Natural Resonance Theory Research Articles

A Rotor Looseness‒Rub-Impact‒Resonance Fault Mechanism Modeling

In view of the limitation of the numerical method for coupling faults of rotating machinery, a modeling method for coupling faults of rotor, DeformationMotion Vector Analysis Method, is purposed in order to explain the fault mechanism more thoroughly and universally. Firstly, the “Deformation-Motion” is defined by fault and the relationship between fault deformation and periodic signal is established by Fourier series. Secondly, the “Vector Analysis” analyzes the deformation-motion in the dynamic coordinate system, and establishes the relationship between the fault deformation-motion and the periodic excitation force by using the dynamic and static coordinate systems. Thirdly, the analytical solution is obtained by harmonic balance method, and the coriolis acceleration term is first found in the analytical solution of rotating machinery failure. By further analysis of the analytical solution, we find that the general trend of the natural frequency of the rotor system will gradually approach the excitation source frequencies and eventually lead to the resonance: that is the law of Natural Frequency Migration Resonance Theory. Finally, the validity of the modeling method and the correctness of the analytical solution are verified by engineering practice

The Relative Stability of Indole Isomers Is a Consequence of the Glidewell-Lloyd Rule

Indole (1) is a heterocyclic aromatic compound consisting of a pyrrole ring (5MR) fused with a benzene ring (6MR). This compound is highly stable, found in several natural products, and is used as a building block for the synthesis of novel organic compounds. On the other hand, its isomers isoindole (2) and indolizine (3) are much less stable and are normally isolated when bonded to other stable compounds. The stability of these compounds has been analyzed in terms of local aromaticity using magnetic, geometric, and delocalization criteria. All criteria used indicate that there is a continuing reduction in aromaticity of the 6MR, whereas for the 5MR the aromaticity increases when going from 1 to 3. This is confirmed by Natural Resonance theory calculations indicating that the resonant structures which retain the aromaticity of the 5MR are the ones having the largest contribution. The results obtained suggest that the relative stability of indole isomers is a consequence of the Glidewell-Lloyd rule.

Superposition of waves or densities: Which is the nature of chemical resonance?

Resonance is a fundamental and widely used concept in chemistry, but there exist two distinct theories of chemical resonance, based on quite different and incompatible premises: the wave-function-based resonance theory (WFRT), assuming the superposition of wave functions, versus the density-matrix-based resonance theory (DMRT), which interprets the resonance phenomenon as the superposition of density matrices. The latter theory, best known to the chemistry community as the natural resonance theory (NRT), has received much more popularity than the WFRT. In this contribution, the DMRT is shown to be inherently inadequate: (i) the exact density matrix expansion is mathematically impossible unless unphysical negative weights are introduced; (ii) any approximate density matrix representing the resonance hybrid lacks the idempotent property. Therefore, the validity of the NRT ansatz should be seriously questioned. The WFRT seems the only reasonable explanation of resonance so far, and has been shown to provide valuable insights into diverse chemical problems.

NBO/NRT Two-State Theory of Bond-Shift Spectral Excitation.

We show that natural bond orbital (NBO) and natural resonance theory (NRT) analysis methods provide both optimized Lewis-structural bonding descriptors for ground-state electronic properties as well as suitable building blocks for idealized “diabatic” two-state models of the associated spectroscopic excitations. Specifically, in the framework of single-determinant Hartree-Fock or density functional methods for a resonance-stabilized molecule or supramolecular complex, we employ NBO/NRT descriptors of the ground-state determinant to develop a qualitative picture of the associated charge-transfer excitation that dominates the valence region of the electronic spectrum. We illustrate the procedure for the elementary bond shifts of SN2-type halide exchange reaction as well as the more complex bond shifts in a series of conjugated cyanine dyes. In each case, we show how NBO-based descriptors of resonance-type 3-center, 4-electron (3c/4e) interactions provide simple estimates of spectroscopic excitation energy, bond orders, and other vibronic details of the excited-state PES that anticipate important features of the full multi-configuration description. The deep 3c/4e connections to measurable spectral properties also provide evidence for NBO-based estimates of ground-state donor-acceptor stabilization energies (sometimes criticized as “too large” compared to alternative analysis methods) that are also found to be of proper magnitude to provide useful estimates of excitation energies and structure-dependent spectral shifts.

