Full Optimized Reaction Space Research Articles

A cautionary tale: Problems in the valence-CASSCF description of the ground state (X1Σ+) of BF.

In the full optimized reaction space and valence-complete active space self-consistent field (vCAS) methods, a set of active orbitals is defined as the union of the valence orbitals on the atoms, all possible configurations involving the active orbitals are generated, and the orbitals and configuration coefficients are self-consistently optimized. Such wave functions have tremendous flexibility, which makes these methods incredibly powerful but can also lead to inconsistencies in the description of the electronic structure of molecules. In this paper, the problems that can arise in vCAS calculations are illustrated by calculations on the BH and BF molecules. BH is well described by the full vCAS wave function, which accounts for molecular dissociation and 2s-2p near-degeneracy in the boron atom. The same is not true for the full vCAS wave function for BF. There is mixing of core and active orbitals at short internuclear distances and swapping of core and active orbitals at large internuclear distances. In addition, the virtual 2π orbitals, which were included in the active space to account for the 2s-2p near degeneracy effect, are used instead to describe radial correlation of the electrons in the F2pπ-like pairs. Although the above changes lead to lower vCAS energies, they lead to higher vCAS+1+2 energies as well as irregularities and/or discontinuities in the potential energy curves. All of the above problems can be addressed by using the spin-coupled generalized valence bond-inspired vCAS wave function for BF, which includes only a subset of the atomic valence orbitals in the active space.

Tribute to Klaus Ruedenberg

“I am indebted to my father for living, but to my teacher for living well said Alexander the Great, the King of Greek Macedonia, about his teacher, the philosopher Aristotle. This statement echoes the widely held belief of the students, research associates, collaborators and admirers of Klaus Ruedenberg regarding his invaluable contribution towards shaping their scientific lives. This special issue of the Journal of Physical Chemistry presents a tribute to Professor Klaus Ruedenberg, on the occasion of his 90th birthday, for his numerous scientific contributions to the field of quantum chemistry. The many outstanding papers that are part of this issue document his seminal contributions to a broad range of quantum chemistry, including the evaluation of electron repulsion integrals, the free-electron network model for conjugated molecules, the origin of covalent bonding, including the central role of the kinetic energy in the covalent bond, and the intrinsic identification of chemical bonding patterns in molecular systems, orbital localization that has enabled a deep understanding of many chemical phenomena, the multi-configurational self-consistent field method and the concept of the Full Optimized Reaction Space (FORS) to study chemical rearrangements and its application to the study of global potential energy surfaces and conical intersections, themore » first construction of systematic, eventempered sequences of orbital sets that approach the complete basis set limit, and the novel simultaneous extrapolation of basis set and level of theory to achieve nearly exact molecular energies and vibrational spectra. In addition, as past students and research associates of Klaus Ruedenberg, that is people whose scientific and personal lives have been critically affected by a great teacher, we wish to point out a less well-known aspect of his professional career, that of an educator. Professor Klaus Ruedenberg has a passion for communicating scientific ideas and educating students, whether they were at the undergraduate, graduate or post-graduate levels or whether they were visitors to his laboratory. No matter how much of his time it took, there were never any shortcuts or excuses, but also no pressure on the students. Knowledge was just there waiting to be gained - for free - by just mining a vast repository of mathematical, physical and chemical concepts. It is not hyperbole to stress his contribution in molding the scientific lives and in turn the personal success of so many people who have had the privilege to learn from him.« less

ChemInform Abstract: The Ring Opening of Cyclopropylidene to Allene and the Isomerization of Allene. Ab initio Interpretation of the Electronic Rearrangements in Terms of Quasi-Atomic Orbitals.

A full optimized reaction space (FORS) remains invariant under arbitrary orthogonal transformations among its configuration-generating molecular orbitals. Localization of the latter for a FORS wavefunction yields molecular orbitals withquasi-atomic character which can be interpreted asmolecule-adapted minimal-basis-set atomic orbitals. In terms of these quasi-atomic FORS MOs, the configuration mixing in the FORS wavefunction, the representation of the density matrix, and the expansions of the natural orbitals provide information about the interactions that are responsible for the molecular energy changes. A basis-set-independent population analysis can be formulated which accomplishes the objectives of Mulliken's population analysis without the drawbacks stemming from the basis-set dependence of the latter. Through application of these procedures, explanations can be found for various features of the potential energy surface governing the ring opening of cyclopropylidene and the isomerization of allene.

Björn O. Roos (1937-2010)

Björn O. Roos (1937-2010)

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.

