The radical character of the acenes: a density matrix renormalization group study

We present a detailed investigation of the acene series using high-level wave function theory. Our ab initio density matrix renormalization group algorithm has enabled us to carry out complete active space calculations on the acenes from napthalene to dodecacene correlating the full pi-valence space. While we find that the ground state is a singlet for all chain lengths, examination of several measures of radical character, including the natural orbitals, effective number of unpaired electrons, and various correlation functions, suggests that the longer acene ground states are polyradical in nature.     

The Antiferromagnetic Spin Coupling in Non‐Kekulé Acenes—Impressive Polyradical Character Revealed by High‐Level Multireference Methods

Complete active space (CASSCF) and multireference (MR‐CISD(Q) and MR‐AQCC) calculations were performed for non‐Kekulé analogues of acenes, dimethylenepolycyclobutadienes, with lengths of up to eight cyclobutadiene (CBD) units. Multireference calculations predict that the most stable energy state of the system is either triplet (if there is an odd number of CBD units) or singlet (if there is an even number of CBD units) due to antiferromagnetic spin coupling, which thus violates Hund's rule in larger molecules. We also show an impressive polyradical character in the system that increases with the size of the molecule, as witnessed by more than eleven unpaired electrons in the singlet state of the molecule with eight CBD units. Together with the small energy gap between singlet and higher multiplicity energy states even above the triplet state, this demonstrates the exceptional polyradical properties of these π‐conjugated oligomeric chains.     

完全活性空间组态相互作用能量的拟合和外推

完全活性空间组态相互作用计算与完全活性空间中的活性电子数和活性轨道数有关,但完全活性空间组态相互作用的能量不是活性电子数和活性轨道数的单调递减函数,因此活性轨道数和活性电子数不能用来外推完全活性空间组态相互作用的能量。为此,我们定义了一个新的变量:活性空间中的最大未占满轨道数。我们对一系列单重态、双重态和三重态分子进行了完全活性空间组态相互作用的计算,并利用活性空间中的活性电子数和最大未占满轨道数这两个变量,对这些基态能量进行了拟合和外推,拟合的均方根误差都在10~(-6)数量级。外推能量的精度优于MP4,对小分子体系,其精度高于CCSD。外推的完全的组态相互作用(FCI)能量值和实际计算的FCI值也很接近。另外,我们还利用外推能量来优化双原子分子的平衡键长,并计算谐振频率,其精度优于CASSCF。     

Oligoacenes: theoretical prediction of open-shell singlet diradical ground states

A series of oligoacenes from benzene to decacene were studied computationally with DFT and CASSCF methods. In contrast to the common view that acenes are closed-shell systems or may have a triplet ground state, these results offer the first theoretical predictions for the singlet ground state and diradical character for oligoacenes. The nature of the ground states of these molecules arises from the disjoint nature of the NBMOs that are singly occupied in the diradical.     

Kekulé versus Lewis: When Aromaticity Prevents Electron Pairing and Imposes Polyradical Character

Some conjugated alternant hydrocarbons, of singlet ground state according to Ovchinnikov’s rule, may exhibit strong polyradical character, despite admitting complete pairing of electrons in bond orbitals between adjacent atoms. Typical organizations of this kind are encountered in polycyclic frames supporting two or more extracyclic methylene groups. Lewis bond pairing would require quinonization of six‐membered rings, whereas safeguarding aromaticity proves sufficient to impose ground‐state open‐shell character, that is, the existence of unpaired electrons, providing the number of benzene rings to be quinonized is larger than two. Several examples built as variations around para‐polyphenylene frames are examined through unrestricted DFT (UDFT) calculations, using various methods for spin decontamination of wavefunctions, geometries, and singlet–triplet energy gaps. They all illustrate how it is possible to conceive architectures that can be written with a closed‐shell bond pairing, although they exhibit a large number of unpaired electrons. The same analyses also apply to systems in which quinonization would not kill but only reduce the number of unpaired electrons.     

