A new way of analyzing vibrational spectra. II. Comparison of internal mode frequencies

Konkoli, Zoran; Larsson, J. Andreas; Cremer, Dieter

doi:10.1002/(sici)1097-461x(1998)67:1<11::aid-qua2>3.0.co;2-1

Cited by 119 publications

(150 citation statements)

References 11 publications

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“…In this way, the off-diagonal elements of the force constant matrix represent the coupling force constants. This becomes clear when realizing that the c-vectors of the transformation matrix C, each of which are associated with a given internal coordinate, can be used as internal localized modes [76]. Hence, a normal mode would be strictly localized if .32 is true.…”

Section: Localized Vibrational Modesmentioning

confidence: 99%

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Generalization of the Badger Rule Based on the Use of Adiabatic Vibrational Modes

Kraka

Larsson

Cremer

2010

Computational Spectroscopy

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113

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Empirical relationships relating bond lengths to the corresponding bond stretching frequencies or bond stretching force constants were first derived in 1920s (see Table 4.1 for a summary) and have ever since been a topic of research on the nature of the chemical bond . It is remarkable that in a time of easily accessible quantum chemical results, there remains a need for empirically based estimates of either bond lengths or stretching frequencies. There are three primary reasons why such empirical rules and relationships are still valuable tools for modern research:(1) Established relationships between bond properties add to our understanding of the chemical bond, especially if they can be rationalized on a quantum mechanical basis because bonding between atoms is a quantum mechanical phenomenon.(2) There are experimental situations in which it is relatively easy to measure one bond property but difficult to obtain other bond properties. For example, it is easier to measure the vibrational spectra of a compound than to carry out a structural analysis. This is especially true for solid materials that do not crystallize, molecules on a surface, or molecules in some form of aggregation. If quantum chemical calculations are feasible only for model systems rather than the actual targets of chemical research, then vibrational spectroscopy may be the only tool for obtaining information that provides an insight into bond properties. (3) In the realm of computational chemistry, there is also a need for empirical relationships. They may be used to determine suitable bonding force fields for molecular mechanics utilizing force constant -bond length relationships. For quantum chemical geometry optimization, there is the need to set up a guess matrix of energy second derivatives (the Hessian matrix corresponding to the force constant matrix of a molecule), which is best done with the help of available geometry information and a suitable force constant -bond length relationship. For example, the standard procedure to calculate the geometry of a molecule is based on an initial guess of the energy Hessian derived with the help of the Badger rule [42,55]. It is due to these three reasons that there is ongoing research exploring the relationships between bond length r, bond stretching Computational Spectroscopy: Methods, Experiments and Applications. Edited by J€ org Grunenberg

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Section: Localized Vibrational Modesmentioning

confidence: 99%

“…The disadvantages of the latter have explicitly been discussed in the literature [76]. The CNM analysis based on the amplitude A nm of Equation 4.52 has been applied with success in various investigations [84].…”

Section: Characterization Of Normal Modes In Terms Of Aicomsmentioning

confidence: 99%

Generalization of the Badger Rule Based on the Use of Adiabatic Vibrational Modes

Kraka

Larsson

Cremer

2010

Computational Spectroscopy

Self Cite

113

150

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“…This becomes clear when we realize that the "c-vectors" of the transformation matrix C, each of which is associated with a given internal coordinate, can be used as localized internal coordinate modes. [16,17] Hence, a normal mode would be strictly localized if…”

Section: Bond Stretching Force Constantsmentioning

confidence: 99%

“…20, 21, and 22 [16,17]: since the AIMs are properly normalized. The AIM mass can be recognized to be identical to element 1/G nn associated with the G matrix and, accordingly, represents a generalization of the reduced mass for internal parameters associated with more than two atoms.…”

