QM/MM study of the absorption spectra of DsRed.M1 chromophores

We report geometries and vertical excitation energies for the red and green chromophores of the DsRed.M1 protein in the gas phase and in the solvated protein environment. Geometries are optimized using density functional theory (DFT, B3LYP functional) for the isolated chromophores and combined quantum mechanical/molecular mechanical (QM/MM) methods for the protein (B3LYP/MM). Vertical excitation energies are computed using DFT/MRCI, OM2/MRCI, and TDDFT as QM methods. In the case of the red chromophore, there is a general blue shift in the excitation energies when going from the isolated chromophore to the protein, which is caused both by structural changes and by electrostatic interactions with the environment. For the lowest ππ* transition, these two factors contribute to a similar extent to the overall DFT/MRCI shift of 0.4 eV. An enlargement of the QM region to include active‐site residues does not change the DFT/MRCI excitation energies much. The DFT/MRCI results are closest to experiment for both chromophores. OM2/MRCI and TDDFT overestimate the first vertical excitation energy by 0.3–0.5 and 0.2–0.4 eV, respectively, relative to the experimental or DFT/MRCI values. The experimental gap of 0.35 eV between the lowest ππ* excitation energies of the red (cis‐acylimine) and green (trans‐peptide) forms is well reproduced by DFT/MRCI and TDDFT (0.32 and 0.37 eV, respectively). A histogram spectrum for an equal mixture of the two forms, generated by OM2/MRCI calculations on 450 snapshots along molecular dynamics trajectories, matches the experimental spectrum quite well, with a gap of 0.23 eV and an overall blue shift of about 0.3 eV. DFT/MRCI appears as an attractive choice for calculating excitation energies in fluorescent proteins, without the shortcomings of TDDFT and computationally more affordable than CASSCF‐based approaches. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Approximately size extensive local Multireference Singles and Doubles Configuration Interaction

Multi-reference Configuration Interaction (MRCI) is often used to predict the electronic structures and reaction energetics of small molecules with very high accuracy. Unfortunately, MRCI is inapplicable to large or even medium-sized molecules for two reasons: its computational cost scales poorly with molecule size and MRCI methods are not size extensive, leading to large energy errors. We have developed a new local (L) and approximately size extensive MRCI method that addresses both shortcomings. Truncating long-range electron correlation in a local orbital basis as well as efficient processing of two-electron integrals via Cholesky decomposition (CD) and integral screening reduce the computational cost to O(N(3)) with a small prefactor. A priori and a posteriori size extensivity corrections are both considered. The Multi-reference Averaged Coupled-Pair Functional (MRACPF) provides approximate size extensivity by modifying the energy functional. The very inexpensive Davidson-Silver and Pople a posteriori schemes also produce quite accurate corrections over a large range of molecular size. Employing CD-LMRACPF is slightly more expensive than using a Davidson-type correction, but the former gives superior results. Molecules with up to 50 heavy atoms can be treated with our CD-LMRACPF method thus far.     

Spectroscopic constants and molecular properties of the X2Π and a4Σ− electronic states of the SiF radical

The potential energy curves (PECs) of the X²Π and a⁴Σ^? electronic states of the SiF radical have been studied by an ab initio quantum chemical method. The calculations have been made using the complete active space self‐consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with several correlation‐consistent basis sets. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third‐order Douglas–Kroll Hamiltonian approximation. The relativistic corrections are made at the level of cc‐pV5Z basis set. The core‐valence correlation corrections are performed using the cc‐pCV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the total‐energy extrapolation scheme. Using these PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs obtained by the MRCI+Q/CV+DK+56 calculations, the vibrational levels, inertial rotation, and centrifugal distortion constants of the first 20 vibrational state of each electronic state are calculated when the rotational quantum number J equals zero. Comparison with the Rydberg‐Klein‐Rees (RKR) data shows that the present results are reliable and accurate. The molecular constants of the X²Π and a⁴Σ^? electronic states determined by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb-Ba)+

We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.     