Chemical bonding in trimers of Ge2 with monovalent metals

AbstractChemical bonding of the monovalent metal‐doped germanium Ge2M (M belonging the groups IA and IB) clusters is investigated by using quantum chemical calculations combined with the analyses of natural atomic orbital (NAO), natural bond orbital (NBO) and natural resonance theory (NRT). All of the clusters have a ground state in isosceles triangle shape with two quasi‐degenerate electronic states (2A1, 2B1). The clusters doped with metals of the group IB are more stable than those doped with the alkali metals of the group IA due to the stronger Ge‐M bond of the former ones. Most clusters have the electron transfer from the dopant atoms to the dimer Ge2. This study reveals that the Ge‐M bonds is very weak and highly ionic with M being alkali metals, while they are stronger and possess both ionic and covalent nature with a larger contribution of the ionic character for M being IB elements. The participation of AO‐d in the Ge‐M bonds of the IB elements is the reason for their larger strength and covalent character.

Probing Au⋯O and Au⋯P regium bonding interaction in AuX (X = F, Cl, Br)⋯RPHOH (R = CH3, F, CF3, NH2, CN) complexes

CCSD(T) and MP2/aug-cc-pVTZ (PP) calculations have been carried out to investigate interaction energies and binding properties on the regium bonding intermolecular interaction between AuX (X = F, Cl, Br) and RPHOH (R = CH3, F, CF3, NH2, CN). For the AuX⋯RPHOH complexes, four types of configurations (trans-P, trans-O, cis-P and cis-O) are observed. The magnitude of molecular interaction energies is in the order of NH2 > CH3 > F > CF3 > CN, F > Cl > Br with the nature of the substituent directly affecting the strength of the interaction. The transition structures which present the energy barriers to the inter-conversion between the trans-type and the cis-type structures and the Boltzmann distribution to quantitatively determine the proportion of the cis-type and the trans-type geometries have been obtained. The natural resonance theory confirms the presence of the Au⋯O and the Au⋯P regium bonds with two major secondary resonance structures X-Au:RPHOH (ωI) ↔ X:Au-RPHOH (ωII). In addition, LMO-EDA energy decomposition analysis is performed on the regium bonded complexes to predict the dominant energy component and the nature of the Au⋯O and the Au⋯P regium bonded interaction.

Coupled Cluster Study of the Interactions of AnO2, AnO2+, and AnO22+ (An = U, Np) with N2 and CO.

Thermochemical and spectroscopic properties for actinyl complexes involving UO22+/1+/0 and NpO22+/1+/0 with N2 and CO, together with the UO2-O2, UO2+-O2, and UO2+-NO complexes, have been studied for the first time using an accurate composite coupled cluster approach. Two general bonding motifs were investigated, end-on (η1) and side-on (η2) relative to the metal center of the actinyls. For end-on CO complexes, both C-coordinated (An-C) and O-coordinated (An-O) structures were examined, with the former always being lower in energy. All of the η1 complexes were calculated to be stable, with dissociation energies ranging from 2 to 36 kcal/mol, except for that of UO2+-O2 (the η1 orientation for UO2+-NO was not amenable to single reference coupled cluster). In agreement with a previous study, the η2 structure for UO2+-O2 was calculated to be relatively strongly bound, by 22.3 kcal/mol in this work. The closely related NO complex, however, had a calculated dissociation energy of just 4.0 kcal/mol. The binding energy of O2 to neutral UO2 in a η2 orientation was calculated to be very strong, 75.4 kcal/mol, and strongly resembled a UO2+(O2-) complex at equilibrium. The N-N and C-O bonds were found to be somewhat activated for all the side-on (η2) neutral An(IV) complexes, with stretching frequencies of N2 or CO being red-shifted by as much as 480 cm-1 with a 0.06 Å bond length elongation. Dissociation energies for the η1 complexes are strongly correlated with the extent of electron transfer from ligand to actinyl. The nature of bonding in the actinyl complexes is examined using natural resonance theory (NRT). The correlation between bonding motif and small molecule activation is in agreement with experiments in condensed phases.

Unsymmetrical Coordination of Bipyridine in Three-Coordinate Gold(I) Complexes.

