Walsh Diagrams Research Articles

The Continuum Between Hexagonal Planar and Trigonal Planar Geometries.

New heterometallic hydride complexes that involve the addition of {Mg-H} and {Zn-H} bonds to group 10 transition metals (Pd, Pt) are reported. The side-on coordination of a single {Mg-H} to Pd forms a well-defined σ-complex. In contrast, addition of three {Mg-H} or {Zn-H} bonds to Pd or Pt results in the formation of planar complexes with subtly different geometries. We compare their structures through experiment (X-ray diffraction, neutron diffraction, multinuclear NMR), computational methods (DFT, QTAIM, NCIPlot), and theoretical analysis (MO diagram, Walsh diagram). These species can be described as snapshots along a continuum of bonding between ideal trigonal planar and hexagonal planar geometries.

The Continuum Between Hexagonal Planar and Trigonal Planar Geometries**

AbstractNew heterometallic hydride complexes that involve the addition of {Mg−H} and {Zn−H} bonds to group 10 transition metals (Pd, Pt) are reported. The side‐on coordination of a single {Mg−H} to Pd forms a well‐defined σ‐complex. In contrast, addition of three {Mg−H} or {Zn−H} bonds to Pd or Pt results in the formation of planar complexes with subtly different geometries. We compare their structures through experiment (X‐ray diffraction, neutron diffraction, multinuclear NMR), computational methods (DFT, QTAIM, NCIPlot), and theoretical analysis (MO diagram, Walsh diagram). These species can be described as snapshots along a continuum of bonding between ideal trigonal planar and hexagonal planar geometries.

Oxidative Addition of Methane and Reductive Elimination of Ethane and Hydrogen on Surfaces: From Pure Metals to Single Atom Alloys.

Oxidative addition of CH4 to the catalyst surface produces CH3 and H. If the CH3 species generated on the surface couple with each other, reductive elimination of C2H6 may be achieved. Similarly, H's could couple to form H2. This is the outline of nonoxidative coupling of methane (NOCM). It is difficult to achieve this reaction on a typical Pt catalyst surface. This is because methane is overoxidized and coking occurs. In this study, the authors approach this problem from a molecular aspect, relying on organometallic or complex chemistry concepts. Diagrams obtained by extending the concepts of the Walsh diagram to surface reactions are used extensively. C-H bond activation, i.e., oxidative addition, and C-C and H-H bond formation, i.e., reductive elimination, on metal catalyst surfaces are thoroughly discussed from the point of view of orbital theory. The density functional theory method for structural optimization and accurate energy calculations and the extended Hückel method for detailed analysis of crystal orbital changes and interactions play complementary roles. Limitations of monometallic catalysts are noted. Therefore, a rational design of single atom alloy (SAA) catalysts is attempted. As a result, the effectiveness of the Pt1/Au(111) SAA catalyst for NOCM is theoretically proposed. On such an SAA surface, one would expect to find a single Pt monatomic site in a sea of inert Au atoms. This is desirable for both inhibiting overoxidation and promoting reductive elimination.

Computational Investigation of the Metal and Ligand Substitution Effects on the Structure and Electronic States of the Phosphoranimide Tetramer Complexes of Cu(I), Ni(I), Co(I), and Fe(I).

The structurally unique saddle-shaped paramagnetic tetrametallic clusters of Co(I) and Ni(I) with phosphoranimide ligands have been synthesized and proposed as catalyst precursors. The analogous Cu(I) nanocluster is planar and diamagnetic. These notable variations in geometry and ground electronic states indicate that the effect of metal and ligand substituents on the structure and electronic properties of these complexes requires investigation. We present a computational study of a series of these novel homoleptic complexes containing Co(I), Ni(I), and Cu(I) as well as Fe(I) coordinated to phosphoranimides with electron-donating and withdrawing substituents, conducted at the relativistic density functional theory level using ZORA-PBE/TZP. The optimized structures of the saddle-shaped Co(I) and Ni(I) and planar Cu(I) tetramers with linear N-M-N coordination are validated with respect to X-ray diffraction determinations. The ground-state analysis indicates that Cu(I) complexes are diamagnetic, whereas Ni(I) and Co(I) complexes are in high-spin states, in agreement with magnetic susceptibility measurements. The computational results show that Fe(I) complexes are saddle shaped and high spin. The Co(I) complex is stabilized by a metal macrocycle distortion from square to diamond, as elucidated from its Walsh diagram. The effects of metals and ligand substituents on the ground electronic state, metal center coordination environment, and energy of the complexes are investigated. The bulky tertiary butyl substituent causes the largest saddle-shape distortion of the tetramer marcocycle, which partially offsets its electron-donating effect. Macrocycle distortions with N-M-N site angles ranging from obtuse to alternating obtuse reflex are correlated with the increasing number of unpaired electrons. The phenyl-substituted complexes are expected to have the highest reactivity toward electrophiles. Understanding the interplay between structural and electronic parameters is intended to guide the development of synthetic cooperative systems for multielectron redox reactions, models of biological systems, and molecular magnets.

