Decoding chemical information from vibrational spectroscopy data: Local vibrational mode theory

Abstract

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.

Comment on “Exploring nature and predicting strength of hydrogen bonds: A correlation analysis between atoms‐in‐molecules descriptors, binding energies, and energy components of symmetry‐adapted perturbation theory”

“…31 Concerning the detailed mathematical derivation of local vibrational mode theory, interested readers are referred to a recent review article. 13 We observed a rather strong correlation between the local stretching force constant k a HB and the electron density ρ(r) at the BCP for the 28 neutral hydrogen bonds (see Figure 2(A)) and this correlation is marginally stronger than that between BE and ρ(r) according to the coefficient of determination (R 2 ). For hydrogen bonding denoted as D-HÁÁÁA (D: donor atom/group; A: acceptor atom/group), the (3,−1) BCP of hydrogen bond HÁÁÁA is a point between two bonding atoms (H and A) where the first derivative of electron density vanish (i.e., rρ(r) = 0) while the Hessian of dimension (3×3) for ρ(r) has two negative eigenvalues and one positive eigenvalue.…”

“…They advocated the use of this correlation between BE and ρ(r) as a convenient way to predict in the molecular systems the BE of individual hydrogen bonds when these BEs are unattainable. We reassessed the correlation between BE and ρ(r) for those hydrogen bonds in the 28 neutral complexes by utilizing the local vibrational mode theory 12,13 and obtained interesting insights which provide a different perspective complementing the work of Emamian and co-workers.…”

“…On the other hand, the local stretching force constant k a HB with its physical nature as the curvature of PES in the direction of hydrogen bond stretching has been widely recognized as an intrinsic bond strength descriptor derived from vibrational spectroscopy. 13 Therefore, it is of interest to check in more detail to what extent BE and k a HB as two different hydrogen bond strength descriptors are compatible with each other.…”

Exceptionally Long Covalent CC Bonds—A Local Vibrational Mode Study

“…The nature of the CC bonds was characterized following the Cremer-Kraka criterion, which implies that covalent bonding is characterized by a negative energy density, i.e., < 0 whereas electrostatic interactions are indicated by positive energy density values, i.e., > 0 [ 78 , 79 , 80 ]. Following geometry optimization and normal mode analysis, LMA was employed to quantify the intrinsic strength of the targeted CC bonds utilizing the LModeA software [ 58 , 81 ]. A comprehensive discussion of the underlying theory of LMA is provided in Reference [ 58 ], therefore in the following only a summary of the essential features are given.…”

“…In this situation the local vibrational mode analysis (LMA), originally introduced by Konkoli and Cremer [ 53 , 54 , 55 , 56 , 57 ], offers an attractive alternative by providing local vibrational stretching force constants ( ) as an ideal measure of the intrinsic strength of a bond and/or weak chemical interaction [ 58 ] including ultra long C−C bonds [ 11 ].…”