Molecular quantum similarity methods

Two objects are similar and have similar properties to the extent that they have similar distributions of charge in real space. Thus chemical similarity should be defined and determined using the atoms of QTAIM whose properties are directly determined by their spatial charge distributions [32]. Current measures of molecular similarity are couched in terms of Carbo s molecular quantum similarity measure (MQSM) [33-35], a procedure that requires maximization of the spatial integration of the overlap of the density distributions of two molecules the similarity of which is to be determined, and where the product of the density distributions can be weighted by some operator [36]. The MQSM method has several difficulties associated with its implementation [31] ... 

The book covers a gamut of related topics such as methods for determining atoms-in-molecuies, population analysis, electrostatic potential, molecular quantum similarity, aromaticity, and biological activity. It also discusses the role of reactivity concepts in industrial and other practical applications. Whether you are searching for new products or new research projects, this is the ultimate guide for understanding chemical reactivity. 

It is worthwhile to introduce molecular similarity as a broader field before starting the discussion on molecular quantum similarity. Molecular similarity is a well-studied area and continues to be a major topic in modern chemical research. It is that area in which we look for methods to identify a degree of similarity between molecules in a dataset or in which we apply these... 

It is beyond the scope of this chapter to discuss the range of structure-based methods that chemists can use for molecular afignment. This field of research has been, and continues to be, very active. One algorithm, called TGSA, will be presented here in some detail, however, because of its popularity in molecular quantum similarity studies. Structure-based techniques differ from the aforementioned techniques in several respects. First, they not attempt to maximize the MQSM for a pair of molecules. Second, they do not make a specific reference to molecular quantum similarity as such, they are aimed at a wider range of applications. Third, they are not based on electron density in a formal way, but instead they take a more familiar approach based on chemical topology. Consequently, they apply well-known concepts such as chemical bonds and try to overlap the most similar and largest common structure elements in both molecules. 

As a final note, on several occasions, alignment-free methods have been used to quantify molecular similarity in the field of molecular quantum similarity, these methods have not yet fovmd extensive application. One method to obtain molecular quantum similarity measures without the need for molecular alignment was published by Boon et al. They use statistical techniques, more specifically, the autocorrelation function. This technique offers an interesting alternative method for similarity studies by removing completely the important obstacle of molecular alignment. 

A field that has attracted special attention on different occasions is that of the similarity between two atoms located in two different molecules. Eor example, we can imagine calculating the similarity between two carbonyl carbon atoms, one in molecule A and one in molecule B, or calculating the similarity between a carbon atom in a molecule and the isolated atom, or between two different carbon atoms in the same molecule. From the perspective of molecular quantum similarity, calculating the similarity measure will require atomic electron densities within the molecule. Therefore, before turning to the similarity calculation, two methods for obtaining such densities will be briefly presented. 

Goodford P (2006) The basic principles of GRID. In Cruciani G (ed) Molecular interaction fields. Applications in drug discovery and ADME prediction. Methods and principles in medicinal chemistry, vol 27. Wiley-VCH, Weinheim, pp 3-26 Hoskuldsson A (1988) PLS regression methods. J Chemom 2(3) 211-228 Fradera X, Amat L, Besalu E, Carbo-Dorca R (1997) Application of molecular quantum similarity to QSAR. Quant Struct-Act Rel 16(l) 25-32... 

Combined Quantum and Molecular Mechanical Simulations. A recentiy developed technique is one wherein a molecular dynamics simulation includes the treatment of some part of the system with a quantum mechanical technique. This approach, QM/MM, is similar to the coupled quantum and molecular mechanical methods introduced by Warshel and Karplus (45) and at the heart of the MMI, MMP2, and MM3 programs by AUinger (60). These latter programs use quantum mechanical methods to treat the TT-systems of the stmctures in question separately from the sigma framework. 

The usefulness of quantum-chemical methods varies considerably depending on what sort of force field parameter is to be calculated (for a detailed discussion, see [46]). There are relatively few molecular properties which quantum chemistry can provide in such a way that they can be used directly and profitably in the construction of a force field. Quantum chemistry does very well for molecular bond lengths and bond angles. Even semiempirical methods can do a good job for standard organic molecules. However, in many cases, these are known with sufficient accuracy a C-C single bond is 1.53 A except under exotic circumstances. Similarly, vibrational force constants can often be transferred from similar molecules and need not be recalculated. 

Quantum mechanical methods follow a similar path, except that the starting point is the solution of the Schrodinger equation for the system under investigation. The most successful and widely used method is that of Density Functional Theory. Once again, a key point is the development of a realistic model that can serve as the input to the computer investigation. Energy minimization, molecular dynamics, and Monte Carlo methods can all be employed in this process. 

In the next two subsections, we describe collections of calculations that have been used to probe the physical accuracy of plane-wave DFT calculations. An important feature of plane-wave calculations is that they can be applied to bulk materials and other situations where the localized basis set approaches of molecular quantum chemistry are computationally impractical. To develop benchmarks for the performance of plane-wave methods for these properties, they must be compared with accurate experimental data. One of the reasons that benchmarking efforts for molecular quantum chemistry have been so successful is that very large collections of high-precision experimental data are available for small molecules. Data sets of similar size are not always available for the properties of interest in plane-wave DFT calculations, and this has limited the number of studies that have been performed with the aim of comparing predictions from plane-wave DFT with quantitative experimental information from a large number of materials. There are, of course, many hundreds of comparisons that have been made with individual experimental measurements. If you follow our advice and become familiar with the state-of-the-art literature in your particular area of interest, you will find examples of this kind. Below, we collect a number of examples where efforts have been made to compare the accuracy of plane-wave DFT calculations against systematic collections of experimental data. 

Quantum chemical methods may be divided into two classes wave function-based techniques and functionals of the density and its derivatives. In the former, a simple Hamiltonian describes the interactions while a hierarchy of wave functions of increasing complexity is used to improve the calculation. With this approach it is in principle possible to come arbitrarily close to the correct solution, but at the expense of interpretability of the wave function the molecular orbital concept loses meaning for correlated wave functions. In DFT on the other hand, the complexity is built into the energy expression, rather than in the wave function which can still be written similar to a simple single-determinant Hartree-Fock wave function. We can thus still interpret our results in terms of a simple molecular orbital picture when using a cluster model of the metal substrate, i.e., the surface represented by a suitable number of metal atoms. 

It was further possible to demonstrate the favorable charge-transfer interactions of the C60-oFL -exTTF systems in a series of quantum chemical calculations and hypothetically expand this series to the trimer-based system, i.e. that bearing three oligofluorene units as linker. In order to compare the molecular-wire behavior of the oFL wires, we have used very similar methods as for the corresponding C6o-oPPE -exTTF systems (see Sect. 9.1.1). 

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