The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

Density Functional Characterization of the Electronic Structure and Visible‐Light Absorption of Cr‐Doped Anatase TiO2

To evaluate the electronic and optical properties of Cr‐doped anatase TiO₂, three possible Cr‐doped TiO₂ models, including Cr at a Ti site (model I), Cr at a Ti site with an oxygen vacancy compensation (model II), and an interstitial Cr site (model III), are studied by means of first principles density functional theory calculations. In model I, the splitting behavior of the Cr 3d states and the insulating properties are successfully depicted by the GGA+U method, from which it is proposed that Cr at a Ti site should exist as Cr⁴⁺ instead of the generally believed Cr³⁺. As a result, the electron transitions between these impurity states, the conduction band (CB), and the valence band (VB), as well as the d–d transitions between occupied and unoccupied Cr 3d states, provide a reasonable explanation for the experimentally observed major and minor absorption bands. In models II and III, the impurity states and associated optical transition processes—as well as the corresponding electron configurations—are examined.     

Bifurcations on potential energy surfaces of organic reactions

A single transition state may lead to multiple intermediates or products if there is a post-transition-state reaction pathway bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy minimum. For such systems, the shape of the potential energy surface and dynamic effects, rather than transition-state energetics, control selectivity. This Minireview covers recent investigations of organic reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect experimental observables such as kinetic isotope effects and product distributions.     

Pericyclic and Heteroelectrocyclic Mechanisms for the Cyclization of 1,3,5-Hexatrien-1-one and Its 6-Aza Analog

The cyclization of 1,3,5-hexatrien-1-one, 1, and the Z- and E-isomers of 1-aza-1,3-butadienylketene 3 were studied using the semiempirical AM1 and PM3 methods. Cyclizations of compounds 1 and Z-3 are shown to occur via a mono-rotation mechanism with barriers of 15.49 and 32.85 kcal/mol respectively. The reactions proceed via non-planar transition states which result from rotation of the methylene group for compound 1 and the imino group for compound Z-3. Cyclization of E-3 proceeds via a non-rotatory mechanism through a planar transition state. The activation barrier is 4.83 kcal/mol (AM1). The electronic structures of the initial and final states, and of some intermediate structures, including the transition states for the cyclization of compounds 1 and 3, were analyzed by the natural orbital method using HF/6-31G*//AM1 calculations. Energetic, structural, and orbital criteria indicate the heteroelectric mechanism for the cyclization of compound E-3 and the pericyclic mechanism for the cyclization of compounds 1 and Z-3.     

Random-walk theory for localization

A continuous-time random-walk theory has been developed for Anderson localization. On a continuous time scale random walks are performed along extended (i.e., propagating) and localized (i.e., trap) states. Complete information of disorder is contained in a distribution function called “hopping time distribution function” ψ_nm(t), which gives the probability per unit time for transition from state m to state n in time t. The “stay-put” probability ??(t = ∞), which is the probability to rediscover an excitation at a site “0” at time t = ∞ if it was there at t = 0, is obtained in terms of ψ_nm(t). Appropriate forms for ψ_nm(t) are constructed which are in conformity with the photoconductivity experiments on dispersive transport, and ??(∞) are calculated. The results indicate that the entire spectrum consists of three regimes, namely, those of (i) “diffusion,” (ii) “weak diffusion,” and (iii) “no diffusion,” which, respectively, designate the extension, the power-law localization, and the exponential localization of states. The results also shed light on the question of “continuous or discontinuous (?)” transition across the mobility edge.     

The origin of energy functional in Roothaan open shell SCF theory

Different methods of averaging of energy over the states of electronic configurations γ^N (n_γ = 1, 2, 3 and N = 1, 2, …, 2n_γ ? 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t^N (N = 2–4) and e² there exist states for which VCC are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such “non-Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.     

Exploring the potential energy hypersurface of histamine monocation: Tautomerism in gas phase

The potential energy hypersurface of the histamine monocation is determined by ab initio methods at the STO -4G level using analytical gradient techniques. Three transition states and two minima have been found for the N_τ? H tautomer. One of the transition states connects the trans conformational region with a minimum gauche structure, where the proton of the ammonium group is approximately halfway between the N_π of the imidazole group and the N of the ammonium group, but nearer to the N_π. This minimum connects the potential energy surface of the N_τ? H tautomer with the imidazolium one. In the latter region, three transition states and two minima have been found. Critical points are discussed in relation with experimental data and histamine H₂ receptor models.     