Electronic spectrum of boron dichloride. theoretical study of vibronic levels of the ground and first excited states

As expected by the Walsh diagram of AB2 molecules, the electronic spectrum of BCl2 radical involves bent-linear transitions between the ground and first excited states that form the two degenerate components of the 2Π electronic state of the linear molecule. A high level ab-initio theoretical study on BCl2 radical has been undertaken by constructing potential energy surfaces (PES) using the coupled-cluster singles and doubles with perturbative triples (CCSD(T)) with aug-cc-pVQZ for boron and aug-cc-pV(Q + d)Z for chlorine atoms. Vibronic energy levels were determined variationally, from the obtained PES, up to ~35,000 cm−1 above the relative minima of the ground and excited states. Low-lying vibrational levels of the ground and first excited electronic states were obtained, which showed a very complex structure which is known to be as a result of large Renner-Teller vibronic coupling. For the most abundant isotopologue, 11B35Cl2, the ground state fundamental frequencies are; ω10= 696.0 cm−1, ω20= 281.0 cm−1 and ω30=981.8 cm−1. For the same isotopologue, vibrational fundamentals of the excited state were estimated by fitting Σ vibronic levels to be ω10= 463.2 cm−1, ω20= 281.7 cm−1 and ω30=1245.1 cm−1.

Theoretical Studies of Au<sub>3</sub><sup>+/0/- </sup> Clusters Using Density Funtional Theory

In this study, the PW91PW91 method with LANL2DZ level was carried out to settle the dispute about the most stable structure of Au3+/0/-. Molecular orbital analyses and Walsh diagram were adopted to rationalize our computational result about the ground state geometry of Au3+/0/-. Our results show that the most stable geometry of Au3 is bent structure (C2v) with bond angle 146.0°. The less stable structure is equilateral triangle structure (D3h) with relative energies of 1.74 eV. The D3h structure possesses multiplicity 4 while the C2v structure 2. In addition, the most stable geometry of Au3+ and Au3- are equilateral triangle structure (D3h) and linear structure (D∞h), respectively. The preference of geometric change can be rationalized simply by using Walsh diagram. Besides, the linear structure of Au3 is found to be transition states (TS) of inversion of B-Au3. The inversion barrier is estimated to be 0.04 eV.

Walsh Diagrams: Molecular Orbital and Structure Computational Chemistry Exercise for Physical Chemistry

The increasing importance of computational chemistry in modern chemistry provides an impetus to increase the incorporation of computational exercises in the undergraduate chemistry curriculum. Herein, a computational chemistry exercise that can be used in a physical chemistry course is described. In this exercise, students build a series of AH2 molecules in the computational chemistry software Spartan and construct Walsh diagrams for the molecules from calculations of the molecular orbital energies as a function of bond angle. The Walsh diagrams are then used to predict the bond angle of the ground state of each molecule. The exercise focuses on creating a connection between molecular orbital theory and molecular structure and investigating the effects of using different methods and basis sets on the molecular orbital energies. This exercise provides a means for students to visualize and explore the molecular orbitals of small molecules.

The exceptions to the Walsh rules: Linear and cyclic structures of EX2 (E = C, Si, Ge, Sn, Pb and X = O, S, Se)

The stable minima of the EX2 molecule (E=C, Si, Ge, Sn, Pb, and X=O, S, Se) with linear and cyclic structures were calculated at CCSD(T) and B3LYP levels. Most of dioxides favor linear structure following Walsh rules. However, lead dioxide is stabilized as cyclic structure. For sulfides, both cyclic SnS2 and PbS2 are found to be lower in energy while CS2 and SiS2 keep linear structure as most stable formula. As for selenides, more cyclic structures are located in lower energy than linear structures. The great difference between the linear and cyclic structures was mainly caused by relativistic effects, where greater size difference between valence s and p orbital in heavier atoms have lower tendency to form sp hybrid orbital. Finally the cyclic structure was analyzed in detailed according to NBO data and selected molecule orbital.