A systematic multireference perturbation-theory study of the low-lying states of SiC3

The three known lowest-energy isomers of SiC(3), two cyclic singlets (2s and 3s) and a linear triplet (1t), have been reinvestigated using multireference second-order perturbation theory (MRPT2). The dependence of the relative energies of the isomers upon the quality of the basis sets and the sizes of the reference active spaces is explored. When using a complete-active-space self-consistent-field reference wave function with 12 electrons in 11 orbitals [CASSCF (12, 11)] together with basis sets that increase in size up to the correlation-consistent polarized core-valence quadruple zeta basis set (cc-pCVQZ), the MRPT2 method consistently predicts the linear triplet to be the most stable isomer. A new parallel direct determinant MRPT2 code has been used to systematically explore reference spaces that vary in size from CASSCF (8,8) to full optimized reaction space [FORS or CASSCF (16,16)] with the cc-pCVQZ basis. It is found that the relative energies of the isomers change substantially as the active space is increased. At the best level of theory, MRPT2 with a full valence FORS reference, the 2s isomer is predicted to be more stable than 3s and 1t by 4.7 and 2.2 kcal/mol, respectively.

Franck–Condon effects in low-energy states of C 10H 8+ radical. : Ab initio MCSCF study of absorption and resonance Raman spectra

The Franck–Condon (FC) effects in the low-energy states of the C 10H 8 + radical are investigated in terms of ab initio FORS (full optimized reaction space) and SDE (single and double excitations) MCSCF calculational scheme applied with Dunning's double-zeta (DZV) basis set. This scheme is used to determine the excitation energies, the transition dipole moments and displacement (Franck–Condon) parameters for the three low-energy dipole-allowed 1 2 A u (D 0)→ 1 2 B 3 g (D 2), 1 2 A u (D 0)→ 1 2 B 1 g (D 3) and 1 2 A u (D 0)→ 2 2 B 1 g (D 4) transitions. The results of FORS MCSCF computations are compared to the QCFF/PI+CI and ROHF/3-21G results reported most recently for the C 10H 8 + radical. The resonance Raman (RR) spectra available in the region corresponding to the lowest-energy dipole-allowed 1 2 A u (D 0)→ 1 2 B 3 g (D 2) transition are discussed in some detail in the non-empirical fashion.

Full-Optimized Reaction Space MCSCF+MP2 Study on Reactions of Diradical Systems: o-C6H4(CH)2, o-C6H4CHN, and o-C6H4N2

Thermal reactivity of the ortho isomers of the titled compounds has been investigated by using the full-optimized reaction space multiconfiguration self-consistent field (MCSCF) method with the STO-3G and 6-31G(d) basis sets, followed by multireference second-order Moller−Plesset perturbation calculation (MCSCF+MP2). The MCSCF+MP2 calculations lead to the prediction that all the ortho isomers have a singlet ground state but the lowest triplet state lies above the singlet ground state by less than 3 kcal/mol. Fortunately, since the spin−orbit coupling between the two states of interest is small and the singlet ground state is more likely to be produced in the photolysis, the thermal behavior of the isomers has been analyzed on the singlet energy surface. In o-phenylenebis(methylene), the E,E stereoisomer undergoes ring-closure reaction with no energy barrier to give a bicyclic compound, while the Z,Z isomer exhibits a situation of competition between the ring-opening reaction and the CH inversion followed by the ring-closure reaction. In (o-nitrenophenyl)methylene, the E isomer exhibits a competitive feature between the ring-opening and ring-closure reactions, whereas the Z isomer reacts into a linear compound with no energy barrier. In o-phenylenebis(nitrene), a spontaneous ring-opening reaction takes place definitely with the formation of a linear compound. These calculated results are in good agreement with the available experimental evidences.

Quantum field theoretical methods in chemically bonded systems. V. Potential energy curves for N2(X1?g+) ? 2N (4S)

Many-body perturbation theory is applied to the nitrogen triple bond for bond distances ranging from the atomic regime to about 0.6a0 shorter than equilibrium. A full-optimized reaction space model is used to compute orbital spaces with an even-tempered gaussian-type basis set and also with a nominal Bagus–Gilbert Slater-type basis set. Conservation of orbital angular momentum in the atomic regime leads to perturbative theory for Hartree–Fock plus proper dissociation. Angular momentum conservation can also be enforced with a scaled Slater–Condon parameter. Third-order dissociation energies and spectroscopic constants approach limits of the chosen basis sets. © 1993 John Wiley & Sons, Inc.