A theoretical study of the lowest-energy singlet and triplet electronic states p-iminophosphaalkyne and nitrilimine

The equilibrium geometries and fundamental vibrational frequencies of the two energetically lowest-lying electronic states of p-iminophosphaalkyne (HCPNH) and nitrilimine (HCNNH) were determined using a split-valence basis set with polarization functions on the heavy atoms. The most extensively correlated functions used in the geometry optimizations were of the Complete Active Space Self-Consistent Field (CASSCF) variety and included eight electrons distributed among seven active orbitals for HCPNH and six active orbitals for HCNNH. The effects on predicted geometry of the size of the CASSCF active space were investigated for HCPNH and are reported. Multi-Reference Configuration Interaction with Single and Double excitations calculations have been performed at the equilibrium geometries using larger basis sets to determine more accurately the relative energetics of the electronic states. It was found that nitrilimine has the expected singlet ground state, with the triplet lying 38.5 kcal mol⁻¹ higher in energy; however, p-iminophosphaalkyne has a triplet ground state, lying 9.7 kcal mol⁻¹ below the singlet.     

Low-lying excited states of C120 and C151: a multireference perturbation theory study

Excited states of two 7-aminocoumarin derivatives, coumarin 120 (7-amino-4-methylcoumarin) and coumarin 151 (7-amino-4-trifluoromethylcoumarin), were investigated using generalized multiconfigurational quasidegenerate perturbation theory (GMC-QDPT), multiconfigurational quasidegenerate perturbation theory (MC-QDPT) and time-dependent density functional theory (TDDFT) with the B3LYP and CAM-B3LYP functionals. The absorption and fluorescence spectra of C120 and C151 were calculated. We elucidated the characters of the low-lying states of C120 and C151. The absorption spectra calculated with GMC-QDPT and TDDFT B3LYP agreed well with the experimental data, while for the fluorescence spectra, the TDDFT calculations overestimated the fluorescence spectra compared to GMC-QDPT calculations. Utilizing active spaces with large numbers of electrons and orbitals for reference functions, GMC-QDPT showed a better performance than MC-QDPT with a complete active space self-consistent field (CASSCF) reference of active space with smaller number of electrons and orbitals. In our gas phase calculation, we found that the optimized structures for the first excited states have a planar amino group with a CN single bond, while the amino group is pyramidal in the ground state.     

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.     

Molecular mechanics-valence bond method for planar conjugated hydrocarbon cations

We present an extension of the molecular mechanics-valence bond (MMVB) hybrid method to study ground and excited states of planar conjugated hydrocarbon cations. Currently, accurate excited state calculations on these systems are limited to expensive ab initio studies of smaller systems: up to 15 active electrons in 16 pi orbitals with complete active space self-consistent field (CASSCF) theory using high symmetry. The new MMVB extension provides a faster, cheaper treatment to investigate larger cation systems with more than 24 active orbitals. Extension requires both new matrix elements and new parameters: In this paper we present both, for the limited planar case. The scheme is tested for the planar radical cations of benzene, naphthalene, anthracene, and phenanthrene. Calculated MMVB relative energies are in good agreement with CASSCF results for equilibrium geometries on the ground and first excited states, and conical intersections.     

Very-low-lying electronic states result from n --> pi excitations in open-shell annulenes, annelated with alpha-dicarbonyl groups

UB3LYP/6-31G* calculations find that alpha-dicarbonyl-annelated cyclopentadienyl radical 1 has a sigma ground state, which is formed by excitation of an electron from the in-phase combination of carbonyl lone-pair orbitals into the singly occupied pi orbital. Similarly, tetrakis-annelated cyclooctatetraene 3 is calculated to have very-low-lying singlet and triplet excited states, which result from excitations of electrons from the b1g combination of lone pair orbitals into the empty pi nonbonding MO of the COT ring.     

