Nonorthogonal Configuration Interaction Research Articles

Vibrational Properties of Hydrogen-Bonded Systems Using the Multireference Generalization to the "On-the-Fly" Electronic Structure within Quantum Wavepacket ab Initio Molecular Dynamics (QWAIMD).

We discuss a multiconfigurational treatment of the "on-the-fly" electronic structure within the quantum wavepacket ab initio molecular dynamics (QWAIMD) method for coupled treatment of quantum nuclear effects with electronic structural effects. Here, multiple single-particle electronic density matrices are simultaneously propagated with a quantum nuclear wavepacket and other classical nuclear degrees of freedom. The multiple density matrices are coupled through a nonorthogonal configuration interaction (NOCI) procedure to construct the instantaneous potential surface. An adaptive-mesh-guided set of basis functions composed of Gaussian primitives are used to simplify the electronic structure calculations. Specifically, with the replacement of the atom-centered basis functions positioned on the centers of the quantum-mechanically treated nuclei by a mesh-guided band of basis functions, the two-electron integrals used to compute the electronic structure potential surface become independent of the quantum nuclear variable and hence reusable along the entire Cartesian grid representing the quantum nuclear coordinates. This reduces the computational complexity involved in obtaining a potential surface and facilitates the interpretation of the individual density matrices as representative diabatic states. The parametric nuclear position dependence of the diabatic states is evaluated at the initial time-step using a Shannon-entropy-based sampling function that depends on an approximation to the quantum nuclear wavepacket and the potential surface. This development is meant as a precursor to an on-the-fly fully multireference electronic structure procedure embedded, on-the-fly, within a quantum nuclear dynamics formalism. We benchmark the current development by computing structural, dynamic, and spectroscopic features for a series of bihalide hydrogen-bonded systems: FHF(-), ClHCl(-), BrHBr(-), and BrHCl(-). We find that the donor-acceptor structural features are in good agreement with experiments. Spectroscopic features are computed using a unified velocity/flux autocorrelation function and include vibrational fundamentals and combination bands. These agree well with experiments and other theories.

Non-orthogonal configuration interaction for the calculation of multielectron excited states

We apply Non-orthogonal Configuration Interaction (NOCI) to molecular systems where multielectron excitations, in this case double excitations, play a substantial role: the linear polyenes and β-carotene. We demonstrate that NOCI when applied to systems with extended conjugation, provides a qualitatively correct wavefunction at a fraction of the cost of many other multireference treatments. We also present a new extension to this method allowing for purification of higher-order spin states by utilizing Generalized Hartree-Fock Slater determinants and the details for computing ⟨S(2)⟩ for the ground and excited states.

A partitioned correlation function interaction approach for describing electron correlation in atoms

The traditional multiconfiguration Hartree–Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis. For atoms with many closed core shells, or complicated shell structures, a large orbital basis is needed to saturate the different electron correlation effects such as valence, core–valence and correlation within the core shells. The large orbital basis leads to massive configuration state function (CSF) expansions that are difficult to handle, even on large computer systems. We show that it is possible to relax the orthonormality restriction on the orbital basis and break down the originally very large calculations into a series of smaller calculations that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The expansion coefficients of the PCFs are determined from a low dimensional generalized eigenvalue problem. The interaction and overlap matrices are computed using a biorthonormal transformation technique (Verdebout et al 2010 J. Phys. B: At. Mol. Phys. 43 074017). The new method, called partitioned correlation function interaction (PCFI), converges rapidly with respect to the orbital basis and gives total energies that are lower than the ones from ordinary MCHF and CI calculations. The PCFI method is also very flexible when it comes to targeting different electron correlation effects. Focusing our attention on neutral lithium, we show that by dedicating a PCF to the single excitations from the core, spin- and orbital-polarization effects can be captured very efficiently, leading to highly improved convergence patterns for hyperfine parameters compared with MCHF calculations based on a single orthogonal radial orbital basis. By collecting separately optimized PCFs to correct the MR function, the variational degrees of freedom in the relative mixing coefficients of the CSFs building the PCFs are inhibited. The constraints on the mixing coefficients lead to small off-sets in computed properties such as hyperfine structure, isotope shift and transition rates, with respect to the correct values. By (partially) deconstraining the mixing coefficients one converges to the correct limits and keeps the tremendous advantage of improved convergence rates that comes from the use of several orbital sets. Reducing ultimately each PCF to a single CSF with its own orbital basis leads to a non-orthogonal CI approach. Various perspectives of the new method are given.