Cyclic SiS2: A New Perspective on the Walsh Rules

Cyclic SiS₂: A New Perspective on the Walsh Rules

The electronic spectrum of the previously unknown HAsO transient molecule

The Ã(1)A('')-X̃(1)A(') electronic spectrum of the jet-cooled transient molecule HAsO and its deuterated isotopologue has been observed for the first time by pulsed discharge jet laser spectroscopy. The techniques of laser-induced fluorescence and single vibronic level emission were employed to probe the electronic properties of the species. The bending and AsO stretching frequencies have been determined in both states. A rotational analysis of the 0(0)(0) bands of both HAsO and DAsO has been completed and the following effective (r(0)) structures were derived: r(")(HAs) = 1.576(3) Å, r(")(AsO) = 1.8342(5) Å, and θ(") = 101.5(4)°; and r(')(HAs) = 1.569(4) Å, r(')(AsO) = 1.7509(9) Å, and θ(') = 93.1(10)°. In the rotational analysis, lines induced by axis-tilting were observed, and calculated spectra with an axis tilting angle of 3.0(5)° reproduced the intensity of these lines. The change in geometry on electronic excitation is similar to that observed for the molecule HPO, with an increase in the X-O bond length and a decrease in the HXO angle, but contrary to the predictions of the Walsh diagram for generic HAB triatomic molecules. Our ab initio calculations show that the correlation between orbital energy and bond angle changes upon electronic excitation, resulting in the atypical angle change.

CASPT2 study on low-lying states of HBS+ and HSB+ cations

Some low-lying states of the nine-valence-electron systems HBS+ and HSB+ cations have been studied by large-scale theoretical calculations using three methods CASSCF, CASPT2, and DFT B3LYP with the contracted atomic natural orbital and cc-pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces were optimized and the energies were calculated. The potential energy curves of isomerization reactions between HBS+ and HSB+ were calculated as a function of HBS bond angle. The calculated results indicated that the ground-state HBS+ is linear, while the ground-state HSB+ is bent, which is in contradiction to Walsh's rules predicting linear structures for the HXY systems containing 10 or less valency electrons.

Geometrical Embedding Governs a Dramatic Variation of Electron Paramagnetic Resonance Hyperfine Coupling Constants of Disulfide Radical Anions

Among the large variety of experimental techniques amenable to probe disulfide radical anions, electron paramagnetic resonance (EPR) spectroscopy provides the most definitive assignment of these versatile transient intermediates in biochemistry [Stubbe et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 8979-84; J. Am. Chem. Soc. 2009, 131, 200-211]. EPR parameters along both a series of 12 aliphatic 1,2-dithia-cycloalkane radical anions and a representative set of 18 short-loop peptides are investigated by means of density functional theory. While the g-tensor remains quasi-isotropic (with diagonal terms very close to 2.0, as expected for a σ* singly occupied orbital), we evidence a dramatic conformational dependence of isotropic sulfur hyperfine coupling constants (hcc). Potential energy surface exploration of the prototypical dimethyldisulfide rationalizes their 3-4-fold amplitude, with values ranging between 10 and 29 G for aliphatic moieties. Sulfur hcc's are readily decomposed into three geometrical components: intersulfur distance, dihedral, and valence angles, with the latter being predominant. Increasing (respectively decreasing) contribution of sulfur atomic s orbital to the σ* molecular orbital, with a concomitant higher (respectively weaker) density around the sulfur nuclei, can be monitored on Walsh diagrams along each degree of motion. In peptidic disulfide radical anionic systems, sulfur hcc's are dissymmetrized and span an even larger range of values, from 14 to 40 G. Again, dependence is governed by the mechanical embedding of the -CH(2)-S∴S-CH(2)- motif, this time with a noticeable contribution from the hemibond lenghtening and some punctual short-range additive electrostatic contributions. This analysis comes within the scope of a unified picture of both spectroscopy and reactivity of the mechanochemistry of disulfide hemibonds.