Theoretical calculation about the valence and Rydberg excited states of hydrogen cyanide

The singlet and triplet excited states of hydrogen cyanide have been computed by using the complete active space self-consistent field and completed active space second order perturbation methods with the atomic natural orbital (ANO-L) basis set. Through calculations of vertical excitation energies, we have probed the transitions from ground state to valence excited states, and further extensions to the Rydberg states are achieved by adding 1s1p1d Rydberg orbitals into the ANO-L basis set. Four singlet and nine triplet excited states have been optimized. The computed adiabatic energies and the vertical transition energies agree well with the available experimental data and the inconsistencies with the available theoretical reports are discussed in detail.     

Ab initio calculations of triplet excited states and potential-energy surfaces of vinyl chloride: insights into spectroscopy and photodissociation dynamics

The equilibrium geometries and harmonic vibrational frequencies of three low-lying triplet excited states of vinyl chloride have been calculated using the state-averaged complete active space self-consistent field (CASSCF) method with the 6-311++G(d,p) basis set and an active space of four electrons distributed in 13 orbitals. Both adiabatic and vertical excitation energies have been obtained using the state-averaged CASSCF and the multireference configuration-interaction methods. The potential-energy surfaces of six low-lying singlet states have also been calculated. While the 3(pi, pi*) state has a nonplanar equilibrium structure, the 3(pi, 3s) and 3(pi, sigma*) states are planar. The calculated vertical excitation energy of the 3(pi, pi*) state is in agreement with the experiment. The singlet excited states are found to be multiconfigurational, in particular, the first excited state is of (pi, 3s) character at the planar equilibrium structure, of (pi, sigma*) as the C-Cl bond elongates, and of (pi, pi*) for highly twisted geometries. Avoided crossings are observed between the potential-energy surfaces of the first three singlet excited states. The absorption spectra of vinyl chloride at 5.5-6.5 eV can be unambiguously assigned to the transitions from the ground state to the first singlet excited state. The dissociation of Cl atoms following 193-nm excitation is concluded to take place via two pathways: one is through (pi, sigma*) at planar or nearly planar structures leading to fast Cl atoms and the other through (pi, pi*) at twisted geometries from which internal conversion to the ground state and subsequent dissociation produces slow Cl atoms.     

On the stability of Be3: a benchmark complete active space self-consistent field + averaged quadratic coupled cluster study

The optimized geometries and binding energies for the linear and triangular isomers of the beryllium trimer have been obtained through benchmark multireference averaged quadratic coupled cluster (AQCC) calculations using very large complete active space SCF (CASSCF) references (12 active electrons in 13 and 14 orbitals). Geometries were optimized with the cc-pV5Z basis, while the binding energies (including counterpoise correction) were obtained with the significantly larger aug-cc-pV5Z basis set. The binding energies (27.3 and 16.3 kcal/mol for the equilateral and linear isomers, respectively) are larger than the previous full CI benchmark values, while the corresponding Be-Be equilibrium distances of 4.101 and 4.088 a.u. are smaller. In view of the near-size consistency character of the CASSCF + AQCC method, the fact that all 12 electrons are fully correlated, the active reference space includes 14 orbitals, and the very large basis set used here, we propose to consider these results as reference data for Be(3). Using the electron pair localization function obtained at the CASSCF(12,15) level, it is clearly illustrated that the 2p orbitals lying in the molecular plane play a dominant role in the bonding pattern for the equilateral isomer.     

Theoretical study of the vertical electronic spectrum of O2: Mixing of valence and Rydberg states

All-valence-electron CM calculations are reported for a large number of electronic states of O₂ at the ground state equilibrium bond length. The configuration subspaces considered include all single and double excitations with respect to a series of the most important terms in the expansion of each state. The importance of the choice of such reference configurations as well as of the use of approximate natural orbitals in these calculations is discussed Mixing at Rydberg and valence states is observed in numerous cases and the significance of this phenomenon in the interpretation of the electrons spectrum of this system is considered.     