STEREOELECTRONIC PROPERTIES OF PHOTOSYNTHETIC AND RELATED SYSTEMS — V. AB INITIO CONFIGURATION INTERACTION CALCULATIONS ON THE GROUND AND LOWER EXCITED SINGLET AND TRIPLET STATES OF ETHYL CHLOROPHYLLIDE a AND ETHYL PHEOPHORBIDE a

Abstract— Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying excited singlet and triplet states of ethyl pheophorbide a (Et-Pheo a) and ethyl chlorophyllide a (Et-Chl a), and are employed in an analysis of the electronic absorption spectra of these systems. In both molecules the visible spectrum is found to consist of transitions to the two lowest-lying ¹(π, π*) states, S₁ and S₂. The configurational compositions of S₁ and S₂ in both molecules are similar, and are described qualitatively in terms of a four-orbital model. The S₁← S₀ transition in each case is predicted to be intense, and is largely in-plane y-polarized, while the S₂← S₀ transition is predicted to be extremely weak and in-plane polarized. The orientation of the S₂← S₀ transition dipole is not conclusively established in the present calculations. The Soret band in both molecules is composed of transitions to no less than ten states (S_3-S₁₂ in Et-Chl a and S₃-S₇S₉-S₁₂. and S₁₄ in Et-Pheo a), which exhibit primarily (π, π*) character. The configurational compositions of these states are generally a complex mixture of excitations from both occupied macrocyclic π molecular orbitals and occupied orbitals with electron density in the cyclopen-tanone ring and the carbomethoxy chain. No clear correspondences are evident between respective Soret states of the two systems. Transitions to these states are generally intense and display a variety of in-plane polarizations. Two additional Soret states of Et-Pheo a, S₈ and S₁₃, exhibit primarily (n. π*) character. S₈ is characterized by excitations from u and non-bonding regions of the carbomethoxy chain, while S₁₃ is described by n →π* excitations involving the nitrogen atom of ring II. No corresponding (n, π*) states were found for Et-Chl a. In both molecules the lowest two triplet states, T₁ and T₂, are found to lie lower in energy than S₁. while T, and S₁ are approximately degenerate. The configurational compositions of T₁-T₄ of both molecules are nearly identical, and may be described by a four-orbital model. However, the compositions of T₁-T₄ differ sharply from those of S₁ and S₂. A number of higher-lying ³(π, π*) states of both molecules (T₅-T₁₃ in Et-Chi a and T₈-T₉, T₁₁-T₁₃ in Et-Pheo a) are found to have energies similar to the singlet Soret states, relative to S₀. They are characterized by a complex mixture of configurations which do not include significant contributions involving the four-orbital model. In addition, two ³(n, π*) states of Et-Pheo a, T₁₀ and T₁₄, are found, which are somewhat analogous to S₈ and S₁₃. Additional data presented include the charge distributions and molecular dipole moments of the S₀. S₁, and T₁ states of both molecules, as well as energies and oscillator strengths of computed S_n←S₁ and T_n←₁ transitions.     

Energy-band structure and charge distribution for BaC6

An ab initio self-consistent calculation has been carried out for the electronic properties of BaC₆. Energy bands and charge densities are presented for BaC₆ and compared with those of LiC₆. The results show that the band originating from Ba states has a mixture of s and d character and the d component hybridizes appreciably with the π bands of graphite. The Fermi level intersects this band as well as the graphite π bands, giving rise to a complicated Fermi surface with several types of carriers. Depending on the type of volumetric partitioning, the charge transfer from Ba to graphite layers is determined to be between 0.7 and 1.0 electron per Ba atom. The calculated results are consistent with available transport and optical measurements.     

Theoretical investigations of Rh-catalyzed asymmetric 1,4-addition to enones using planar-chiral phosphine-olefin ligands

Recently, planar-chiral phosphine-olefin ligands based on (η⁶-arene)chromium(0) and (η⁵-cyclopentadienyl)manganese(I), which are known as first- and second-generation, respectively, have been developed. These ligands were employed for Rh-catalyzed asymmetric 1,4-addition to enones. First-generation ligands involve high enantioselectivity for cyclic enones (>98% ee). Second-generation ligands involve high enantioselectivity for not only cyclic enones but also for acyclic enones (>98% ee). In this study, we have performed DFT calculations to investigate the origin of enantioselectivity. The theoretical values of enantioselectivities were found to be in good agreement with the experimental values obtained for a cyclic enone, 2-cyclopenten-1-one, using both the first- and second-generation ligands. Regarding an acyclic enone, 3-penten-2-one, it was found that the s-cis type decreases the enantioselectivity because the transition states in the s-cis type have a large steric repulsion. Energy decomposition analysis (EDA) and natural bond orbital (NBO) analysis indicate that it is important to study the orbital interactions in the transition states of the insertion step for the acyclic enone attacked from si-face with the second-generation ligand. © 2018 Wiley Periodicals, Inc.     

New type of turbulence,or how symmetry results in chaos

Pattern formation and transition to chaos in a macroscopic dissipative system is discussed. It is supposed that the system has a continuous family of spatially uniform states, which can be transformed into each other by a certain symmetry transformation. If such a system undergoes instability against spatially periodic perturbations with a finite wavenumber, interplay of short‐wavelength modes associated with the instability and long‐wavelengths modes generated by the symmetry transformation affects the dynamics of the system dramatically. In particular, it may result in direct transition from a spatially uniform state to spatiotemporal chaos, analogous to second order phase transition in equilibrium systems. The obtained results may be applied to kinetic of polymerization, to reaction‐diffusion problems, to flame propagation, to some hydrodynamic problems, etc.     