Understanding the Unusually Straight: A Search For MO Insights into Linear {FeNO}7 Units

Ferrous-nitrosyl {FeNO}(7) complexes, whether S = 1/2 or 3/2, generally exhibit bent FeNO angles of around 140-145 degrees . There are, however, a handful of exceptions, which are characterized by linear or quasi-linear FeNO units. Presented herein is a relatively comprehensive DFT-based MO analysis of these unusual {FeNO}(7) complexes. DFT-derived FeNO bending potentials indicate that the unusual, experimentally observed quasi-linear geometries indeed correspond to minimum-energy structures on the potential energy surfaces of the isolated molecules/ions. Walsh diagram analyses support our earlier suggestion that the linearity of the {FeNO}(7) units in question is most commonly attributable metal d(sigma)-p(sigma) mixing resulting from the lack of a ligand trans to the NO. Importantly, this effect explains the linearity of both S = 1/2 {FeNO}(7) complexes such as [Fe(CN)(4)(NO)](2-)and Fe(dtc-Me(2))(2)(NO) (dtc-Me(2) = N,N'-dimethyldithiocarbamate) and S = 3/2 complexes such as [Fe(S(t)Bu)(3)(NO)](-). However, Roussin's black salt anion, [Fe(4)(mu-S)(3)(NO)(7)](-), which also contains a linear {FeNO}(7) unit, entails additional, special metal-ligand orbital interactions. The well-known brown-ring complex [Fe(H(2)O)(5)(NO)](2+) also contains a linear {FeNO}(7) unit; the linearity in this case is attributable to the weakness of the trans water ligand.

Heavy atom nitroxyl radicals. I: An ab initio study of the ground and lower electronic excited states of the H2As=O free radical

A series of ab initio calculations have been undertaken to predict the spectroscopic properties of the ground and first two excited states of the recently discovered arsenyl (H(2)AsO) free radical. This 13 valence electron species can be viewed as similar to the formaldehyde radical anion with a ground state electron configuration of cdots, three dots, centered(pi)(2)(n)(2)(pi( *))(1). The arsenyl radical is nonplanar (pyramidal) in the ground state with a 59 degrees out-of-plane angle and a 1.67 A AsO bond length. It has a low-lying n-pi( *)(A (2)A(")) excited state (T(e) approximately 5000 cm(-1)) which has a much larger out-of-plane angle (86 degrees ) and longer AsO bond length (1.81 A). The pi-pi( *)(B (2)A(')) excited state at approximately 20 500 cm(-1) is less pyramidal (out-of-plane angle=70 degrees ) and has a somewhat shorter AsO bond (1.77 A). Similar trends are found for the H(2)PO and H(2)NO free radicals, although the latter has a planar ground state, due to sp(2) hybridization of the N atom, and a very long B state AsO bond length. The geometric variations of the ground and excited states of the H(2)EO (E=N, P, As) radicals, as well as the ground states of the corresponding anions and cations, can be readily rationalized from the Walsh diagram of the anion. The variations in the E-O bond length are a result of changes in both the orbital occupancy and pyramidalization of the molecule. The results of the present work have been employed in the analysis of the B (2)A(')-X (2)A(') electronic band system of the H(2)AsO free radical as reported in the companion paper.

The bonding structure and dipole polarizability of two near-isoenergetic isomers of Si3

Theoretical studies were carried out on the ground state of Si$_{3}$. Two low-lying states were identified, namely, a singlet state of C$_{2v}$ symmetry with a bond angle of around 80°, and a triplet state of D$_{3h}$ symmetry. The two spin states are predicted to be very close in energy at their optimized geometries, with, for example, the ab initio methods with CCSD(T) and CASSCF(12,12) predicting the singlet state to be lower in energy by between 0.06 and 4.6 kcal/mol, respectively; whereas the DFT methods at (U)B3LYP/cc-pVQZ level predicting the opposite order with an energy difference of 1.62 kcal/mol. Walsh diagram is presented to explain the preferred spin state at the two different bond angles; and the bonding structures for the two isomers are proposed in light of the natural bond order analysis results by using the resonance hybrids model. However, unlike the energies, the two spin states are predicted to have fairly different dipole polarizability values: the mean α¯ =105.1 for the singlet and 100.4 for the triplet (in atomic units) at the (U)CCSD/Sadlej level of theory.