A Peri‐tetracene Diradicaloid: Synthesis and Properties

Peri‐acenes are good model compounds for zigzag graphene nanoribbons, but their synthesis is extremely challenging owing to their intrinsic open‐shell diradical character. Now, the successful synthesis and isolation of a stable peri‐tetracene derivative PT‐2ClPh is reported; four 2,6‐dichlorophenyl groups are attached onto the most reactive sites along the zigzag edges. The structure was confirmed by X‐ray crystallographic analysis and its electronic properties were systematically investigated by both experiments and theoretical calculations. It exhibits an open‐shell singlet ground state with a moderate diradical character (y₀=51.5 % by calculation) and a small singlet–triplet gap (ΔE_S‐T=?2.5 kcal mol^?1 by SQUID measurement). It displays global aromatic character, which is different from the smaller‐size bisanthene analogue BA‐CF3 .     

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.     

Bonding and structure of copper nitrenes

Copper nitrenes are of interest as intermediates in the catalytic aziridination of olefins and the amination of C-H bonds. However, despite advances in the isolation and study of late-transition-metal multiply bonded complexes, a bona fide structurally characterized example of a terminal copper nitrene has, to our knowledge, not been reported. In anticipation of such a report, terminal copper nitrenes are studied from a computational perspective. The nitrene complexes studied here are of the form (beta-diketiminate)Cu(NPh). Density functional theory (DFT), complete active space self-consistent-field (CASSCF) electronic structure techniques, and hybrid quantum mechanical/molecular mechanical (QM/MM) methods are employed to study such species. While DFT methods indicate that a triplet (S = 1) is the ground state, CASSCF calculations indicate that a singlet (S = 0) is the ground state, with only a small energy gap between the singlet and triplet. Moreover, the ground-state (open-shell) singlet copper nitrene is found to be highly multiconfigurational (i.e., biradical) and to possess a bent geometry about the nitrene nitrogen, contrasting with the linear nitrene geometry of the triplet copper nitrenes. CASSCF calculations also reveal the existence of a closed-shell singlet state with some degree of multiple bonding character for the copper-nitrene bond.     

Ab initio CI calculations on benzene with an extended basis set

An extended basis set of triple zeta plus polarization quality is employed to carry out configuration interaction (CI ) calculations of the three lowest singlet and triplet excited states of benzene. The CI calculation is carried out by taking into account single and double excitations of π and σ electrons. In the CI , composite natural orbitals (CNO s), which are constructed from the natural orbitals of the ground state of ethylene, are used as virtual orbitals. The aim of using CNOs is to reduce the number of virtual orbitals to be used in constructing configuration-state functions, thus cutting down CI dimensions without losing reasonable accuracy. The excitation energies resulting from the CI are in fairly good agreement with experiment. The root mean square of the deviation is 0.22 eV for the six calculated energies and the largest disagreement is 0.37 eV for the third singlet excited state. To obtain better excitation energies by an ab initio calculation, it seems likely that we need to take into account more electron correlation than in the present calculation. © 1994 John Wiley & Sons, Inc.     

Numerical MC SCF and CI calculations of the ground-state potential energy curve of N2

The numerical procedure of McCullough is used in calculations of Hartree-Fock and MC SCF wavefunctions for ground state of N₂. The latter are derived using the complete set of 18 spin and symmetry adapted configurations in the space of MOs that arise from 2p atomic orbitals. An increase in dissociation energy of 0.17 eV is observed when compared to MC SCF calculations in a large basis of Slater-type functions and the same set of configurations. Integrals involving the numerical MC SCF MOs are used in CI calculations in which substitutions involving the 1s and 2s electrons are included. The increase in dissociation energy due to numerical versus basis set valence CI is 0.08 eV. Spectroscopic constants and molecular quadrupole moments are reported.