Section: Bond Stretching Force Constantsmentioning

confidence: 99%

“…As noted above these force constants are associated with vectors c n of matrix C. Following the AIM approach, one can define local modes also for force constants k c n and, in this way, associate a stretching frequency ω c n with a c-vector mode. [16,17] Therefore, we will consider the possibility of describing chemical bonds with either k c n or k a n . In total, eight different bond stretching force constants can be considered when the strength of a given bond should be described: (24) which are either directly obtained from a quantum chemical calculations or derived from measured vibrational frequencies [19] (k exp ) as described in ref [18].…”

Section: Bond Stretching Force Constantsmentioning

confidence: 99%

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Some Thoughts about Bond Energies, Bond Lengths, and Force Constants

2000

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IntroductionA primary goal of molecular modeling is the prediction of structure, stability, and chemical reactivity of molecules that are difficult to investigate by experimental means. Today, there are many methods ranging from simple structure descriptions to molecular mechanics and quantum chemical approaches to fulfill this goal. Each of these models is based on simplifications and assumptions, which should facilitate the task of molecular modeling. Molecular modeling does provide new insights into the properties of molecules and molecular reactivity provided one considers appropriately the assumptions and simplifications made within the model used.Despite the enormous potential and possibilities of molecular modeling with the help of advanced quantum chemiAbstract The bond energy (BE) of a polyatomic molecule cannot be measured and, therefore, determination of BEs can only be done within a model using a set of assumptions. The bond strength is reflected by the intrinsic BE (IBE), which is related to the intrinsic atomization energy (IAE) and which represents the energy of dissociation under the provision that the degree of hybridization is maintained for all atoms of the molecule. IBE and BE differ in the case of CC and CH bonds by the promotion, the hybridization, and the charge reorganization energy of carbon. Since the latter terms differ from molecule to molecule, IBE and BE are not necessarily parallel and the use of BEs from thermochemical models can be misleading. The stretching force constant is a dynamical quantity and, therefore, it is related to the bond dissociation energy (BDE). Calculation and interpretation of stretching force constants for local internal coordinate modes are discussed and it is demonstrated that the best relationship between BDEs and stretching force constants is obtained within the model of adiabatic internal modes. The valence stretching force constants are less suitable since they are related to an artificial bond dissociation process with geometrical relaxation effects suppressed, which leads to an intrinsic BDE (IBDE). In the case of AX n molecules, symmetric coordinates can be used to get an appropriate stretching force constant that is related to the BE. However, in general stretching force constants determined for symmetry coordinates do not reflect the strength of a particular bond since the related dissociation processes are strongly influenced by the stability of the products formed.Keywords Bond energy (BE), Intrinsic bond energy (IBE), Bond dissociation energy (BDE), Force constants, Adiabatic internal mode cal methods, there is still a need to understand the properties and behavior of molecules on the basis of simple models that require no sophisticated calculations. One wants to connect the properties of a molecule with those of atoms, bonds, or small functional groups so that the knowledge of these group properties makes it possible to describe whatever molecule may be constructed from atoms, bonds (diatomic groups) or functional groups. Central to many of the...

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A new way of analyzing vibrational spectra. I. Derivation of adiabatic internal modes

Konkoli

Cremer

1998

Int. J. Quant. Chem.

205

309

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A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler᎐Lagrange equations for molecular fragments n described by internal parameters . An internal mode is localized in a molecular n fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants k , adiabatic force constants. a Minimization of the kinetic energy of the vibrating fragment yields the adiabatic mass n Ž . m corresponding to 1rG of Wilson's G matrix and, by this, adiabatic frequencies . a n n aAdiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates.

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A new way of analyzing vibrational spectra. II. Comparison of internal mode frequencies

Cited by 119 publications

References 11 publications

Generalization of the Badger Rule Based on the Use of Adiabatic Vibrational Modes

Generalization of the Badger Rule Based on the Use of Adiabatic Vibrational Modes

Some Thoughts about Bond Energies, Bond Lengths, and Force Constants

A new way of analyzing vibrational spectra. I. Derivation of adiabatic internal modes

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