The unsymmetrical coordination of gold(I) by 2,2'-bipyridine (bipy) in some planar, three-coordinate cations has been examined by crystallographic and computational studies. The salts [(Ph3P)Au(bipy)]XF6 (X = P, As, Sb) form an isomorphic series in which the differences in Au-N distances range from 0.241(2) to 0.146(2) Å. A second polymorph of [(Ph3P)Au(bipy)]AsF6 has also been found. Both polymorphs exhibit similar structures. The salts [(Et3P)Au(bipy)]XF6 (X = P, As, Sb) form a second isostructural series. In this series the unsymmetrical coordination of the bipy ligand is maintained, but the gold ions are disordered over two unequally populated positions that produce very similar overall structures for the cations. Although many planar, three-coordinate gold(I) complexes are strongly luminescent, the salts [(R3P)Au(bipy)]XF6 (R = Ph or Et; X = P, As, Sb) are not luminescent as solids or in solution. Computational studies revealed that a fully symmetrical structure for [(Et3P)Au(bipy)]+ is 7 kJ/mol higher in energy than the observed unsymmetrical structure and is best described as a transition state between the two limiting unsymmetrical geometries. The Au-N bonding has been examined by natural resonance theory (NRT) calculations using the "12 electron rule". The dominant Lewis structure is one with five lone pairs on Au and one bond to the P atom, which results in a saturated (12 electron) gold center and thereby inhibits the formation of any classical, 2 e- bonds between the gold and either of the bipy nitrogen atoms. The nitrogen atoms may instead donate a lone pair into an empty Au-P antibonding orbital, resulting in a three-center, four-electron (3c/4e) P-Au-N bond. The binuclear complex, [μ2-bipy(AuPPh3)2](PF6)2, has also been prepared and shown to have an aurophillic interaction between the two gold ions, which are separated by 3.0747(3) Å. Despite the aurophillic interaction, this binuclear complex is not luminescent.

The reaction of O(3P) with alkynes: a dynamic and computational study focusing on formyl radical production.

Production of formyl radical, HCO, from reactions of O(3P) with alkynes (acetylene, propyne, 1-butyne, and 1-pentyne) has been investigated using cavity ringdown laser absorption spectroscopy (CRDLAS) and computational methods. No HCO was detected from reaction with acetylene, while the amount of HCO increased for propyne and 1-butyne, dropping off somewhat for 1-pentyne. These results differ from trends previously observed for reactions of O(3P) with alkenes, which exhibit the largest HCO production for the smallest alkene and drop off as the alkene size increases. Computational studies employing density functional and coupled cluster methods have been employed to investigate the triplet and singlet state pathways for HCO production. Because intersystem crossing (ISC) has been shown to be important in these processes, the minimum energy crossing point (MECP) between the triplet and singlet surfaces has been studied. We find the MECP for propyne to possess C1 symmetry and to lie lower in energy than previous studies have found. Natural Bond Orbital and Natural Resonance Theory analyses have been performed to investigate the changes in spin density and bond order along the reaction pathways for formation of HCO. Explanations are suggested for the trend in HCO formation observed for the alkynes. The trend in alkyne HCO yield also is compared and contrasted with the trend previously observed for the alkenes.

Ground State Destabilization in Uracil DNA Glycosylase: Let's Not Forget "Tautomeric Strain" in Substrates.

Enzymes like uracil DNA glycosylase (UDG) can achieve ground state destabilization, by polarizing substrates to mimic rare tautomers. On the basis of computed nucleus independent chemical shifts, NICS(1)zz, and harmonic oscillator model of electron delocalization (HOMED) analyses, of quantum mechanics (QM) and quantum mechanics/molecular mechanics (QM/MM) models of the UDG active site, uracil is strongly polarized when bound to UDG and resembles a tautomer >12 kcal/mol higher in energy. Natural resonance theory (NRT) analyses identified a dominant O2 imidate resonance form for residue bound 1-methyl-uracil. This "tautomeric strain" raises the energy of uracil, making uracilate a better than expected leaving group. Computed gas-phase SN2 reactions of free and hydrogen bonded 1-methyl-uracil demonstrate the relationship between the degree of polarization in uracil and the leaving group ability of uracilate.

Acidity of the chlorinated phenols: DFT study and experiential affirmation.