Ab initio calculations of the lowest electronic states in the CuNO system

The lowest singlet and triplet electronic levels of the A' and A" symmetry species of the neutral copper-nitrosyl (CuNO) system are calculated by ab initio methods at the multi-reference configuration interaction (MRCI) level of theory with single and double excitations, and at the coupled cluster level of theory with both perturbational (CCSD(T)) and full inclusion of triple excitations (CCSDT). Experimental data are difficult to obtain, hence the importance of carrying out calculations as accurate as possible to address the structure and dynamics of this system. This paper aims at validating a theoretical protocol to develop global potential energy surfaces for transition metal nitrosyl complexes. For the MRCI calculations, the comparison of level energies at linear structures and their values from C(2v) and C(s) symmetry restricted calculations has allowed to obtain clear settings regarding atomic basis sizes, active orbital spaces and roots obtained at the multi-configurational self-consistent field (MCSCF) level of theory. It is shown that a complete active space involving 18 valence electrons, 11 molecular orbitals and the prior determination of 12 roots in the MCSCF calculation is needed for overall qualitatively correct results from the MRCI calculations. Atomic basis sets of the valence triple-zeta type are sufficient. The present calculations yield a bound singlet A' ground state for CuNO. The CCSD(T) calculations give a quantitatively more reliable account of electronic correlation close to equilibrium, while the MRCI energies allow to ensure the qualitative assessment needed for global potential energy surfaces. Relativistic coupled cluster calculations using the Douglas-Kroll-Hess Hamiltonian yield a dissociation energy of CuNO into Cu and NO to be (59 ± 5) kJ mol(-1) ((4940 ± 400) hc?cm(-1)). Favorable comparison is made with some of previous theoretical results and a few known experimental data.     

Geometrical energy derivative evaluation with MRCI wave functions

The theory of MCSCF and CI energy derivatives with respect to geometrical variations is briefly reviewed with special attention given to the MCSCF and MRCI energy gradients. A computational procedure is proposed for MRCI energy gradients that does not require the solution to any “coupled-perturbed MCSCF ” equations, it does not require any expensive direct-CI matrix-vector products involving derivative integrals, and it does not require any derivative integrals to be transformed from the AO basis to the MO basis. An additional feature is that it does not require any changes to existing MCSCF gradient evaluation programs in order to compute MRCI gradients. The only difference in the two cases is the exact nature of the data passed to the gradient evaluation program from the previous steps in the computational procedure. The additional effort required to compute the entire MRCI energy gradient vector is approximately that required for one additional iteration of the MRCI diagonalization procedure and for one additional MCSCF iteration. For large scale MRCI wave functions, the MRCI energy gradient evaluation should only require about 10% of the effort of computing the wave function itself. This computational procedure removes a major computational botleneck of potential energy surface evaluation.     

Ab initio potential energy surface for HeF2 in its ground electronic state

The ground state potential energy surface for He–F₂ has been generated using the coupled-cluster singles and doubles excitation approach with perturbative treatment of triple excitations [CCSD(T)] and multi-reference configuration interaction (MRCI) methodologies, with augmented correlation consistent quadruple zeta basis set and diffused functions. Both the CCSD(T) and MRCI surfaces are compared and the results analyzed. The CCSD(T) surface exhibits van der Waals minima at different distances for different orientations of He approaching F₂ and is adequate to describe accurately only in the region around the equilibrium bond distance of F₂. The MRCI surface, on the other hand, yields reliable results for a wider range of F–F bond distances leading to the correct asymptote. Davidson correction to the MRCI surface makes it purely repulsive over the regions investigated.     