A dimensionless reaction coordinate for quantifying the lateness of transition states

The Hammond‐Leffler postulate asserts that transition states of exothermic reactions are reactant‐like (early), whereas transition states of endothermic reactions are product‐like (late). Related postulates have been proposed to describe the sensitivity of activation barriers for reactions occurring on catalytic surfaces to the catalyst structure. To evaluate the validity of these postulates for different chemical reactions, a general method for classifying transition states as either early or late is needed. One can envision a dimensionless reaction coordinate that changes continuously and monotonically from 0 to 1 along a minimum energy reaction pathway. The value of the dimensionless reaction coordinate for the transition state (W_TS) classifies transition states as (a) early when W_TS < 0.5, (b) late when W_TS > 0.5, and (c) equidistant between reactants and products when W_TS = 0.5. In this article, we derive such a dimensionless reaction coordinate and illustrate its usefulness for several different chemical reactions. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A detailed analysis of pseudorotation in PH4F

Summary Pentacoordinated molecules are thought to undergo intramolecular isomerization by the widely accepted Berry pseudorotation mechanism. Through our investigations, we have found that the actual pseudorotation for the PH₄F system is more complex than that envisioned by Berry. The potential energy surface of PH₄F is mapped out at the RHF/6-311G(d, p) level. According to the Berry mechanism, this system is expected to have two minima and two maxima; however, the system actually has two transition states and one global minimum. The minimum energy path from the highest transition state is followed to the second transition state, which in turn has a minimum energy path leading to the global minimum. Along the path between the two transition states there is a branching region. This portion of the potential energy surface is probed extensively.Dedicated to Prof. Klaus Ruedenberg     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Ab initio study on the internal rotation of five π-conjugated hydrocarbons at MP2 level

The potential-energy curves of internal rotation were calculated for 1,3-butadiene at the MP2/6-311G** level, for isoprene and 1,3-pentadiene at the MP2/6-311G* level, and for 2,3-dimethyl-1,3-butadiene and styrene at the MP2/6-31G* level. The geometries of the energy minima (stable conformers) and maxima (transition states) on the curves are completely optimized. For butadiene and its methyl derivatives, two stable rotamers, s-trans and gauche conformers, are obtained. s-trans forms have the lowest energies and gauche conformers twisted by 39.9°–48.3° around the central bond of the butadiene skeleton are, on average, 9.8 kJ/mol above the trans forms. s-cis forms are rotational transition states. The computed gauche–cis barriers range from 4.30 to 11.70 kJ/mol. The regular effects of methyl substitutions at the end and central carbons are found. For styrene, the planar form is calculated to be a saddle point which is only about 1 kJ/mol higher in total energy than a twisted minimum, in which the torsional angle between the phenyl and vinyl planes is 27.4°. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 659–667, 1998     

Electrochemically distinguishable states of ferricytochrome c and their transition with changes in temperature and pH

The biphasic behavior of the formal potential (E^o') of cytochrome c with variations of pH (2.5–9) and temperature (4–52° C) is discussed. From an analysis of the dependence of E^o' on pH and temperature it was found that the biphasic behavior of E^o' is due to ferricytochrome c and not ferrocytochrome c. Four conformational states in ferricytochrome c have been identified from the electrochemical measurements. The linear change in E^o' of the individual states with pH and temperature was explained by a simple equation of the electrode reaction with an apparent protonation number. A pH versus temperature diagram which shows the stable regions of the four states has been obtained. These four states correspond to states that have been suggested by other methods such as spectrophotometry and resonance Raman spectroscopy. Since the biphasic changes of E^o' with pH and temperature were very sharp, a conformational transition instead of a change by an equilibrium reaction was introduced to explaine this feature. The high temperature dependence of E^o' (2 mV K⁻¹) of some states has been explained partly by the concentration dependent effect of protons on the entropy change of the electrode reaction.     

An Unusually Small Singlet–Triplet Gap in a Quinoidal 1,6‐Methano[10]annulene Resulting from Baird’s 4n π‐Electron Triplet Stabilization

Within the continuum of π‐extended quinoidal electronic structures exist molecules that by design can support open‐shell diradical structures. The prevailing molecular design criteria for such structures involve proaromatic nature that evolves aromaticity in open‐shell diradical resonance structures. A new diradical species built upon a quinoidal methano[10]annulene unit is synthesized and spectroscopically evaluated. The requisite intersystem crossing in the open‐shell structure is accompanied by structural reorganization from a contorted Möbius aromatic‐like shape in S₀ to a more planar shape in the Hückel aromatic‐like T₁. This stability was attributed to Baird’s Rule which dictates the aromaticity of 4n π‐electron triplet excited states.     

Anionic polymerization of butadiene: A MNDO study of the potential energy surface of the propagation reaction in polar and non-polar media

The anionic polymerization of butadiene, to both the 1,2- and 1,4-addition products, is an important industrial process. It is known that the reaction can be steered to either the 1,2- or 1,4-product by the addition, or absence, of a complexing solvent such as ether. The goals of the current study were to map the MNDO Potential Energy Surfaces (PES) of the propagation reactions both in the presence and absence of dimethyl ether to gain insight into the factors influencing the reaction's selectivity. Single point ab initio calculations at the DZP level were run on all reactants, products and transition states as a cross check on the MNDO results.