A quantum mechanical density functional theory (DFT) was successfully developed for the estimation of pKa values of chlorinated phenols in aqueous solution with a precision of 0.9 pKa units. The MP2/6-311++G(d,p)//B3LYP/6-31+G(d) level of theory was used for the gas phase calculation. For computation in the solution phase and to calculate the energy difference of the acid-base, the polarized continuum model (PCM) at the HF/6-31G(d,p) level was used. The pKa value was computed for each involved species using pentachlorophenol (PCP) as a reference molecule. Natural bond orbital (NBO) analysis considering the natural resonance theory (NRT) was carried out on an optimized geometry of studied compounds to give information about the nature of bonds. Graphical abstract Chlorinated phenols.

NBO 7.0: New vistas in localized and delocalized chemical bonding theory.

We briefly outline some leading features of the newest version, NBO 7.0, of the natural bond orbital (NBO) wavefunction analysis program. Major extensions include: (1) a new NPEPA module implementing Karafiloglou's "polyelectron population analysis" in the NBO framework; (2) new RDM2 program infrastructure for describing electron correlation effects based on full evaluation of the second-order reduced density matrix; (3) improved convex-solver implementation of natural resonance theory (NRT), allowing a greatly expanded range of applications and associated "resonance NBO" (RNBO) visualization of chemical reactivity; (4) a variety of other improvements in well-established NBO algorithms. We also provide brief introduction to the new NBOPro@Jmol utility program, a plugin to the Jmol chemical structure viewer that serves as a convenient tool to provide on-demand NBO descriptors or orbital visualizations for a broad variety of chemical inquiries in research or classroom applications. © 2019 Wiley Periodicals, Inc.

What Is the Nature of Supramolecular Bonding? Comprehensive NBO/NRT Picture of Halogen and Pnicogen Bonding in RPH2···IF/FI Complexes (R = CH3, OH, CF3, CN, NO2).

We employ a variety of natural bond orbital (NBO) and natural resonance theory (NRT) tools to comprehensively investigate the nature of halogen and pnicogen bonding interactions in RPH2···IF/FI binary complexes (R = CH3, OH, CF3, CN, and NO2) and the tuning effects of R-substituents. Though such interactions are commonly attributed to “sigma-hole”-type electrostatic effects, we show that they exhibit profound similarities and analogies to the resonance-type 3-center, 4-electron (3c/4e) donor-acceptor interactions of hydrogen bonding, where classical-type “electrostatics” are known to play only a secondary modulating role. The general 3c/4e resonance perspective corresponds to a continuous range of interatomic A···B bond orders (bAB), spanning both the stronger “covalent” interactions of the molecular domain (say, bAB ≥ ½) and the weaker interactions (bAB ˂ ½, often misleadingly termed “noncovalent”) that underlie supramolecular complexation phenomena. We show how a unified NBO/NRT-based description of hydrogen, halogen, pnicogen, and related bonding yields an improved predictive utility and intuitive understanding of empirical trends in binding energies, structural geometry, and other measurable properties that are expected to be manifested in all such supramolecular interaction phenomena.

Efficient optimization of natural resonance theory weightings and bond orders by gram-based convex programming.

We describe the formal algorithm and numerical applications of a novel convex quadratic programming (QP) strategy for performing the variational minimization that underlies natural resonance theory (NRT). The QP algorithm vastly improves the numerical efficiency, thoroughness, and accuracy of variational NRT description, which now allows uniform treatment of all reference structures at the high level of detail previously reserved only for leading "reference" structures, with little or no user guidance. We illustrate overall QPNRT search strategy, program I/O, and numerical results for a specific application to adenine, and we summarize more extended results for a data set of 338 species from throughout the organic, bioorganic, and inorganic domain. The improved QP-based implementation of NRT is a principal feature of the newly released NBO 7.0 program version. © 2019 Wiley Periodicals, Inc.

