Modern vibrational spectroscopy is more than just an analytical tool. Information about the electronic structure of a molecule, the strength of its bonds, and its conformational flexibility is encoded in the normal vibrational modes. On the other hand, normal vibrational modes are generally delocalized, which hinders the direct access to this information, attainable only via local vibration modes and associated local properties. Konkoli and Cremer provided an elegant solution to this problem by deriving local vibrational modes from the fundamental normal modes, obtained in the harmonic approximation of the potential, via mass-decoupled Euler-Lagrange equations. This review gives a general introduction into the local vibrational mode theory of Konkoli and Cremer and elucidates how this theory unifies earlier attempts to obtain easy to interpret chemical information from vibrational spectroscopy: i) the local mode theory furnishes bond strength descriptors derived from force constant matrices with a physical basis, ii) provides the highly sought after extension of the Badger rule to polyatomic molecules, iii) and offers a simpler way to derive localized vibrations compared to the complex route via overtone spectroscopy. Successful applications are presented, including a new measure of bond strength, a new detailed analysis of IR/Raman spectra, and the recent extension to periodic systems, opening a new avenue for the characterization of bonding in crystals. At the end of this review the LMODEA software is introduced, which performs the local mode analysis (with minimal computational costs) after a harmonic vibrational frequency calculation or by using measured frequencies as input.

Information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes result from a coupling of local vibrational modes, which means that only the latter can provide detailed insight into bonding and other structural features. In this work, it is proven that the adiabatic internal coordinate vibrational modes of Konkoli and Cremer [Int. J. Quantum Chem. 67, 29 (1998)] represent a unique set of local modes that is directly related to the normal vibrational modes. The missing link between these two sets of modes are the compliance constants of Decius, which turn out to be the reciprocals of the local mode force constants of Konkoli and Cremer. Using the compliance constants matrix, the local mode frequencies of any molecule can be converted into its normal mode frequencies with the help of an adiabatic connection scheme that defines the coupling of the local modes in terms of coupling frequencies and reveals how avoided crossings between the local modes lead to changes in the character of the normal modes.

Analytical second derivatives for the normalized elimination of the small component (NESC) method are derived for the first time and implemented for the routine calculation of NESC vibrational frequencies and other second order molecular properties using the scalar relativistic form of NESC. Using response theory, the second derivatives of the transformation matrix U connecting the large and the pseudolarge components of the relativistic wave function are correctly derived. The 24 derivative terms involving the NESC Hamiltonian and the NESC renormalization matrix are individually tested, and their contributions to the energy Hessian are calculated. The influence of a finite nucleus model and that of the picture change is determined. Different ways of speeding up the calculation of the NESC second derivatives are tested. It is shown that second order properties can routinely be calculated in combination with Hartree-Fock, density functional theory, Moller-Plesset perturbation theory, and any other electron correlation corrected quantum chemical method provided analytic second derivatives are available in the nonrelativistic case. The general applicability of the analytic NESC Hessian is demonstrated by benchmark calculations for NESC/DFT calculations involving up to 1500 basis functions.

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For the first time, nonclassical hydrogen (H)-bonding involving a B-H···π interaction is described utilizing both quantum chemical predictions and experimental realization. In the gas phase, a B-H···π H-bond is observed in either B2H6···benzene (ΔE = -5.07 kcal/mol) or carborane···benzene (ΔE = -3.94 kcal/mol) complex at reduced temperatures. Ir-dimercapto-carborane complexes [Cp*Ir(S2C2B10H10)] are designed to react with phosphines PR3 (R = C6H4X, X = H, F, OMe) to give [Cp*Ir(PR3)S2C2B10H10] for an investigation of B-H···π interactions at ambient temperatures. X-ray diffraction studies reveal that the interaction between the carborane BH bonds and the phosphine aryl substituents involves a BH···π H-bond (H···π distance: 2.40-2.76 Å). (1)H NMR experiments reveal that B-H···π interactions exist in solution according to measured (1)H{(11)B} signals at ambient temperatures in the range 0.0 ≤ δ ≤ 0.3 ppm. These are high-field shifted by more than 1.5 ppm relative to the (1)H{(11)B} signals obtained for the PMe3 analog without B-H···π bonding. Quantum chemical calculations suggest that the interaction is electrostatic and the local (B)H···ring stretching force constant is as large as the H-bond stretching force constant in the water dimer.

We extend our previous formulation of time-dependent four-component relativistic density-functional theory [J. Gao, W. Liu, B. Song, and C. Liu, J. Chem. Phys. 121, 6658 (2004)] by using a noncollinear form for the exchange-correlation kernel. The new formalism can deal with excited states involving moment (spin)-flipped configurations which are otherwise not accessible with ordinary exchange-correlation functionals. As a first application, the global potential-energy curves of 16 low-lying omega omega-coupled electronic states of the AuH molecule have been investigated. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are grossly in good agreement with those of ab initio multireference second-order perturbation theory and the available experimental data.

The analytical energy gradient of the normalized elimination of the small component (NESC) method is derived for the first time and implemented for the routine calculation of NESC geometries and other first order molecular properties. Essential for the derivation is the correct calculation of the transformation matrix U relating the small component to the pseudolarge component of the wavefunction. The exact form of ∂U/∂λ is derived and its contribution to the analytical energy gradient is investigated. The influence of a finite nucleus model and that of the picture change is determined. Different ways of speeding up the calculation of the NESC gradient are tested. It is shown that first order properties can routinely be calculated in combination with Hartree-Fock, density functional theory (DFT), coupled cluster theory, or any electron correlation corrected quantum chemical method, provided the NESC Hamiltonian is determined in an efficient, but nevertheless accurate way. The general applicability of the analytical NESC gradient is demonstrated by benchmark calculations for NESC/CCSD (coupled cluster with all single and double excitation) and NESC/DFT involving up to 800 basis functions.

At the averaged quadratic coupled-cluster (AQCC) level, a number of selected rare gas (Rg) containing systems have been studied using the quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO), and several other analysis methods. According to the criteria for a covalent bond, most of the Rg-M (Rg = He, Ne, Ar, Kr, Xe; M = Be, Cu, Ag, Au, Pt) bonds in this study are assigned to weak interactions instead of van der Walls or covalent ones. Our results indicate that the rare gas bond is a new kind of weak interaction, like the hydrogen bond for example.