Correlation between intramolecular bond distances and stretching vibrations for polar molecules: An ab initio study

The correlation between intramolecular bond length and vibrational frequency shifts was calculated at the MP4(aug-cc-PVTZ) ab initio level for a number of molecules (LiH, BH, HF, OH⁻, HDO, BF, CN⁻, and HCI) exposed to uniform electric fields in the range from −0.10 to +0.10 au. The “ω vs. r_e” correlation curves always consist of two branches, each approximately linear. The slopes for the molecules investigated here vary between −2500 and −16600 cm⁻¹/Å. The slopes are well described by an expression containing only the free-molecule second- and third-order force constants and the reduced mass for the stretching mode. Experimental data for polar molecules can be expected to show deviations from a linear “ω vs. r_e” correlation (i) for molecules where the maximum of the frequency vs. field curve occurs at a positive field and (ii) for molecules where the maximum of the frequency vs. field curve falls on the negative-field side but very close to the zero-field case, and (iii) in bonding situations when there is much electron overlap. As opposed to uniform-field situations, anharmonicity and electronic overlap have a substantial influence on the “frequency vs. r_e” slopes in molecular environments. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 537–546, 1997     

The Flipping of CO Ligand Groups in Metal Carbonyl Compounds and its Frequency in Fe(CO)5

It has been proven qualitatively by a number of authors using variable temperature NMR experiments that most metal carbonyl complexes are nonrigid. A quantitative determination of the ligand exchange frequency v_e is often achieved by a line shape analysis or by measurement of the transverse relaxation time T₂ using the Carr-Purcell method. In the case of a “very fast” exchange, however, both methods prove unsuccessful. It is shown in this study that a simultaneous fit of IR or Raman spectra on the one hand and NMR spectra on the other can make possible the determination of v_e for the “very fast” exchange and can also facilitate the determination of v_e in “slow” and “medium” exchange cases considerably. The ligand exchange frequency thus found for Fe(CO)₅, 1.1 × 10¹⁰s^?1, is unexpectedly high; comparison with variable temperature measurements on solid Fe(CO)₅, yields similar energy barriers. A mechanism of exchange closely related to the “Berry mechanism” is proposed. Finally the consequences of this surprisingly large ligand exchange rate are discussed with respect to IR band assignments for molecular “fragments” M(CO)^x (where x=coordination number, and M is a transition metal, typically lanthanoid or actinoid).     

Looking at orbitals in the laboratory: The experimental investigation of molecular wavefunctions and binding energies by electron momentum spectroscopy

The experimental technique of electron momentum spectroscopy (EMS ) (i.e., binary (e, 2e) spectroscopy) is discussed together with typical examples of its applications over the past decade in the area of experimental quantum chemistry. Results interpreted within the framework of the plane wave impulse and the target Hartree—Fock approximations provide direct measurements of, spherically averaged, orbital electron momentum distributions. Results for a variety of atoms and small molecules are compared with calculations using a range of Fourier transformed SCF position space wavefunctions of varying sophistication. Measured momentum distributions (MD ) provide a “direct” view of orbitals. In addition to offering a sensitive experimental diagnostic for semiempirical molecular wavefunctions, the MD's provide a chemically significant, additional experimental constraint to the usual variational optimization of wavefunctions. The measured MD's clearly reflect well known characteristics of various chemical and physical properties. It appears that EMS and momentum space chemistry offer the promise of supplementary perspectives and new vistas in quantum chemistry, as suggested by Coulson more than 40 years ago. Binding energy spectra in the inner valence region reveal, in many cases, a major breakdown of the simple MO model for ionization in accord with the predictions of many-body calculations. Results are considered for atomic targets, including H and the noble gases. The measured momentum distribution for H₂ is also compared with results from Compton scattering. Results for H₂ and H are combined to provide a direct experimental assessment of the bond density in H₂, which is compared with calculations. The behavior of the outer valence MD ''s for small row two and row three hydride molecules such as H₂O and H₂S, NH₃, HF, and HCl are consistent with well known differences in chemical and physical behavior such as ligand-donor activity and hydrogen bonding. MD measurements for the outermost valence orbitals of HF, H₂O and NH₃ show significant differences from those calculated using even very high-quality wavefunctions. Measurements of MD's for outer σ_g orbitals of small polyatomic molecules such as CO₂, COS, CS₂, and CF₄ show clear evidence of mixed s and p character. It is apparent that EMS is a sensitive probe of details of electronic structure and electron motion in atoms and molecules.     

