On the internally contracted multireference CI method with full contraction

The configuration interaction (CI ) method where the efficiency of the generators of the unitary group is most fully exploited is the internally contracted multireference CI method. In the most recent version of this method the semi-internal configurations were kept uncontracted, which means that the number of configurations can still be quite large. In the present study the necessary formulas are derived for the case where the semi-internal states are also contracted. The highest density matrix that appears in these formulas is of order 5, and the computational treatment of this large matrix is discussed in detail.     

Communication: Second-order multireference perturbation theory with explicit correlation: CASPT2-F12

An explicitly correlated complete active space second-order perturbation (CASPT2-F12) method is presented which strongly accelerates the convergence of CASPT2 energies and properties with respect to the basis set size. A Slater-type geminal function is employed as a correlation factor to represent the electron-electron cusp of the wave function. The explicitly correlated terms in the wave function are internally contracted. The required density matrix elements and coupling coefficients are the same as in conventional CASPT2, and the additional computational effort for the F12 correction is small. The CASPT2-F12 method is applied to the singlet-triplet splitting of methylene, the dissociation energy of ozone, and low-lying excited states of pyrrole.     

Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules

The use of energy selected bases (ESB) with iterative diagonalization of the Hamiltonian matrix is described for vibrations of tetra-atomic systems. The performance of the method is tested by computing vibrational states of HOOH below 10,000 cm(-1) (1296 A+ symmetry states) and H(2)CO below 13,500 cm(-1) (729 A(1) symmetry states). For iterative solutions, we tested both the implicitly restarted Lanczos method (IRLM) and the standard (nonreorthogonalizing) Lanczos approach. Comparison with other contracted basis approach as well as direct product grid representation shows superior performance of the ESB/IRLM approach. Of the two systems, H(2)CO is found to be more challenging than HOOH since it has much stronger couplings among vibrational modes, which leads to a drastically larger primitive basis set. For H(2)CO we also discuss some interesting behavior of the molecule in the high internal energy regime.     

Communication: extended multi-state complete active space second-order perturbation theory: energy and nuclear gradients

The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented.     

Extensive theoretical study on the low-lying electronic states of silicon monofluoride cation including spin-orbit coupling

Ab initio calculations on the low-lying electronic states of SiF+ are performed using the internally contracted multireference configuration interaction method with the Davidson correction and entirely uncontracted aug-cc-pV5Z basis set. The effects of spin-orbit coupling are accounted for by the state interaction approach with the full Breit-Pauli Hamiltonian. The entire 23 Omega states generated from the 12 valence Lambda-S states, which correlate with the first dissociation channel are studied for the first time. Good agreement is found between the calculated results and the available experimental data. The spin-orbit coupling effects on the potential energy curves and spectroscopic properties are studied. Various curve crossings are revealed, which could lead to the predissociation of the a3Pi, A1Pi, and (2)3Sigma+ states and the predissociation pathways are analyzed based upon the calculated spin-orbit matrix elements. The calculated ionization potentials of the ground-state SiF to a few states of SiF+ are in good agreement with the available experimental measurements. Moreover, the transition dipole moments of the dipole-allowed transitions and the transition properties for the A3Pi0+ -X1Sigma+ 0+ and B3Pi1-X1Sigma+ 0+ transitions are predicted, including the Franck-Condon factors and the radiative lifetimes.     

Ground and valence excited states of BI: a MR-CISD+Q study

Ab initio calculations on the valence electronic states of the BI molecule have been performed by using the entirely uncontracted all-electronic aug-cc-pVQZ (for the B atom) and Sadlej-pVTZ (for the I atom) basis sets and the internally contracted multireference singles and doubles configuration interaction method with Davidson size-extensively correction and Douglas-Kroll scalar relativistic correction. The potential energy curves of all valence states and the spectroscopic constants of bound states are fitted. It is the first time that the 12 Lambda-S states of BI molecule and all of the 23 Omega states generated from the former are studied in a theoretical way. Calculation results reproduce well most of the experimental data. The effects of the spin-orbit coupling and the avoided crossing rule between Omega states of the same symmetry are analyzed. The transition properties of the A3Pi0+, B3Pi1, and C1Pi1 states to the ground-state transitions are predicted, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes. The radiative lifetime of the C1Pi1 state of BI molecule is less than 1 micros, while that of the A3Pi0+ and B3Pi1 states are the order of 1 ms.     