Explorative computational study of the singlet fission process

Different ab initio methods, namely multi-reference and nonorthogonal configuration interaction techniques, are explored for their applicability in studying the singlet fission problem. It has been shown for 2-methyl-1,5-hexadiene that the 1TT state can be identified using multi-reference techniques. The geometrical and vibrational properties of the 1TT state are such that they can be approximated with those of the 5TT state. A proof of principle is given for the calculation of the singlet fission pathway driven by nuclear motion: efficient singlet fission can take place if the 1TT and S1 states are close in energy with a large non-adiabatic coupling matrix element at the S1 geometry, and the energy of the S0 state is well below that of the 1TT state at the 1TT geometry. The nonorthogonal configuration interaction method was used to treat a tetracene trimer. It has been shown that the first excited states can be interpreted as delocalised states; interaction with charge-transfer base states plays an important role. The 1TT states are localised on one pair of molecules. The electronic coupling between the diabatic S[n] and 1TT[m] states is in the meV range, confirming previous estimates. The charge-transfer base states enhance the coupling between the S[1]/S[2] and 1TT[2] excited states.

Hartree–Fock solutions as a quasidiabatic basis for nonorthogonal configuration interaction

Using the method of self-consistent field metadynamics, we locate some of the low-energy solutions to the Hartree-Fock (HF) equations on LiF and O(3). The located solutions qualitatively resemble the adiabatic electronic states in these systems. We formulate the method of nonorthogonal Configuration Interaction (CI) to interact these solutions with cubic scaling with system size and quadratic scaling with the number of solutions. The resultant solutions display the avoided crossings and, in O(3), a conical intersection expected of the adiabatic states. In LiF the relevant solutions coalesce and disappear from Unrestricted HF space indicating a more general HF theory is required.

Substituent Effects on the Vibronic Coupling for the Phenoxyl/Phenol Self-Exchange Reaction

The impact of substituents on the vibronic coupling for the phenoxyl/phenol self-exchange reaction, which occurs by a proton-coupled electron transfer mechanism, is investigated. The vibronic couplings are calculated with a grid-based nonadiabatic method and a nuclear-electronic orbital nonorthogonal configuration interaction method. The quantitative agreement between these two methods for the unsubstituted phenoxyl/phenol system and the qualitative agreement in the predicted trends for the substituted phenoxyl/phenol systems provides a level of validation for both methods. Analysis of the results indicates that electron-donating groups enhance the vibronic coupling, while electron-withdrawing groups attenuate the vibronic coupling. Thus, if all other aspects of the reaction are the same, then electron-donating groups will increase the rate, while electron-withdrawing groups will decrease the rate. Correlations between the vibronic coupling and physical properties of the phenol are also analyzed. Negative Hammett constants correspond to higher vibronic couplings, while positive Hammett constants correspond to similar or slightly lower vibronic couplings relative to the unsubstituted phenoxyl/phenol system. In addition, lower bond dissociation enthalpies, ionization potentials, and redox potentials, as well as higher pKa values, tend to correspond to higher vibronic couplings relative to the unsubstituted phenoxyl/phenol system. The observed trends enable the prediction of the impact of general substituents on the vibronic coupling, and hence the rate, for the phenoxyl/phenol self-exchange reaction. The fundamental physical insights obtained from these studies are applicable to other proton-coupled electron transfer systems.

Radiative decay from doubly to singly excited states of He via generalization of Laguerre-type orbitals: A non-orthogonal formalism

By taking full account of the non-orthogonality of the orbitals between the low-lying doubly excited states 1Po and the singly excited states 1Se and 1De of He, the corresponding radiative decay rates have been investigated theoretically via analytic generalized Laguerre-type atomic orbitals at a nearly numerical multi-configuration self-consistent field accuracy in a general non-orthogonal configuration interaction scheme. From these rates, we calculate the VUV photon emission and metastable atom spectra, and both are found to be in good qualitative agreement with recent excellent measurements. We obtain, successfully, the enhancement of the VUV photon spectrum, experimentally observed at the energy of (2s4p-4s2p)/(2p,3d) 1Po as compared with other nearby lying states. The mechanism proposed by Odling-Smee et al is verified, implying that taking appropriate account of the overlap existing between orbitals of the low-lying doubly excited and singly excited states (especially important for the compact orbitals) can reveal basic physical dominant mechanism and is crucial in understanding these spectra.