Structural and theoretical investigations of the Rh(III) and Co(III) complexes containing symmetrical edta-type ligands with mixed carboxylate and diamine rings: Quantum-mechanical/NBO insight into stability of geometrical isomers

The trans(O5O6) isomer of the Na[Rh(eddadp)]·4H2O and the K[Co(eddadp)]·3H2O (eddadp = ethylenediamine-N,N′-diacetate-N,N′-di-3-propionate) were synthesized and Na[Rh(eddadp)]·4H2O structure was confirmed by X-ray diffraction analysis. The percentage of particular isomers found in reaction equilibrium mixtures of [M(eddadp)]− complex has been reported. Single crystal X-ray diffraction of the complex revealed an octahedral geometry of the Rh(III) centre. Improved structural distortion analysis of M(III) (M = Rh, Co) complexes with symmetric edta-type of ligands containing mixed carboxylate and diamine rings was made. Structural distortion analysis has determined high values of total deviation of the octahedral angles (Δ(Oh)) for both existing trans(O5) (34°) and trans(O5O6) (41°) isomers of [Rh(eddadp)]− complex, while in the case of a similar Co(III) complex, relatively low value (31°) for trans(O5) has been established. Extensive QM/NBO calculations were made for both systems [M(eddadp)]− and [M(1,3-pddadp)]− using different DFT methods (B3LYP/SDD, M06/SDD, MP2/SDD). By correlating the structural parameters obtained from X-ray and DFT optimized 3D structures, the B3LYP/SDD method was used as the method of choice. Based on the correlation between the energies of the optimized systems and the strain parameters, the existence of the trans(O6) isomer of the [Rh(1,3-pddadp)]− complex was predicted. NRT (Natural Resonance Theory) analysis gave the best resonances for each isomer. Here the stability of particular isomer has been described in terms of 3-CHB bonds involving metal ions and Second Order Perturbation Theory analysis using Donor/Acceptor energies. Further, to explain the bonding nature of M-edta-type complexes the Natural Coulomb Electrostatics (NCE) analysis has been done as well. The pairwise steric exchange interaction EI,Jpwx results obtained for the best-ranked resonances of different isomers are in excellent agreement with favored isomers reported so far. For the energy limit of the possibility of forming geometric isomers, a value of about 6 kcal mol−1 is proposed.

To Be or Not to Be: Demystifying the 2nd-Quantized Picture of Complex Electronic Configuration Patterns in Chemistry with Natural Poly-Electron Population Analysis.

We provide a didactic introduction to 2nd-quantized representation of complex electron-hole (e/h) excitation patterns in general configuration interaction wave functions built from orthonormal local orbitals of natural atomic orbital or natural bond orbital (NBO) type. Such local excitation patterns of chemically oriented basis functions can be related to the resonance concepts of valence bond theory, and quantitative evaluation of the associated excitation probabilities then provides an alternative assessment of resonance "weighting" that may be compared with those of NBO-based natural resonance theory. We illustrate the usefulness of anticommutation relations in deriving Pauli-compliant expressions for allowed excitation patterns, showing how the exciton-like promotions φλ → φν (creating an e/h excitation with h in φλ and e in φν ) impose strict constraints on associated e/h-probabilities (requiring, e.g., that the e-probability for an electron "to be" or "not to be" in φν must be rigorously linked to the complementary h-probabilities in φλ ). Specific examples are presented of the quantum Boolean logic for four or six local spin-orbitals, with emphasis on Natural Poly-Electron Population Analysis (NPEPA) evaluation of VB-type covalent and ionic contributions in conventional 2-center bonding, resonance weightings in 3-center hydrogen bonding, and general characteristics of higher-order m-center bonding motifs for m > 3. Numerical results are presented for methylamine, acrolein, and water dimer to illustrate current NPEPA implementation in the NBO program. © 2019 Wiley Periodicals, Inc.

Resonance Theory Reboot.

What is now called "resonance theory" has a long and conflicted history. We first sketch the early roots of resonance theory, its heritage of diverse physics and chemistry conceptions, and its subsequent rise to reigning chemical bonding paradigm of the mid-20th century. We then outline the alternative "natural" pathway to localized Lewis- and resonance-structural conceptions that was initiated in the 1950s, given semi-empirical formulation in the 1970s, recast in ab initio form in the 1980s, and successfully generalized to multi-structural "natural resonance theory" (NRT) form in the 1990s. Although earlier numerical applications were often frustrated by the ineptness of then-available numerical solvers, the NRT variational problem was recently shown to be amenable to highly efficient convex programming methods that yield provably optimal resonance weightings at a small fraction of previous computational costs. Such convexity-based algorithms now allow a full "reboot" of NRT methodology for tackling a broad range of chemical applications, including the many familiar resonance phenomena of organic and biochemistry as well as the still broader range of resonance attraction effects in the inorganic domain. We illustrate these advances for prototype chemical applications, including (i) stable near-equilibrium species, where resonance mixing typically provides only small corrections to a dominant Lewis-structural picture, (ii) reactive transition-state species, where strong resonance mixing of reactant and product bonding patterns is inherent, (iii) coordinative and related supramolecular interactions of the inorganic domain, where sub-integer resonance bond orders are the essential origin of intermolecular attraction, and (iv) exotic long-bonding and metallic delocalization phenomena, where no single "parent" Lewis-structural pattern gains pre-eminent weighting in the overall resonance hybrid.