A comparison of variational and non-variational internally contracted multiconfiguration-reference configuration interaction calculations

Summary The internally contracted multiconfiguration-reference configuration interaction (CMRCI) method and several non-variational variants of this method (averaged coupled pair approximation (ACPF), quasidegenerate variational perturbation theory (QD-VPT), linearized coupled pair many electron theory (LCPMET)) have been employed to compute potential energy functions and other properties for a number of diatomic molecules (F₂, O₂, N₂, CN, CO) using large basis sets and full valence CASSCF reference wavefunctions. In most cases the variational CMRCI wavefunctions yield more accurate spectroscopic constants than any of the employed non-variational methods. Several basis sets are compared for the N₂ molecule. It is found that atomic natural orbital (ANO) contractions led to significant errors in the computedr _e , _e , andD _e values.     

Experimentally determined temperature–concentration phase diagrams of monodisperse alkanes with chains containing between 100 and 200 carbons

The temperature–concentration phase (T–c) diagrams of the uniform n-alkanes C₁₀₂H₂₀₆, C₁₂₂H₂₄₆, C₁₆₂H₃₂₆, and C₁₉₈H₃₉₈ in toluene have been determined for solution concentrations in the range 0.1 to 6% (w/w). The shorter alkanes display a “classical” behavior with the expected, strong dependence of dissolution temperature on solution concentration. The longest alkane displays a very different, “polymeric” type behavior with a concentration independent dissolution temperature (for both extended and folded chain crystals). It is argued that no current theory of polymer dissolution is able to explain this behavior. It is suggested that a locally higher concentration occurs when molecules are partially attached to a crystal either during crystallization or dissolution, and that this increased local concentration accounts for the independence of dissolution temperature on the global concentration. There are some small variations in the dissolution temperature of crystals of the same thickness grown at the same concentration, but at different temperatures. These are ascribed to differences in the stacking of the separate layers. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3188–3200, 1999     

A quantum-chemical study on the Mannich reaction with polynitromethanes

According to the results of SCF-CNDO/2 computation, we propose employing the “ladder weighting summation” to define a G_e index which is used to measure the relative magnitude of the nucleophilicity of the relevant amine and pseudo acid components in a Mannich reaction. We also put forward an A_e index to measure the relative magnitude of the electrophilicity of methyleneamine cationic species in the same reaction. A combined use of both G_e and A_e indices is suggested to evaluate the feasibility of a Mannich reaction for the polynitromethanes and the stability of the products. These results are consistent with those conclusions drawn from “soft-hard acid-base theory”.     

Viscoelasticity of dilute chain-molecule solutions: Evaluation of hydrodynamic interaction

The viscoelastic properties of chain molecules varying in flexibility and length have been calculated by use of the bead-spring model theory of Zimm. In the evaluation of the hydrodynamic interaction parameter, the number of springs in the bead-spring model, N, has been selected from the range in which the properties predicted by the theory are insensitive to the value of N. The results for limiting viscosity number agree with those predicted by the Yamakawa–Fujii theory of the limiting viscosity number of wormlike chains. The theory also fits the experimental data of Johnson on a sample of polystyrene of molecular weight 860,000 in theta solvents at infinite dilution. The viscoelastic properties of some moderate molecular weight deoxyribonucleic acid solutions are predicted to deviate from the non-free-draining behavior toward the free-draining behavior.     

Ferroelectric and piezoelectric properties of a quenched poly(vinylidene fluoride-trifluoroethylene) copolymer

The ferroelectric and piezoelectric properties of melt-quenched unoriented poly(vinylidene fluoride-trifluoroethylene) (73 : 27) copolymer films as a function of the number of poling cycles have been studied. The investigation revealed that quenched films exhibit a decrease in D-E hysteresis behavior as the number of poling cycles increases when the samples are poled at room temperature. Corresponding decreases in remanent polarization, Pr, as well as small increases in the coercive field, Ec, were observed as the material was subjected to successive poling cycles. The piezoelectric coefficients, d₃₁ and e₃₁, also decreased as the number of poling cycles increased. In addition, a clear reduction in the “apparent” Curie transition temperature between unpoled and poled material was observed. Preliminary evidence indicates that films quenched from the melt to below T_c do not form a stable ferroelectric crystal phase as previously believed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2671–2679, 1997     

Concentrated solutions of polydisperse rodlike polymers in the isotropic and lyotropic liquid-crystalline phases. II. Model simulation of the dielectric relaxation behavior of poly(n-alkylisocyanates) in toluene and comparison with experimental results

A simulation has been made of the dielectric relaxation behavior of poly(n-hexylisocyanate) in solution covering the isotropic, biphasic, and anisotropic ranges. The simulation incorporates the Flory-Abe statistical mechanical theory for the phase behavior of rodlike macromolecules in solution and the Warchol, Vaughan, Wang, and Pecora theory for the dynamics of a rodlike molecule in a virtual cone prescribed by the neighboring molecules. It is shown that asymmetric Gaussian, Gaussian, or Poisson distributions of molecular weight do not lead to dielectric behavior of the type observed experimentally by Moscicki, Williams, and Aharoni but addition of a high-molecular-weight “tail” to such distributions and taking account of the dependence of relaxation time on molecular length gives a simulation of the dielectric increment Δε, the loss maximum ε, and frequency of maximum loss f_m, which vary with polymer concentration in a manner entirely consistent with the experimental data.     