Application of valence-bond techniques to the study of weakly bound complexes. The potential energy surface of the Ne–CH4system

We present a comprehensive survey of the Molecular Orbital-Valence Bond (MO-VB) method, a theoretical scheme developed within the framework of the Valence Bond theory to deal with weakly bound intermolecular complexes. According to the MO-VB, the wavefunction of the system is expressed as a truncated non-orthogonal Configuration Interaction expansion, which is size extensive and a priori free of basis set superposition error. We report on the recent developments of the method, which extend the range of application of the MO-VB to intermolecular complexes with a quite large number of correlated electrons, showing that VB-based methods are nowadays a valid alternative to Molecular Orbital approaches also in this field. The MO-VB has been applied to study extensively the Ne-CH(4) complex, and compared with the more standard MP4 and CCSD(T) results. We determined two analytical Potential Energy Surfaces (PES) for this system, computed at MO-VB and MP4 level, which represent the first ones coming entirely from ab initio computations. The features of our potentials are discussed, and compared to the single analytical potential which includes the anisotropy available in the literature, determined about twenty years ago by Udo Buck and co-workers using a semiempirical approach [U. Buck, A. Kolhase, D. Secrest, T. Phillips, G. Scoles and F. Grein, Mol. Phys., 1985, 55, 1233]. The differences among the three PES are quite relevant, and are due to play a relevant role in the theoretical simulations of the dynamical properties of the Ne-CH(4) system.

Ni 3s-hole states in NiO by non-orthogonal configuration interaction

The origin of the features in the Ni 3s X-ray photoelectron spectrum of NiO is investigated using a non-orthogonal configuration interaction approach for an embedded [NiO 6] cluster. We study the interplay of inter-atomic screening with the metal core hole and intra-atomic exchange and electron correlation effects. We show that the spectrum can be described in terms of only few key configurations, provided that orbital relaxation effects are explicitly taken into account for the excited charge transfer configurations. The strength of this approach has been demonstrated earlier for those final states that have a high-spin coupling. In the present contribution the analysis is extended to include low-spin coupled 3s-hole states. The effects of enlarging the embedded cluster and of an improved representation of the nearest cluster surroundings were studied for the high-spin final states. We found only minor effects on the computed peak separations.

Resonating broken‐symmetry approach to biradicals and polyradicals

AbstractWe present a resonating broken‐symmetry (RBS) approach for strongly correlated electron systems. This is a nonorthogonal configuration interaction (CI) using symmetry‐broken Hartree–Fock (HF) references. We have applied it to the hydrogen molecule, linear hydrogen chain model systems, and to the fluorine molecule. As is known, spin contamination of biradical system with S = 1/2 can be removed by taking the resonance of two spin‐unrestricted HF (UHF) configurations. In contrast, more configurations were required to do spin projections perfectly in polyradical systems. The implications of the computational results are discussed in relation to the applicability of the RBS molecular orbital (MO) approach to more complex systems, such as metal clusters. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Nuclear-electronic orbital nonorthogonal configuration interaction approach

The nuclear-electronic orbital nonorthogonal configuration interaction (NEO-NOCI) approach is presented. In this framework, the hydrogen nuclei are treated quantum mechanically on the same level as the electrons, and a mixed nuclear-electronic time-independent Schrodinger equation is solved with molecular orbital techniques. For hydrogen transfer systems, the transferring hydrogen is represented by two basis function centers to allow delocalization of the nuclear wave function. In the two-state NEO-NOCI approach, the ground and excited state delocalized nuclear-electronic wave functions are expressed as linear combinations of two nonorthogonal localized nuclear-electronic wave functions obtained at the NEO-Hartree-Fock level. The advantages of the NEO-NOCI approach are the removal of the adiabatic separation between the electrons and the quantum nuclei, the computational efficiency, the potential for systematic improvement by enhancing the basis sets and number of configurations, and the applicability to a broad range of chemical systems. The tunneling splitting is determined by the energy difference between the two delocalized vibronic states. The hydrogen tunneling splittings calculated with the NEO-NOCI approach for the [He-H-He]+ model system with a range of fixed He-He distances are in excellent agreement with NEO-full CI and Fourier grid calculations. These benchmarking calculations indicate that NEO-NOCI is a promising approach for the calculation of delocalized, bilobal hydrogen wave functions and the corresponding hydrogen tunneling splittings.

