Kronecker-Product Periodic Systems of Small Gas-Phase Molecules and the Search for Order in Atomic Ensembles of Any Phase

The periodic law, manifested in the chart of the elements, is so fundamental in chemistry and related areas of physics that the question arises “Might periodicity among molecules also be embodied in a periodic system?” This review paper details how a particular periodic system of gas-phase diatomic molecules, allowing for the forecasting of thousands of new data, was developed. It can include ionized and even quarked-nuclei molecules and it coincides with locality (averaging) and the additivity found in some data; it has interesting vector properties, and it may be related in challenging ways to partial order. The review then explains how periodic systems for triatomic and four-atomic species are evolving along a similar path. The systems rest largely upon exhaustive comparisons of tabulated data, relate to some extent to the octet rule, and include reducible representations of the dynamic group SO(4) in higher spaces. Finally, the paper shows how periodicity can be quantified in data for larger molecules. Data for properties of homologous or substituted molecules, in any phase, are quantified with a vector index, and the index for one set can be transformed into that for another set

Two Descriptors for Series of Congeneric Molecules

Two quantitative characterizations are compared for series, each of which consists of a central atom or molecule and successively attached functional groups. The vector index component V2 brings out the periodicity related to the central entity and to the ligands (if they are atoms) or brings out the periodicity related to the substituents (if they are atoms) put into an originating molecule. The Zenkevich parameters also show the periodicity seen in V2 but are valuable for treating data farther from linearity with respect to the number of attached groups provided that there is not an inflection point. An algebraic comparison shows that it is not possible to derive the vector index components from the Zenkevich parameters or visa versa except when the data are exactly linear. </p

Preliminary results in working with molecular modeling software

In order to help facilitate the growing need for an understanding of periodic trends in molecules, an attempt was made to use a molecular modeling software package (ChemCad) to make a series of ab initio calculations of various properties of diaton1ic molecules. limitations of the package precluded calculations for strictly diatomic molecules, as well as precluding consecutive substitution of a large series of atoms into a larger molecule. This attempt does have significance in that it has allowed the physics department at Southern College to more effectively communicate with molecular modeling software developers and users

A graph-theory approach to global determination of octet molecules

Set theory is used to forecast the existence of all possible octet-rule cyclic and acyclic molecules formed from main-group atoms and having ionic and/or covalent bonding with orders up to three

An Atlas of Forecasted Molecular Data. 2. Vibration Frequencies of Main-Group and Transition-Metal Neutral Gas-Phase Diatomic Molecules in the Ground State

This atlas of diatomic-molecular vibration frequencies parallels the previously offered Atlas of Internuclear Separations. The Atlas was produced by mining the data from Huber and Herzberg and training neural network software to forecast new data. New protocols were employed with the powerful software, which was originally designed for forecasting the financial markets. The Atlas presents 1920 additional vibration frequencies for use until critical tables are available to fill the needs more precisely. The precision of the predictions is characterized by the average fractional 1% confidence limit, that is, 10.66%. The accuracies of the predictions are determined in two ways. First, 221 of the 224 Huber and Herzberg data values used for training and validation fall within the prediction confidence limits or fall outside by less than 10% of the Huber and Herzberg values, and 181 values agree (within the limits). Second, 87 of 101 comparison data values, consisting of literature data and some additional Huber and Herzberg values, fall within the prediction confidence limits or fall outside by less than half the prediction values, and 44 of the 101 values agree (within the limits)

The Higgs Boson in the Periodic System of Elementary Particles

It is proposed that the observed Higgs Boson at the LHC is the Standard Model Higgs boson that adopts the existence of the hidden lepton condensate. The hidden lepton is in the forbidden lepton family, outside of the three lepton families of the Standard Model. Being forbidden, a single hidden lepton cannot exist alone; so it must exist in the lepton condensate as a composite of μ’ and μ’± hidden leptons and their corresponding antileptons. The calculated average mass of the hidden lep-ton condensate is 128.8 GeV in good agreements with the observed 125 or 126 GeV. The masses of the hidden lepton con-densate and all elementary particles including leptons, quarks, and gauge bosons are derived from the periodic system of elementary particles. The calculated constituent masses are in good agreement with the observed values by using only four known constants: the number of the extra spatial dimensions in the eleven-dimensional membrane, the mass of electron, the mass of Z boson, and the fine structure constant