Size extensive modification of local multireference configuration interaction

We recently developed a reduced scaling multireference configuration interaction (MRCI) method based on local correlation in the internal (occupied) and external (virtual) orbital spaces. This technique can be used, e.g., to predict bond dissociation energies in large molecules with reasonable accuracy. However, the inherent lack of size extensivity of truncated CI is a disadvantage that in principle worsens as the system size grows. Here we implement an a priori size-extensive modification of local MRCI known as the averaged coupled pair functional (ACPF) method. We demonstrate that local MR-ACPF recovers more correlation energy than local MRCI, in keeping with trends observed previously for nonlocal ACPF. We test the size extensivity of local ACPF on noninteracting He atoms and a series of hydrocarbons. Basis set and core correlation effects are explored, as well as bond breaking in a variety of organic molecules. The local MR-ACPF method proves to be a useful tool for investigating large molecules and represents a further improvement in predictive accuracy over local MRCI.     

Comparing electronic structure predictions for the ground state dissociation of vinoxy radicals

This paper reports a series of electronic structure calculations performed on the dissociation pathways of the vinoxy radical (CH(2)CHO). We use coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)), complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), and MRCI with the Davidson correction (MRCI+Q) to calculate the barrier heights of the two unimolecular dissociation pathways of this radical. The effect of state averaging on the barrier heights is investigated at the CASSCF, MRCI, and MRCI+Q levels. The change in mixing angle along the reaction path is calculated as a measure of derivative coupling and found to be insufficient to suggest nonadiabatic recrossing. We also present a new analysis of previous experimental data on the unimolecular dissociation of ground state vinoxy. In particular, an error in the internal energy distribution of vinoxy radicals reported in a previous paper is corrected and a new analysis of the experimental sensitivity to the onset energy (barrier height) for the isomerization reaction is given. Combining these studies, a final "worst case" analysis of the product branching ratio is given and a statistical model using each of the calculated transition states is found to be unable to correctly reproduce the experimental data.     

Theoretical predictions of red and near-infrared strongly emitting X-annulated rylenes

The optical properties of rylenes are extremely interesting because their emission colors can be tuned from blue to near-infrared by simply elongating the chain length. However, for conjugated chains, the dipole-allowed odd-parity 1B(u) excited state often lies above the dipole-forbidden even-parity 2A(g) state as the chain length increases, thus preventing any significant luminescence according to Kasha's rule. We systemically investigated the 1B(u)∕2A(g) crossover behaviors with respect to the elongating rylene chain length with various quantum chemistry approaches, such as time-depended density functional theory (TDDFT), complete active space self-consistent field theory (CASSCF∕CASPT2), multireference configuration interaction (MRCI)∕Zerner's intermediate neglect of diatomic overlap (ZINDO), and MRCI∕modified neglect of differential overlap. The calculated results by CASSCF∕CASPT2 and MRCI∕ZINDO are completely coherent: the optical active 1B(u) state lies below the dark B(3g) or 2A(g) state for perylene and terrylene, which results in strong fluorescence; while a crossover to S(1) = 2A(g) occurs and leads to much weaker fluorescence for quaterrylene. Then we put forward a molecular design rule on how to recover fluorescence for the longer rylenes by introducing heteroatom bridges. Several heteroatom-annulated rylenes are designed theoretically, which are predicted to be strongly emissive in the red and near-infrared ranges. These are further confirmed by theoretical emission spectra as well as radiative and nonradiative decay rate calculations by using the vibration correlation function formalisms we developed earlier coupled with TDDFT.     

An ab initio benchmark study of the H + CO --> HCO reaction

The H + CO --> HCO reaction has been characterized with correlation consistent basis sets at five levels of theory in order to benchmark the sensitivities of the barrier height and reaction ergicity to the one-electron and n-electron expansions of the electronic wave function. Single and multireference methods are compared and contrasted. The coupled cluster method RCCSD(T) was found to be in very good agreement with Davidson-corrected internally-contracted multireference configuration interaction (MRCI+Q). Second-order Moller-Plesset perturbation theory (MP2) was also employed. The estimated complete basis set (CBS) limits for the barrier height (in kcal/mol) for the five methods, including harmonic zero-point energy corrections, are MP2, 4.66; RCCSD, 4.78; RCCSD(T), 4.15; MRCI, 5.10; and MRCI+Q, 4.07. Similarly, the estimated CBS limits for the ergicity of the reaction are: MP2, -17.99; RCCSD, -13.34; RCCSD(T), -13.79; MRCI, -11.46; and MRCI+Q, -13.70. Additional basis set explorations for the RCCSD(T) method demonstrate that aug-cc-pVTZ sets, even with some functions removed, are sufficient to reproduce the CBS limits to within 0.1-0.3 kcal/mol.     