Importance of interatomic hole screening in core-level spectroscopy of transition metal oxides: Mn3shole states in MnO

Ab initio theoretical results are reported to determine the role of interatomic screening of the metal core hole in Mn 3s x-ray photoelectron spectra (XPS) of MnO. We present information that finally resolves the controversy about the relative importance of intra-atomic and interatomic effects to the XPS spectra of ionic manganese compounds. We focus on the transitions to high-spin 3s core hole states, using a nonorthogonal configuration interaction method. This method allows for a balanced treatment of configurations that involve different degrees of screening of the core hole. The differences between MnO and NiO are analyzed. Although at first glance the two XPS spectra seem to have similar features, the 3s hole final states have completely different characteristics. In MnO, interatomic screening of the core hole is found to play a minor role. This is in contrast with NiO, where the inclusion of interatomic screening of the metal core hole has been shown to be crucial for a proper explanation of the Ni 3s XPS. The main reason for the difference is an essentially atomic effect, namely the smaller electron affinity of Mn as compared to Ni. We have assigned the weak feature observed in the Mn 3s XPS spectrum of MnO at around 10 eV to be a charge-transfer-type high spin satellite.

The electronic structure of NiO for Ni 3s-hole states including full orbital relaxation and localization

The electronic structure of NiO, with emphasis on the Ni 3s-hole ionic states, is studied using non-orthogonal configuration interaction, NOCI, wavefunctions for an NiO6 model of the crystal. Orbital sets are relaxed, or optimized, separately for each configuration used in the NOCI and orbital symmetry breaking, or localization, is allowed. This localization is important for configurations that involve large amounts of charge transfer from O(2p) to the Ni(3d) shell. The NOCI method insures an unbiased treatment of the relative energies of configurations that involve different degrees of charge transfer from O(2p) to Ni(3d). The use of fully relaxed orbitals is shown to be necessary to obtain accurate energies and intensities for core level ionic states observed with X-ray photoelectron spectroscopy, XPS. The NOCI energies and intensities for the lowest and first excited, high spin coupled, 3s-hole states are in good agreement with XPS spectra. Both high spin 3s-hole states are found to have significant, but partial, charge transfer character.

Bound states in screened and bare Coulomb potentials: A nonorthogonal CI-based route to effective Hamiltonians for two-electron systems

One- and two-electron bound states in screened and bare Coulomb potentials are calculated by adopting a discretized multiconfiguration generator coordinate (GC) method which leads to an iterative nonorthogonal configuration interaction procedure with the optimization of GCs. The GCs are optimized either by the method of simulated annealing or by a genetic algorithm. Critical scanning lengths for which bound states disappear in one-electron atoms are computed. A noninteracting model Hamiltonian for a two-electron atom based on the idea of screened Coulomb interaction is proposed and used for calculating electric dipole polarizability and establishing the threshold value of z for the appearance of autoionizing ground state of two-electron systems.

New basis set superposition error free ab initio MO-VB interaction potential: Molecular-dynamics simulation of water at critical and supercritical conditions

Recently, a controversy has come to light in literature regarding the structure of water in nonambient conditions. Disagreement is evident between the site–site pair correlation functions of water derived from neutron diffraction and those obtained by computer simulations which employ effective pairwise potentials to express the intermolecular interactions. In this paper the SCFMI method (self-consistent field for molecular interaction) followed by nonorthogonal CI (configuration interaction) calculations was used to determine a new water–water interaction potential, which is BSSE (basis set superposition error) free in an a priori fashion. Extensive calculations were performed on water dimer and trimer and a new parametrization of a NCC-like (Niesar–Corongiu–Clementi) potential was accomplished. This was employed in the molecular-dynamics simulation of water. The effect of temperature and density variations was examined. Acceptable agreement between site–site correlation functions derived from neutron diffraction data and from computer simulation was reached. In particular, a weakening of the hydrogen bonded structure was observed on approaching the critical point, which reproduces the experimental behavior. The simulations were performed using the MOTECC (modern techniques in computational chemistry) suite of programs. The present results show the importance of BSSE-free nonorthogonal orbitals in an accurate description of the intermolecular potential of water.