MCSCF/6-31G(d,p) calculations of one-electron spin-orbit coupling constants in diatomic molecules

The effective nuclear charges, which are empirical parameters in the approximate spin-orbit Hamiltonian, are determined for the first- and second-row elements in the periodic table using the experimental results of the fine structure splittings in the doublet and triplet Π states of AH molecules (A is an atom in the first or second row). All calculations are performed using the full optimized reaction space multiconfiguration self-consistent-field wave functions with the 6-31G(d,p) basis set

The ring opening of cyclopropylidene to allene and the isomerization of allene:ab initio interpretation of the electronic rearrangements in terms of quasi-atomic orbitals

A full optimized reaction space (FORS) remains invariant under arbitrary orthogonal transformations among its configuration-generating molecular orbitals. Localization of the latter for a FORS wavefunction yields molecular orbitals withquasi-atomic character which can be interpreted asmolecule-adapted minimal-basis-set atomic orbitals. In terms of these quasi-atomic FORS MOs, the configuration mixing in the FORS wavefunction, the representation of the density matrix, and the expansions of the natural orbitals provide information about the interactions that are responsible for the molecular energy changes. A basis-set-independent population analysis can be formulated which accomplishes the objectives of Mulliken's population analysis without the drawbacks stemming from the basis-set dependence of the latter. Through application of these procedures, explanations can be found for various features of the potential energy surface governing the ring opening of cyclopropylidene and the isomerization of allene.

Chemical binding and electron correlation in diatomic molecules as described by the FORS model and the FORS-IACC model

Using the model of the Full Optimized Reaction Space including the Intra-Atomic Correlation Correction, binding energies and other electronic properties have been calculated for several states of a number of diatomic molecules. In most cases this theoretical approach yields results agreeing with experimental values to within 0.2 eV. The investigation covers the molecules BH, CH, NH, OH, FH, N2, O2, F2.

Are atoms sic to molecular electronic wavefunctions? II. Analysis of fors orbitals

Electronic wavefunctions that describe molecules in the full optimized reaction space (FORS) are multiconfigurational wavefunctions which are invariant under non-singular linear transformations of the occupied molecular orbitals. They offer therefore a considerably wider scope for orbital interpretations than the single-configuration Hartree-Fock approximation. For example they can be analyzed in terms of natural MOs and in terms of localized MOs. The latter turn out to be remarkably atomic in character and a new localization procedure can be formulated which yields atom-adapted molecular orbitals. These have the character of minimal-basis-set AOs that are optimally adapted to the molecular environment and furnish an unambigious atomic population analysis. On the other hand, chemically adapted molecular orbitals can be defined by an appropriate compromise between natural orbitals and localized orbitals. The freedom to use, as configuration-generating molecular orbitals, atom-adapted FORS MOs as well as chemically adapted FORS MOs makes FORS wavefunctions particularly suitable for chemical interpretations. The ensuing analysis establishes the minimal basis set (in molecule-adapted form) as a theoretically sound concept for the understanding of accurate molecular wavefunctions. An illustrative example is discussed.

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model

The model of the full optimized reaction space describes the electronic structure of a molecule in terms of the best wave-function that can be obtained as a superposition of all those configurations which are generate possible occupancies and couplings from a “formal minimal basis” of valence, orbitals on the constituent atoms. These configurations span a “full reaction space”, and MC SCF optimization of the orbitals in terms of an extended set of quantitative basis orbitals determines the full optimized reaction space (FORS). Basic justifications, methodological specifics and sample applications are discussed.

The sudden polarization effect: MC-SCF calculations on planar and 90.degree. twisted methylenecyclopropene

Ab initio MC-SCF molecular orbitals are reported for electronic ground and excited states of planar and 90/sup 0/ twisted methylenecyclopropene within the framework of a four ..pi..-orbital FORS (full optimized reaction space) model. For planar methylenecyclopropene, individual state MC-SCF results include: ground state dipole moment, 1.33 D, and excitation energies, 3.32 eV (/sup 3/B/sub 2/), 4.71 eV (/sup 1/B/sub 2/), 4.87 eV (/sup 3/A/sub 1/), and 9.36 eV (2/sup 1/A/sub 1/). The SCF first ionization potential is 8.1 eV. Calculations for the 90/sup 0/ twisted species at a MNDO optimized geometry for the lowest diradical state (/sup 1/D/sub 1/) yield states having diradical (D) or pronounced zwitterionic (Z) character. Variational MC-SCF results are (excitation energy, dipole moment): /sup 1/A/sub 2/ (/sup 1/D/sub 1/) 0.0 eV, 0.67 D; /sup 3/A/sub 2/ (/sup 3/D/sub 1/) -0.06 eV, 0.65 D; /sup 3/B/sub 1/ (/sup 3/D/sub 2/) 0.53 eV, -0.96 D; 1/sup 1/A/sub 1/ (/sup 1/Z/sub 1/) 0.59 eV, 5.34 D; /sup 1/B/sub 1/ (/sup 1/D/sub 2/) 0.65 eV, -0.94 D. CI results for the second zwitterionic state 2/sup 1/A/sub 1/ (/sup 1/Z/sub 2/) are 7.58 eV and -5.83 D. These calculated properties, especially for the case of the twisted species, are highly sensitivemore » to the method of calculation. CI calculations using ground state (/sup 1/D/sub 1/) orbitals led to significantly exaggerated dipole moments and state energies. 3 figures, 5 tables.« less