Multireference perturbation theory with optimized partitioning. II. Applications to molecular systems

The second‐order multireference perturbation theory using an optimized partitioning, denoted as MROPT(2), is applied to calculations of various molecular properties—excitation energies, spectroscopic parameters, and potential energy curves—for five molecules: ethylene, butadiene, benzene, N₂, and O₂. The calculated results are compared with those obtained with second‐ and third‐order multireference perturbation theory using the traditional partitioning techniques. We also give results from computations using the multireference configuration interaction (MRCI) method. The presented results show very close resemblance between the new method and MRCI with renormalized Davidson correction. The accuracy of the new method is good and is comparable to that of second‐order multireference perturbation theory using Møller‐Plesset partitioning. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1390–1400, 2003     

Computational studies on the ground and excited states of BrOOBr

In this work, theoretical computations for the ground and excited states of BrOOBr have been performed at high-level ab initio molecular orbital theories. The ground-state geometries of BrOOBr in different forms (trans, cis, and twist form) have been optimized at the couple-cluster CCSD(T) level of theory with cc-pVTZ and aug-cc-pVTZ basis sets, which indicates that at CCSD(T)/cc-pVTZ level of theory, the twist form is 4.96 kcal/mol more stable than the trans form and 10.67 kcal/mol more stable than the cis form; at the CCSD(T)/aug-cc-pVTZ basis set the twist form is 4.33 kcal/mol more stable than the trans form and 9.54 kcal/mol more stable than the cis form. The vertical excitation energies and potential-energy curves for the singlet and triplet low-lying excited states of BrOOBr were calculated at both the complete active space self-consistent-field (CASSCF) level of theory and the multireference internally contracted configuration interaction (MRCI) level of theory. The differences of potential-energy curves at CASSCF and MRCI levels of theory are found for the BrOOBr excited states. At CASSCF level of theory, none of the BrOOBr excited states are bound. However, at MRCI level of theory, all the BrOOBr states studied in this work are bound or slightly bound at the Frank-Condon region. In addition, the scalar relativistic effect and the spin-orbital coupling effect on the vertical excitation energies of the electronic states of BrOOBr were estimated.     

Excited electronic states of the cyclic isomers of O2 and SO2

The low-lying electronic states of O3 and SO2 in their bent and cyclic isomers up to about 10 eV are calculated using the multireference configuration interaction (MRCI) method with a standard Gaussian correlation consistent polarized triple-zeta (cc-pVTZ) basis set. The vertical excitation energies, electron configurations, and oscillator strengths of these states are reported. The molecular orbital structures and excited states of the cyclic isomers are discussed in relation to the bent ones. Coherent anti-Stokes Raman spectroscopy (CARS) schemes for detecting the synthesis of the cyclic isomers are suggested.     

Dissociation energies within selected configuration interaction and perturbation theory

Selected configuration interaction (CI) calculations and second-order perturbational theory are used to truncate systematically multireference single and double excitation CI (MRCI) expansions in the calculation of the bond dissociation energies of several systems like the single-bonded LiF molecule or the multiple-bonded N₂, NO and O₂ diatomic systems. The method is extended to compute the CH bond dissociation energy ofethene C₂H₄. It is shown how the proposed scheme (perturbation-selected MRCI (MRCI-PS)) is able to reproduce the accuracy of complete MRCI expansions with only a small number of configurations variationally evaluated.     

