d are in reasonable agreement with the available experimental values. In the calculation of the 3d CEBEs, a relativistic correction significantly improves the agreements. The effect of polarization functions is also discussed.

Relativistic multireference M�ller-Plesset perturbation theory calculations for siliconlike ions

Relativistic second-order multireference Moller–Plesset perturbation theory calculations are reported for the ground and low-lying excited states of siliconlike ions, Ar+4, Ti+8, Fe+12, Ni+14, Kr+22, and Mo+28. Multiconfiguration Dirac–Fock self-consistent field wave functions were used as reference functions. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 433–445, 2000

Study of low-lying electronic states of ozone by multireference Mo/ller–Plesset perturbation method

The geometry and relative energy of the seven low-lying electronic states of ozone and the ground state of ozonide anion have been determined in C2v symmetry by the complete active space self-consistent field (CASSCF) and the multireference Mo/ller–Plesset perturbation (MRMP) methods. The results are compared with the photodetachment spectra of O−3 observed recently by Arnold et al. The theoretical electron affinity of ozone is 1.965 eV, which is 0.14 eV below the experimental result of 2.103 eV. The calculated adiabatic excitation energies (assignment of Arnold et al. in parentheses) of ozone are 3A2 0.90 eV (1.18 eV), 3B2, 1.19 eV (1.30 eV), 3B1, 1.18 eV (1.45 eV), 1A2, 1.15 eV (∼1.6 eV), 1B1, 1.65 eV (2.05 eV), and 1B2, 3.77 eV (3.41 eV), respectively. Overall the present theory supports the assignment of Arnold et al. However, the simple considerations of geometry and energy are insufficient to determine a specific assignment of the 3B2 and 3B1 states. The dissociation energy of the ground state of ozone is computed to be 0.834 eV at the present level of theory. The present theory also predicts that none of the excited states lies below the ground state dissociation limit of O3.