Ground and valence-excited states of SF: a multireference configuration interaction with single and double excitations+Q study

Ab initio calculations on the ground and valence-excited states of the sulfur monofluoride radical have been performed using entirely uncontracted all-electron augmented correlation consistent polarized valence quintuple zeta basis sets and the internally contracted multireference configuration interaction with single and double excitations method and Davidson correction (+Q). Potential-energy curves of all valence electronic states and the spectroscopic constants of several bound states are fitted. It is the first time that the entire 27-omega states generated from the 12 valence lambda-S states which come from the S(3P(g)) and F(2P(u)) atomic states of SF radical have been studied theoretically. The effects of spin-orbit coupling and the avoided crossing rule between omega states of the same symmetry are analyzed. The calculated results reproduce well the available experimental values and predict the properties of several bound excited states that have never been observed in experiment. The transition properties of the dipole-allowed transitions from bound excited states to the ground state are predicted for the first time, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted basis sets for second row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well balanced basis sets for molecular calculations. The starting primitive sets are 17s12p5d4f for the second row atoms Na-Ar. Corresponding ANO basis sets for first row atoms have recently been published.     

Ab initio study of the electronic spectrum of peroxyacetyl nitrate

A theoretical study of the ground and excited states of peroxyacetyl nitrate (PAN), CH3C(O)OONO2, has been carried out using high level ab initio molecular orbital methods. The ground state geometry and vibrational frequencies are calculated using the coupled-cluster method. The vertical excitation energies for the lowest three excited states are calculated using the complete active space self-consistent field method along with the multireference internally contracted configuration interaction method. These results are compared with vertical excitation energies calculated with the coupled cluster equation of motion method. The calculation provides relevant insight into the origin of PAN absorption in the UV wavelength region from 200 to 300 nm. The nature of the electron transitions for these excited states is discussed.     

Electronically excited-state properties and predissociation mechanisms of phosphorus monofluoride: a theoretical study including spin-orbit coupling

The 51 Ω states generated from the 22 Λ - S states of phosphors monofluoride have been investigated using the valence internally contracted multireference configuration interaction method with the Davidson correction and the entirely uncontracted aug-cc-pV5Z basis set. The spin-orbit coupling is computed using the state interaction approach with the Breit-Pauli Hamiltonian. Based on the calculated potential energy curves, the spectroscopic constants of the bound and quasibound Λ - S and Ω states are obtained, and very good agreement with experiment is achieved. Several quasibound states caused by avoided crossings are found. Various curve crossings and avoided crossings are revealed, and with the help of our computed spin-orbit coupling matrix elements, the predissociation mechanisms of the a(1)Δ, b(1)Σ(+), e(3)Π, g(1)Π, and (3)(3)Π states are analyzed. The intricate couplings among different electronic states are investigated. We propose that the avoided crossing between the A(3)Π(0 +) and b(1)Σ(0+) (+) states may be responsible for the fact that the A(3)Π ν' ≥ 12 vibrational levels can not be observed in experiment. The transition properties of the A(3)Π - X(3)Σ(-) transition are studied, and our computed Franck-Condon factors and radiative lifetimes match the experimental results very well.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted Basis sets for the atoms H-Kr have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANO's are constructed by averaging over the most significant electronic states, the ground state of the cation, the ground state of the anion for some atoms and the homonuclear diatomic molecule at equilibrium distance for some atoms. The contracted basis sets yield excellent results for properties of molecules such as bond-strengths and-lengths, vibrational frequencies, and good results for valence spectra, ionization potentials and electron affinities of the atoms, considering the small size of these sets. The basis sets presented in this article constitute a balanced sequence of basis sets suitable for larger systems, where economy in basis set size is of importance.     

Global ab initio potential energy surfaces for both the ground (X̃1A') and excited (Ã1A') electronic states of HNO and vibrational states of the Renner-Teller Ã1A'-X̃1A' system

The global potential energy surfaces for both the ground (X?(1)A(')) and excited (A?(1)A(')) electronic states of the HNO molecule have been constructed by three-dimensional cubic spline interpolation of more than 17,000 ab initio points, which have been calculated at the internal contracted multi-reference configuration interaction level with the Davidson correction using an augmented correlation-consistent polarized valence quadruple zeta basis set. The low-lying vibrational energy levels for the two electronic states of HNO have also been calculated on our potential energy surfaces including the diagonal Renner-Teller terms. The calculated results have shown a good agreement with the experimental vibrational frequencies of HNO and its isotopomers.     

A state-specific partially internally contracted multireference coupled cluster approach

A state-specific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators ( ?T) which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian ?? =e(- ?T)H?e( ?T) in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of ?? , expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the many-body residuals, do not have any near-singularity and thus, should allow one to solve all the amplitudes without discarding any. There are some relatively minor remaining convergence issues that may arise from an attempt to solve all the amplitudes and an initial analysis is provided in this paper. Applications to the bond-stretching potential energy surfaces for N(2), CO, and the low-lying electronic states of C(2) indicate clear improvements of the results using the many-body residuals over the conventional projected residual equations.     

Binding energies at different momenta for the valence orbitals of HCl by the binary (e, 2e) method

The binding energy spectra for the valence orbitals of hydrogen chloride have been obtained using the binary (e,2e) method at 1200 eV. The strength of the innermost valence orbital (4σ) is severely split among several ion states in the energy range 25 to 41 eV. The measured cross sections are compared with results of calculations using contracted Gaussian basis sets of double-zeta quality, and with a one-particle Green's function calculation.     