Critical phenomena in isoelectronic diatomic sequences—the 14-electron sequence

A theory of isoelectronic molecules which describes stable and metastable members of a sequence has been developed. To achieve this synthesis, it has been necessary to require that the total electronic energy surface E(R,Z,Z') for the sequence contain critical points—that is, values of the nuclear charges Z and Z' at which energy minimum, maximum [at R_e(min) and R_e(max)], and horizontal inflection points occur. For ground state sequences a primary physical source of these extreme points is the screened, coulombic repulsion of like-charged atomic centers in the diatomics. With this realization, we can write analytical forms that have the correct scaling behavior and which properly model the screened, coulombic repulsion for E along certain straight-line trajectories in the (Z,Z') plane. This leads to the observation that R_e(max) values diverge logarithmically in λ-like transitions wherever the screened coulombic repulsion becomes small as the nuclear charges vary along those trajectories. At the horizontal inflection points the E surface contains A₂ folds, as required by Thom's theorem for analytical surfaces containing one control parameter. Within the isoelectronic sequence molecular subgroups have been noted and explained in terms of the underlying atomic shell structures of the molecules' constituent atoms. Using input data for seven stable molecules together with the analytical surface selected for study, we have estimated the equilibrium bond distances R_e(min), dissociation energies D_e(min), and harmonic force constants E⁽²⁾(min) for 18 other neutral and charged species.     

Molecular graphs as topological objects in space

Stereochemistry deals primarily with distinctions based on rigid geometry, e.g., bond angles and lengths. But some chemical species have molecular graphs (such as knots, catenanes, and nonplanar graphs K₅ and K_3.3) that reside in space in a topologically nontrivial way. For such molecules there is hope of using topological methods to gain chemical information. Viewing a molecular graph as a topological object in space makes it unrealistically flexible; but if one proves that a certain graph is “topologically chiral” or that two graphs are “topological diastereomers,” then one has ruled out interconversion under any physical conditions for which the molecular graph still makes sense. In this paper, we consider several kinds of topological questions one might ask about graphs in space, methology and results available, and specific topological properties of various molecules.     

Viscoelastic behavior of low molecular weight polystyrene

The shear creep and creep recovery behavior of narrow molecular weight distribution polystyrene samples of low molecular weight, 1.1 × 10³, 3.4 × 10³, and 1.57 × 10⁴ are reported as a function of temperature, near and above the glass temperature. Time-temperature equivalence for the total creep compliance is found to be nonapplicable, and in fact the steady-state recoverable compliance, J_e, is a strong function of temperature. The time-scale shift factors for the recoverable compliance are analyzed in the light of free volume theory. Viscosity data are presented for samples with molecular weights between 1.1 × 10³ and 6.0 × 10⁵. The temperature dependence of the characteristic time constant ηJ_e can be explained in terms of free volume concepts whereas that of viscosity η cannot. Effects of residual molecular weight heterogeneity are demonstrated.     

Molecular orbital theory of the hydrogen bond. 24. Ground-state water–uracil complexes

Ab initio SCF calculations with the STO -3G basis set have been performed to investigate the structural, energetic, and electronic properties of mixed water–uracil dimers formed at the six hydrogen-bonding sites in the uracil molecular plane. Hydrogen-bond formation at three of the carbonyl oxygen sites leads to cyclic structures in which a water molecule bridges N₁? H and O₂, N₃? H and O₂, and N₃? H and O₄. Open structures form at O₄, N₁? H, and N₃? H. The two most stable structures, with energies of 9.9 and 9.7 kcal/mole, respectively, are the open structure at N₁? H and the cyclic one at N₁? H and O₂. These two are easily interconverted, and may be regarded as corresponding to just one “wobble” dimer. At 1 kcal/mole higher in energy is another “wobble” dimer consisting of an open structure at N₃? H and a cyclic structure at N₃? H and O₄. The third cyclic structure at N₃? H and O₂ collapses to the “wobble” dimer at N₃? H and O₄. The two “wobble” dimers are significantly more stable than the open dimer formed at O₄, which has a stabilization energy of 5.4 kcal/mole. Uracil is a stronger proton donor to water through N₁? H than N₃? H, owing to a more favorable molecular dipole moment alignment when association occurs through H₁. Hydration of uracil by additional water molecules has also been investigated. Dimer stabilization energies and hydrogen-bond energies are nearly additive in most 2:1 water:uracil structures. There are three stable “wobble” trimers, which have stabilization energies that vary from 7 to 9 kcal/mole per water molecule. Hydrogen-bond strengths are slightly enhanced in 3:1 water:uracil structures, but the cooperative effect in hydrogen bonding is still relatively small. The single stable water–uracil tetramer is a “wobble” tetramer, with two water molecules which are relatively free to move between adjacent hydrogen-bonding sites, and a stabilization energy of approximately 8 kcal/mole per water molecule. Within the rigid dimer approximation, successive hydration of uracil is limited to the addition of one, two, or three water molecules.     

