Distribution of Kinetic and Potential Energy in Vibrating Molecules

Fast vibrational analysis of molecular systems

The development of infrared difference spectroscopy provides unprecedented insights on structures of complex molecules like metalloproteins. However, the relevant information can be hard to find among the many bands of the vibrational spectra. The ab initio modeling is very helpful to assign the frequencies to vibrational modes but it is a challenge to process the huge quantity of data into descriptors useful for experimentalists. To this end, we developed a new tool called VIBMOL allowing to analyze vibrational modes of molecules from hessian matrices calculated with common quantum chemistry codes. VIBMOL program runs on Unix machines. Through a new graphical interface, the users can calculate the normal modes of molecules, visualize them, simulate infrared spectra, and explore the Potential Energy Distribution of normal modes among any set of vibration coordinates. It is combined with an interface program (gosdmu) formatting relevant data from the GAUSSIAN program. VIBMOL code is available upon request to the authors. A discussion is provided to help the readers to choose between a large choice of different software and it shows how VIBMOL can make the IR assignment easier in the context of collaborations with experimentalists.

Determining internal coordinate sets for optimal representation of molecular vibration

Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced.

Toward the Observation of the Tin and Lead Analogs of Formaldehyde

Heavy aldehyde and ketone analogues, R₂X═O (X = Si, Ge, Sn, or Pb), differ from their R₂C═O counterparts due to their greater tendency to oligeramize as the X═O bond polarity increases as one goes down the periodic table. To date, H₂Sn═O and H₂Pb═O have eluded experimental detection. Herein we present the most rigorous theoretical study to date on these structures, providing CCSD(T)/pwCVTZ fundamental frequencies computed on CCSD(T)/CBS optimized structures for the H₂X═O (X = Sn, Pb) potential energy surface. The focal point approach is employed to produce the CCSDTQ/CBS relative energies. For the Sn and Pb structures, the carbene-like cis-HXOH was the global minima, with the trans species being less than 0.6 and 1.1 kcal mol^-1 above the cis structures, respectively. The formaldehyde-like H₂X═O structure is in an energy well of at least 34.8 and 25.4 kcal mol^-1 for Sn and Pb, respectively. Our results provide guidance for future work that may detect H₂Sn═O or H₂Pb═O for the first time.

Validation of potential energy distribution by VEDA in vibrational assignment some of β-diketones; comparison of theoretical predictions and experimental vibration shifts upon deutration

The harmonic vibrational frequencies of the cis-enol forms of some of β-diketones with different substitution in beta position, vis. H, CH3, and Ph ring, as the symmetric and asymmetric molecules, were calculated using density functional theory (DFT) at the B3LYP/6-311++G(d,p) level of theory. The results of DFT calculations were used to obtain the potential energy distribution (PED) by VEDA software. The PED results compared with the Gauss View animation, as our reassignments, and the experimental IR shifts upon deuteration of hydrogen in the OH and CHα. According to our study, the PED contributions, Gauss View animation and observed shifts show similar results for most of the bands which are not coupled with the OH and/or CHα bending, such as asymmetric and symmetric CH₃ stretching and in-plane deformations, CH₃ rocking vibrations and 8a, 19b, 9a, 15, 18a, and 12 motions of the phenyl ring. The largest discrepancies were observed in the 1700-1000 cm^-1 region, likely due to the coupling with the OH and CHα in-plane bending vibrations, such as νaC = C-C = Ο, νsC = C-C = Ο and δOH. Furthermore, the calculated PED contributions by VEDA software do not well define the vibrational contributions to those groups in the molecule that are directly involved in the intramolecular hydrogen bond and the observed failure of the VEDA procedure is possibly due to inappropriateness of the default options.

A Critical Evaluation of Vibrational Stark Effect (VSE) Probes with the Local Vibrational Mode Theory

Over the past two decades, the vibrational Stark effect has become an important tool to measure and analyze the in situ electric field strength in various chemical environments with infrared spectroscopy. The underlying assumption of this effect is that the normal stretching mode of a target bond such as CO or CN of a reporter molecule (termed vibrational Stark effect probe) is localized and free from mass-coupling from other internal coordinates, so that its frequency shift directly reflects the influence of the vicinal electric field. However, the validity of this essential assumption has never been assessed. Given the fact that normal modes are generally delocalized because of mass-coupling, this analysis was overdue. Therefore, we carried out a comprehensive evaluation of 68 vibrational Stark effect probes and candidates to quantify the degree to which their target normal vibration of probe bond stretching is decoupled from local vibrations driven by other internal coordinates. The unique tool we used is the local mode analysis originally introduced by Konkoli and Cremer, in particular the decomposition of normal modes into local mode contributions. Based on our results, we recommend 31 polyatomic molecules with localized target bonds as ideal vibrational Stark effect probe candidates.

Vibrational band assignment of 2-ethyl-1-hexanol

The vibrational structure of 2-ethyl-1-hexanol is of great interest because of its industrial and military applications. However, detailed spectral analysis is challenging due to its flexibility. This paper reports a detailed analysis of the gas and liquid phase vibrational spectra of 2-ethyl-1-hexanol using the Fourier transform infrared spectroscopy and Raman experimental data. By performing a detailed exploration of the conformational space in this work, the theoretical spectra reproduced almost all experimental details observed, and assigned internal valence coordinates to all of the experimentally observed bands in the floppy 2-ethyl-1-hexanol molecule. Relative contributions from the various internal valence coordinates to the experimental vibrational bands are directly compared between the liquid phase Raman band and the gas and liquid phase infrared band.

Computational spectroscopy, dynamics, and photochemistry of photosensory flavoproteins

Extensive interest in photosensory proteins stimulated computational studies of flavins and flavoproteins in the past decade. This review is dedicated to the three central topics of these studies: calculations of flavin UV-visible and IR spectra, simulated dynamics of photoreceptor proteins, and flavin photochemistry. Accordingly, this chapter is divided into three parts; each part describes corresponding computational protocols, summarizes computational results, and discusses the emerging mechanistic picture.

Vibrational energy distribution analysis (VEDA): scopes and limitations

The principle of operations of the VEDA program written by the author for Potential Energy Distribution (PED) analysis of theoretical vibrational spectra is described. Nowadays, the PED analysis is indispensible tool in serious analysis of the vibrational spectra. To perform the PED analysis it is necessary to define 3N-6 linearly independent local mode coordinates. Already for 20-atomic molecules it is a difficult task. The VEDA program reads the input data automatically from the Gaussian program output files. Then, VEDA automatically proposes an introductory set of local mode coordinates. Next, the more adequate coordinates are proposed by the program and optimized to obtain maximal elements of each column (internal coordinate) of the PED matrix (the EPM parameter). The possibility for an automatic optimization of PED contributions is a unique feature of the VEDA program absent in any other programs performing PED analysis.