Regium bonds formed by MX (M═Cu, Ag, Au; X═F, Cl, Br) with phosphine-oxide/phosphinous acid: comparisons between oxygen-shared and phosphine-shared complexes

ABSTRACTRegium bonds interaction between phosphine oxide (H3PO), the trans phosphinuous acid (T-PH2OH), the cis phosphinuous acid (C-PH2OH) and MX (M═Cu, Ag, Au; X═F, Cl, Br) complexes were investigated by means of ab initio MP2/aug-cc-pVTZ method. For phosphinuous acid and MX complexes, two types of regium bonded interaction (trans and cis complexes) are observed and the two types of structures are very easily transformed from one type to another due to a low energy barrier. The molecular interaction energies are in the order of Au > Cu > Ag, F > Cl > Br and increase with the decrease of intermolecular distance Rint. Two resonance-type structures of P:M-X (ωI) ↔ P–M:X (ωII), O:M-X (ωI) ↔ O–M:X (ωII) are recognised by the natural resonance theory (NRT) and the natural bond orbitals (NBOs) analysis. The competition between ωI ↔ ωII resonance structures mainly arises from hyperconjugation interactions, in all phosphor-shared complexes, P–M:X resonance accounts for a larger proportion which leads to the covalent characters. All of complexes have been described in terms of their electron density properties.

Resonance Natural Bond Orbitals: Efficient Semilocalized Orbitals for Computing and Visualizing Reactive Chemical Processes.

We describe a practical algorithm for calculating NBO-based "resonance natural bond orbitals" (RNBOs) that can accurately describe the localized bond shifts of a reactive chemical process. Unlike conventional NBOs, the RNBOs bear no fixed relationship to a particular Lewis-structural bonding pattern but derive instead from the natural resonance theory (NRT)-based manifold of all bonding patterns that contribute significantly to resonance mixing (and associated multichannel reactivity) at a chosen point of the potential energy surface. The RNBOs typically retain familiar localized Lewis-structural character for stable near-equilibrium species, yet they freely adopt multicenter character as required to satisfy Pople's prerequisite that no allowed computational basis set should be inherently biased toward a particular nuclear arrangement or bonding pattern. A simple numerical application to intramolecular Claisen rearrangement demonstrates the computational and conceptual advantages of describing reactive bond-shifts with RNBOs rather than other conventional NBO- or MO-based expansion sets.

Theoretical insight to intermolecular hydrogen bond interactions between methyl N-(2-pyridyl) carbamate and acetic acid: substituent effects, cooperativity and energy decomposition analysis

In the present work, the hydrogen bond (HB) interactions between substituted syn and anti rotamers of methyl N-(2-pyridyl) carbamate and acetic acid were investigated using quantum mechanical (QM) calculations. The rotamers have two typical active sites to form hydrogen bonds with acetic acid, such that four stable complexes are found on the potential energy surface. The complexes in which the oxygen atom of carbamate acts as proton acceptor are stabilized by EWSs and are destabilized by EDSs. The trend in the effects of substituents is reversed in the other two complexes, in which the nitrogen atom of ring is involved in the interaction. According to energy data, the substituent effects on the interaction energy can be expressed by Hammett constants. The natural resonance theory (NRT) model was used to investigate the charge distribution on the carbamate group and to discuss the interaction energies. The individual HB energies were estimated to evaluate their cooperative contributions on the interaction energies of the complexes. In addition, the localized molecular orbital energy decomposition analyses (LMO-EDA) demonstrate that the electrostatic interactions are the most important stabilizing components of interactions.