Resonant two-photon ionization spectroscopy of BNB

Triatomic BNB has been produced by laser ablation of a boron nitride rod in a supersonic expansion of helium carrier gas and has been investigated using resonant two-photon ionization spectroscopy in the visible region. The B 2Pi(g)-X 2Sigma(u)+ band system has been recorded near 514 nm and is dominated by a strong origin band, which has been rotationally resolved and analyzed. Both the (11)B(14)N(11)B (64% natural abundance) and the (10)B(14)N(11)B (32% natural abundance) isotopic modifications have been analyzed, leading to the spectroscopic constants (and their 1sigma error limits) of B0"(X 2Sigma(u)+)=0.466 147(70), B0'(B 2Pi(g))=0.467 255(75), and A0'(B 2Pi(g))=6.1563(38) cm(-1) for (10)B(14)N(11)B, corresponding to r(B-N)"(X 2Sigma(u)+)=1.312 47(10) A and r(B-N)'(B 2Pi(g))=1.310 92(11) A. Very similar values are obtained for the more abundant isotopomer, (11)B(14)N(11)B: B0"(X 2Sigma(u)+)=0.444 493(69), B0'(B 2Pi(g))=0.445 606(70), A0'(B 2Pi(g))=6.1455(38) cm(-1), corresponding to r(B-N)"(X 2Sigma(u)+)=1.312 41(10) A and r(B-N)'(B 2Pi(g))=1.310 77(10) A. These results are discussed as they relate to Walsh's rules and are compared to results for related molecules.

VIBRATIONAL AUTOIONIZATION IN POLYATOMIC MOLECULES

The vibrationally autoionizing Rydberg states of small polyatomic molecules provide a fascinating laboratory in which to study fundamental nonadiabatic processes. In this review, recent results on the vibrational mode dependence of vibrational autoionization are discussed. In general, autoionization rates depend strongly on the character of the normal mode driving the process and on the electronic character of the Rydberg electron. Although quantitative calculations based on multichannel quantum defect theory are available for some polyatomic molecules, including H3, only qualitative information exists for most molecules. This review shows how qualitative information, such as Walsh diagrams along different normal coordinates of the molecule, can provide insight into the vibrational autoionization rates.

The study of relationship between chemical geometry and electronic configuration of non-Walsh systems

We are looking for a rather general theory for predicting molecular geometry for Walsh and non-Walsh systems. We found that there exist four deriving forces in molecules in competition with each other to make the molecules bent or non-bent, which are electron–electron repulsion, delocalization, spatial orthogonality and Jahn–Teller effect. We will show how these four forces compete in different molecules to shape them up, and illustrate also the role of perturbation of substituents. The types of molecules, which are considered in this article, are some Walsh and non-Walsh systems. The Walsh systems are those molecules that follow Walsh rules, in which the changing in geometry from bent to non-bent is accompanied with the changing in orbital energies significantly, while the non-Walsh system does not have substantial difference between orbital energies of these two structures. The types of non-Walsh molecules, which are considered in this paper, are cumulenes, nitrosyl, formonitril oxide, hydrazoic acid, acetylene derivatives. This category of molecules has the π–lone pair interaction, which make them to bend.

Use of the group theory for classification of electronic states of acetylene

The electronic states of the acetylene molecule are classified employing the group theory combined with the use of the Walsh diagrams and some elementary quantum chemical considerations. The results of this analysis are compared with those obtained by explicit ab initio calculations. It is shown that the global structure of the electronic spectrum can be reproduced/predicted without carrying out detailed ab initio calculations. .

HPO does not follow Walsh’s rules! Improved molecular structures from the spectroscopy of jet-cooled HPO and DPO

The à 1A″–X̃ 1A′ electronic spectra of jet-cooled HPO and DPO have been studied using the techniques of pulsed discharge jet, laser-induced fluorescence, and wavelength resolved emission spectroscopy. All of the vibrational frequencies in the ground and excited states have been obtained for both isotopomers and vibrational force fields have been determined for both states. Rotational analysis of the high-resolution 000 band spectrum of DPO has yielded the first rotational constants of the deuterated species. By combining the rotational constants of DPO with literature values for the rotational constants of HPO, we have derived reliable structures of HPO in the combining states with estimated equilibrium values of r″(PH)=1.4578(6) Å, r″(PO)=1.4801(1) Å, θ″=104.62(7)°, r′(PH)=1.4671(26) Å, r′(PO)=1.5579(6) Å, and θ′=97.4(4)°. The decrease in the bond angle on n–π* electronic excitation is contrary to predictions based on Walsh diagrams. A quantitative ab initio study shows that the variation of the orbital energies with bond angle differs in the ground and excited states of HPO, and these differences account for the anomalous change in bond angle on electronic excitation.