An Atlas of Forecasted Molecular Data. 1. Internuclear Separations of Main-Group and Transition-Metal Neutral Gas-Phase Diatomic Molecules in the Ground State

Needed spectroscopic data on diatomic molecules can often be found in the superb critical tables of Huber and Herzberg or in the literature published since 1979. Unfortunately, these sources apply to only a fraction of the diatomic species that can exist and so investigators have had to rely on interpolation, additivity, or ad hoc rules to estimate needed values, all of which require other information that is often lacking. This Atlas presents 1001 additional internuclear separations for use until critical tables are available to fill the needs more precisely. The Atlas was produced by mining the data from Huber and Herzberg for trends with least-squares analysis and with neural network software. There are 162 molecules about whose data Huber and Herzberg had no qualifications and whose data were employed for this work; 248 copies of data with low and high magnitudes were added to reduce the effects of frequency. Internuclear separations for 1001 species not found in Huber and Herzberg are presented, and least-squares predictions supplement some of them. The results, i.e., the Atlas, are presented as Table A, Supporting Information. The average error, based on the average of the absolute differences between the predicted values and tabulated values for the molecules having Huber and Herzberg data, is 0.074 Å; if each error is expressed as a percent of the forecast to which it pertains, the average of these errors is 2.94%. There are 25 “questionable” data from Huber and Herzberg, not used in the preparation of the Atlas, for which predictions are included in the Atlas. Of these, 14 agree with the predicted internuclear separations to within twice the stated errors. Additional atlases for other properties of diatomic molecules are in preparation

Periodic Systems of Moiecules from Group Theory

Atoms are indistinguishable particles which can be transformed one into another by the elements of a group G,1 which corresponds to the internal symmetry of their periodic system. We construct a molecular periodic system using G and bosonic creation operators. The vectors li\u3e = b+ ~o\u3e correspond to various atoms where lo\u3e is the vacuum state vector, and b+i is the creation operator for atom i. The annihilation operator is b;; boson symmetry requires fbrbJ = b+ rb+ J = 0, [bi,b+ j] = 1. State vectors lijk ... \u3e correspond to molecules. They can be recast as a direct sum of irreducible representations whose vectors are (often) linear combinations of individual molecular states. The one-particle operator P1 of the lie algebra of G is I:i,j P1(i;j) b+pj We have tested our systems by plotting a variety of tabulated experimental data along principle axes for atomic and for diatomic and triatomic molecular multiplets

Why Do Molecules Echo Atomic Periodicity?

Franck–Condon factors are investigated for sequences of free main-group diatomic molecules. Theory-based Condon loci (parabolas) and Morse-potential loci are plotted on Deslandres tables to verify if they, indeed, follow the largest Franck–Condon factors. Then, the inclination angles of the Condon loci are determined. Thus, entire band systems are quantified by one variable, the angle. For all available isoelectronic sequences, this angle increases from a central minimum toward magic-number molecular boundaries. The theory for the Condon locus gives the angle in terms of the ratio of the upperstate to the lower-state force constants. It is concluded that the periodicity is caused due to the fact that this ratio becomes larger as rare-gas molecules are approached, a trend that probably points to the extreme cases of the rare-gas molecules themselves. Thus, molecular periodicity echoes atomic periodicity in that data plots have extrema at molecules with magic-number atoms, yet it does not echo the details of atomic periodicity in series between those molecules

How Deep in Molecular Space can Periodicity be Found?

We find occasional echoes of periodicity, i.e. the trends found in the chart of the elements, in several-atom (up to 32) molecules and use it to make forecasts for molecular data, some of which have been confirmed