Theoretical electronic studies of aluminum monobromide and aluminum monoiodide

By using CASSCF/MRCI methods, theoretical molecular calculations have been performed for 12 electronic states for AlBr molecule and 12 electronic states for AlI molecule in the representation ^2s+1Λ (neglecting spin‐orbit effects). Calculated potential energy curves are displayed. Spectroscopic constants including the harmonic vibrational wave number ω_e, the electronic energy T_e referred to the ground state and the equilibrium internuclear distance R_e are predicted for these singlet and triplet electronic states for both AlBr and AlI molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Quantum-mechanical treatment of molecules. I. Calculations of the potential energy curves and molecular constants of the ground and ionized states of N2

The self-consistent-field molecular-orbital method in LCAO (linear combination of atomic orbitals) approximation is applied to the ground and three ionized states of N₂ at a number of internuclear distances for the computation of the potential energy curves. In these calculations both the linear coefficients and the screening constants of the atomic orbitals have been optimized. The molecular constants ω_e, ω_ex_e, B_e, α_e, and R_e have also been calculated for the above states from the computed potential energy curves. The computed spectral results are compared with the experimental data as well as with the results reported by others from ab initio calculations.     

Molecular Logic Gates and Switches Based on 1,3,4‐Oxadiazoles Triggered by Metal Ions

Organic molecular devices for information processing applications are highly useful building blocks for constructing molecular‐level machines. The development of “intelligent” molecules capable of performing logic operations would enable molecular‐level devices and machines to be created. We designed a series of 2,5‐diaryl‐1,3,4‐oxadiazoles bearing a 2‐(para‐substituted)phenyl and a 5‐(o‐pyridyl) group (substituent X=NMe₂, OEt, Me, H, and Cl; 1 a – e ) that form a bidentate chelating environment for metal ions. These compounds showed fluorescence response profiles varying in both emission intensity and wavelength toward the tested metal ions Ni²⁺, Cu²⁺, Zn²⁺, Cd²⁺, Hg²⁺, and Pb²⁺ and the responses were dependent on the substituent X, with those of 1 d being the most substantial. The 1,3,4‐oxadiazole O or N atom and pyridine N atom were identified as metal‐chelating sites. The fluorescence responses of 1 d upon metal chelation were employed for developing truth tables for OR, NOR, INHIBIT, and EnNOR logic gates as well as “ON‐OFF‐ON” and “OFF‐ON‐OFF” fluorescent switches in a single 1,3,4‐oxadiazole molecular system.     

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 φ_λ → φ_ν (creating an e/h excitation with h in φ_λ and e in φ_ν) 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 φ_ν must be rigorously linked to the complementary h-probabilities in φ_λ). 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.     

New method for approximate Hartree-Fock calculations using density approximations and coulomb field corrections. II

The HF approximation method that was outlined in Paper I is tested with respect to several molecular properties. Three different levels of approximation a, b, and c are considered. Satisfactory results—compared to corresponding “exact” HF calculations—are obtained with the STO -3G basis and the approximation level a. At this level the error in the binding energy is 0.001–0.025 a.u. for all considered molecules which contain up to six first-row atoms as, e.g., cyclopentanone (C₅OH₈). The error in the reaction energies considered here is about 4 kcal/mol (the maximal error is 9 kcal/mol). Orbital energies, dipole moments, gross charges, equilibrium geometries, and barriers to internal rotation are well reproduced by the approximation method at all three levels.     

Relativistic calculations of dissociation energies and related properties

Methods of calculation of potential energy curves or surfaces, including dissociation energies, bond distances, and vibration frequencies, are discussed as well as recently obtained results for several molecules. The ab initio relativistic methods involve the derivation of “shape-consistent” effective potentials from Dirac–Fock atomic calculations. These effective potentials are averaged and differenced with respect to spin with the differences, p_3/2 – p_1/2, etc., yielding spin-orbit operators. The molecular calculations are then set up in a familiar manner through the SCF stage using spin-averaged effective potentials. The final stage is a configuration-interaction calculation including the spin-orbit terms as well as the electron repulsion terms. Calculations that have been made for several low-lying excited states as well as the ground state for Au₂, TlH, Tl₂, Sn₂, and Pb₂ are reviewed. Good agreement is obtained with spectroscopic data and a number of interesting predictions are made.