Energetics, transition states, and intrinsic reaction coordinates for reactions associated with O(3P) processing of hydrocarbon materials

Electronic structure calculations based on multiconfiguration wave functions are used to investigate a set of archetypal reactions relevant to O(3P) processing of hydrocarbon molecules and surfaces. These include O(3P) reactions with methane and ethane to give OH plus methyl or ethyl radicals, O(3P) + ethane to give CH3O + CH3, and secondary reactions of the OH product radical with ethane and the ethyl radical. Geometry optimization is carried out with CASSCF/cc-pVTZ for all reactions, and with CASPT2/cc-pVTZ for O(3P) + methane/ethane. Single-point energy corrections are applied with CASPT2, CASPT3, and MRCI + Q with the cc-pVTZ and cc-pVQZ basis sets, and the energies extrapolated to the complete basis set limit (CBL). Where comparison of computed barriers and energies of reaction with experiment is possible, the agreement is good to excellent. The best agreement (within experimental error) is found for MRCI + Q/CBL applied to O(3P) + methane. For the other reactions, CASPT2/CBL and MRCI + Q/CBL predictions differ from experiment by 1-5 kcal/mol for 0 K enthalpies of reaction, and are within 1 kcal/mol of the best-estimate experimental range of 0 K barriers for O(3P) + ethane and OH + ethane. The accuracy of MRCI + Q/CBL is limited mainly by the quality of the active space. CASPT2/CBL barriers are consistently lower than MRCI + Q/CBL barriers with identical reference spaces.     

Nonadiabatic decay dynamics of a benzylidene malononitrile

The photoinduced nonadiabatic decay dynamics of 2-[4-(dimethylamino)benzylidene]malononitrile (DMN) in the gas phase is investigated at the semiempirical OM2/MRCI level using surface hopping simulations. A lifetime of 1.2 ps is predicted for the S(1) state, in accordance with experimental observation. The dominant reaction coordinate is found to be the twisting around the C7═C8 double bond accompanied by pronounced pyramidalization at the C8 atom. Motion along this coordinate leads to the lowest-energy conical intersection (CI(01α)). Several other S(0)/S(1) conical intersections have also been located by full optimization but play no role in the dynamics. The time-resolved fluorescence spectrum of DMN is simulated by computing emission energies and oscillator strengths along the trajectories. It compares well with the experimental spectrum. The use of different active spaces in the OM2/MRCI calculations yields similar results and thus demonstrates their internal consistency.     

A new internally contracted multi-reference configuration interaction method

We present a new internally contracted multi-reference configuration interaction (MRCI) method which, at the same time, efficiently handles large active orbital spaces, long configuration expansions, and many closed-shell orbitals in the reference function. This is achieved by treating the closed-shell orbitals explicitly, so that all required coupling coefficients and density matrices only depend on active orbital labels. As a result, closed-shell orbitals are handled as efficiently as in a closed-shell single-reference program, and this opens up the possibility to perform high-accuracy MRCI calculations for much larger molecules than before. The enormously complex equations are derived using a new domain-specific computer algebra system and semi-automatically implemented using a newly developed integrated tensor framework. The accuracy and efficiency of the MRCI method is demonstrated with applications to dioxygen-copper complexes with different ligands, some of which involve more than 30 atoms, and to spin-state splittings of ferrocene.     

Multireference configuration interaction study of bromocarbenes

Multireference configuration interaction (MRCI) calculations of the lowest singlet X(1A') and triplet ?((3)A') states as well as the first excited singlet ?((1)A') state have been performed for a series of bromocarbenes: CHBr, CFBr, CClBr, CBr(2), and CIBr. The MRCI calculations were performed with correlation consistent basis sets of valence triple-ζ plus polarization quality, employing a full-valence active space of 18 electrons in 12 orbitals (12 and 9, respectively, for CHBr). Results obtained include equilibrium geometries and harmonic vibrational frequencies for each of the electronic states, along with ?((3)A') ← X((1)A') singlet-triplet gaps and ?((1)A') ← X((1)A') transition energies. Comparisons have been made with previous computational and experimental results where available. The MRCI calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the bromocarbenes.