Potential energy surface intersections in the C(1D)H2 reactive system

Potential energy surface (PES) intersection seams of two or more electronic states from the 1 1A', 2 1A', 3 1A', 1 1A", and 2 1A" states in the C(1D)H2 reactive system are investigated using the internally contracted multireference configuration interaction method and the aug-cc-pVQZ basis set. Intersection seams with energies less than 20 kcal/mol relative to the C(1D) + H2 asymptote are searched systematically, and finally several seam lines (at the linear H-C-H, linear C-H-H, and C(2v), geometries, respectively) and a seam surface (at Cs geometries) are discovered and determined. The minimum energy crossing points on these seams are reported and the influences of the PES intersections, in particular, conical intersections, on the CH2 spectroscopy and the C(1D) + H2 reaction dynamics are discussed. In addition, geometries and energies of the 1 1A2 and 1 1B2 states of methylene biradical CH2 are reported in detail for the first time.     

Coupled cluster investigation on the low-lying electronic states of CuCN and CuNC and the ground state barrier to isomerization

The observation of several metal cyanides and isocyanides in interstellar space has raised much interest these molecules. Optimum molecular structures, harmonic vibrational frequencies, and dipole moments of the ground electronic states (X1Sigma+), triplet excited states, and open shell singlet excited states of CuCN and CuNC were determined using different levels of nonrelativistic and scalar relativistic (Douglas-Kroll) [Ann. Phys. 82, 89 (1979)] coupled cluster theory in conjunction with atomic natural orbital basis sets and correlation consistent basis sets. For the relativistic computations the specially contracted correlation consistent Douglas-Kroll (DK) basis sets were used. Moreover, barriers to isomerization from CuCN to CuNC were computed. The predicted structures of the X1Sigma+ state for CuCN are re(Cu-C)=1.826 A and re(C-N)=1.167 A, at the most sophisticated level of theory, the scalar relativistic DK-CCSD(T)/cc-pVQZ(DK) method. These results are in excellent agreement with the experimentally determined Cu-C bond length of 1.829 A and C-N bond distance of 1.162 A. At the same level of theory, the zero-point corrected barrier to isomerization from CuCN to CuNC is estimated to be 14.7 kcal mol(-1), and the cyanide is more stable than the isocyanide by 11.5 kcal mol(-1). For both CuCN and CuNC the 3Sigma+ state is the lowest lying excited electronic state. At the DK-CCSD/cc-pVQZ(DK) level of theory, the energetic ordering of excited states of CuCN and CuNC is X1Sigma+相似文献   

Combining explicitly correlated R12 and Gaussian geminal electronic structure theories

Explicitly correlated R12 methods using a single short-range correlation factor (also known as F12 methods) have dramatically smaller basis set errors compared to the standard wave function counterparts, even when used with small basis sets. Correlations on several length scales, however, may not be described efficiently with one correlation factor. Here the authors explore a more general MP2-R12 method in which each electron pair uses a set of (contracted) Gaussian-type geminals (GTGs) with fixed exponents, whose coefficients are optimized linearly. The following features distinguish the current method from related explicitly correlated approaches published in the literature: (1) only two-electron integrals are needed, (2) the only approximations are the resolution of the identity and the generalized Brillouin condition, (3) only linear parameters are optimized, and (4) an arbitrary number of (non-)contracted GTGs can appear. The present method using only three GTGs and a double-zeta quality basis computed valence correlation energies for a set of 20 small molecules only 2.2% removed from the basis set limit. The average basis set error reduces to 1.2% using a near-complete set of seven GTGs with the double-zeta basis set. The conventional MP2 energies computed with much larger quadruple, quintuple, and sextuple basis sets all had larger average errors: 4.6%, 2.4%, and 1.5%, respectively. The new method compares well to the published MP2-R12 method using a single Slater-type geminal (STG) correlation factor. For example, the average basis set error in the absolute MP2-R12 energy obtained with the exp(-r12) correlation factor is 1.7%. Correlation contribution to atomization energies evaluated with the present method and with the STG-based method only required a double-zeta basis set to exceed the precision of the conventional sextuple-zeta result. The new method is shown to always be numerically stable if linear dependencies are removed from the two-particle basis and the zeroth-order Hamiltonian matrix is made positive definite.     

An ab initio study of the ground and low-lying excited states of the permanganate ion

The results of ab-initio self-consistent field calculations for the ground state and configuration interaction calculations for the excited states of the permanganate ion are presented and discussed. The calculations were performed using two large basis sets of contracted gaussian functions, and singly excited configurations were used in the calculations of the excited states. Fair agreement is obtained between these results and the experimental absorption spectra.