Superposition of nonorthogonal Slater determinants towards electron correlation problems

We propose variational and nonvariational methods based on the superposition of nonorthogonal Slater determinants. Properties of the reference functions are discussed. In the nonorthogonal configuration interaction method, all the excited configurations of multiple determinants are integrated into a variational space. An efficient way to manipulate matrix elements over determinants of distinct vacuums is presented by introducing similarity transformed operator and bracket transformations. The method enables us to map a matrix multiplication in the nonorthogonal problem to an orthogonal one, and thus maintains a fundamental scaling property along with the amount of data processed in the corresponding orthogonal configuration interaction method. Furthermore, we discuss a coupled-cluster theory employing a vacuum-dependent wave operator, which is entirely size consistent as well as core extensive. These methods are applied to H2O + nHe(n = 0−2) and a single-bond dissociation of the HF molecule, compared with conventional methods including full and multireference configuration interaction methods.

On the role of relaxed charge-transfer excitations: Ni 3s hole states in NiO

In this Letter a non-orthogonal configuration interaction study is presented for the high-spin coupled final states involved in the Ni 3s X-ray photoelectron spectra of NiO. Charge-transfer effects play an important role in the interpretation of this spectrum. These effects are incorporated in a conceptually attractive way by a non-orthogonal configuration interaction description, in which the wave functions are expressed as linear combinations of the reference configuration and relaxed charge-transfer configurations. The energy separation and relative intensities of the high-spin coupled final states were calculated in good agreement with experiment. Both final states have considerable charge-transfer character.

The fraternal twins of quartet O+4

Eleven stationary geometries of quartet O+4 have been studied by ab initio methods. The geometries were optimized at the complete active space self-consistent field (CASSCF) level of theory and the energies were calculated by the multiconfigurational second order pertubation method (CASPT2), using double-ζ plus polarization (DZP), triple-ζ plus double polarization (TZ2P), average atomic natural orbital (ANO) [5s4p2d] and average ANO [6s5p3d2f] basis sets. The rectangular and trans-planar structures are found to be the most stable, with an energy barrier to conversion between the two at the threshold of dissociation. Both have a delocalized hole and are stable relative to separated O2 and O+2 by 11.0 and 11.5 kcal/mol for the rectangular and the trans-planar structure, respectively, compared with the experimentally deduced energy in the range of 9.2 to 10.8 kcal/mol. The adiabatic ionization potentials of O4 and O2 are computed to be 11.67 and 12.21 eV, while experimental values are 11.66 and 12.07 eV, respectively. The vibrational frequencies have been computed for all degrees of freedom at the CASSCF level of theory. Symmetry breaking is found to be a particular problem in the computation of the antisymmetric stretch frequency for the delocalized structures at the CASSCF level of theory. Attempts to rectify these problems using the restricted active space self-consistent field (RASSCF) method leads to additional difficulties, but further analysis yields insight into the symmetry breaking and problems with earlier calculations. Finally, a nonorthogonal configuration interaction (CI) calculation based on the interaction of localized CASSCF wave functions using the complete active space state interation (CASSI) method leads to a balanced treatment of the antisymmetric stretch which is free from symmetry breaking. The study explains the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of O+4 isolated in solid neon as the antisymmetric OO stretch, and the combination band of the symmetric and antisymmetric OO stretch of both the rectangular and trans-planar structures.

Cluster calculations on localized holes in La 2CuO 4

The electronic structure of [CuO 2] 2− sheets, as occur in La 2CuO 4, is studied by ab initio non-orthogonal configuration interaction (NOCI) calculations on the small copper-oxide clusters CuO 4 and Cu 2O 7. In the NOCI approach the wave function is obtained from CI calculations between relaxed Hartree-Fock states. With this approach important local relaxation effects, as well as charge transfer interactions can be taken into account. The cluster ground states can be characterized by Cu(d 9) O(p 6). States with one extrinsic hole have predominant Cu(d 9) O(p 5) character with admixture of Cu(d 8) O(p 6). This admixture is especially important for states with the extrinsic hole mainly in O( p σ ).

Interactions of Excited Lithium Atom with Molecular Hydrogen. III. Orthogonality Constrained MCSCF+NCI Calculations of Potential Energy Surfaces and Electronic Wave Functions in the Potential Crossing Region

Abstract A method of calculating the excited state MCSCF electronic wave function by constraining it to be orthogonal to the predetermined ground state wave function was applied to calculate wave functions of the Li–H2 system near the center of a conical intersection of the lowest two potential energy surfaces. Combined with an additional nonorthogonal configuration interaction process, it has proved to be an efficient method to get systems of wave functions that are continuous throughout whole geometries. Qualitative characters of wave functions near the center of potential crossing previously inferred have been reconfirmed.