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Systematics of Diatomic Molecular Transition Moments: Encouraging Progress -- II Literature absolute transition moments for A-X(0-0) bands have been compiled and used to obatin "best" values of Re for some 90 transitions. Correlations were sought between Re and various molecular parameters such as multiplicity, average internuclear separation, etc. None was found. The A-X (and related) Re have been plotted for isoelectronic molecules against the nulclear charge difference and fitted with simple curves which seem to approach the Re axis with zero slope. Both of these results are in accord with theory. The concept of isovalence has been clarified to allow for the orbital structure of molecules. It appers that the heavier of two isovalent hydrides has the greater Re. Graphs of Re for groups of isovalent molecules can be fitted with simple curves.
The Periodic Table of Diatomic Molecules -- I. An Algorithm for Retrieval and Predication of Spectrophysical Properties Related
periodicities in properties of diatomic molecules are well known and
periodic tables have already been constructed for some classes of molecules.
The major difficulty is that two orthogonal periodicities are superposed,
at 45° on the Z1,Z2 plane,
on two others. Our proposed complete table is formed by cutting the
plane along the Z1 and Z2 directions
and stacking areas for similar molecules into 15 blocks. Evidence is
presented that 15 is the correct number and that the stacking orders
are optimal. It is shown that generalization to ionized molecules requires
a fouth dimension, but that this 4-d architecture can be mapped
into three dimensions. Computer curve-fitting of data has yielded initial
results for re in three blocks. 116 data fitted to
re = A + ln Öc
(where c is area number, and A depends
on the compartment, in the block) differ from tabulated data by
A Periodic Table of Free Diatomic Molecules -- II. Predicted Internuclear Separations from Curve-Fitted Data Recent theory substantiates the stacking order of the areas in the recently proposed periodic table of the free diatomic molecules. The periodic table suggests curve-fitting algorithms for re which, after semi-empirical perturbations, yield ground-state values for re which agree with literature values and with those from an alternate algorithm from 5 to 8%. 800 predicted re extend to superheavy qausimolecules and to molecules with superheavy atoms, and many pertain to molecules of laser interest.
The Periodic System for Free Diatomic Molecules -- III. Theoretical Articulation A periodic system for free neutral diatomic molecules, previously proposed on the basis of tabulated data, is shown related topologically to the chart of the atoms. The relation is generalized to ionized atoms and ionized molecules. Support is drawn from tabulated data.
Systematics of Ground-State Potential Minima Between Two Main-Group Atoms of Ions The featured figure in this paper was prepared for three purposes: (1) to demonstrate the vivid periodicities among tabulated internuclear separations re of diatomic molecules and quasimolecules formed from main-group atoms and ions,1 (2) graphically to compare the known re for van der Waals molecules to see what might be expected in future experiments on other van der Waals molecules, and (3) to ascertain the extent to which isoelectronic diatomic molecules along the homonuclear direction of the Z1, Z2 plane (e.g., LiCl- and BeAr+) have constant re.2
Priodicheskaya Sistema Dvukhatomnykh Molekul: Teoretiko-gruppovoi Podkhod The group-theoretical construction of the periodic system for diatomic molecules is suggested. Six quantum numbers are introduced for enumerating molecules. The system developed is in good agreement with the periodic system previously proposed on the basis of the tabulated data by Hefferlin ad others.
The Differential Coefficient ( The coefficient (
Periodic Systems of N-atom Molecules The atoms have long been classified into a periodic system, which is now based on quantum mechanics and group theory. A classification of molecules containing any number (N) of atoms is proposed. It is an extension of the periodic system of the atoms. The approach in this paper is that of group theory, although the proposed system has been subjected to exhaustive comparison with experimental and ab initio computational results for diatomic molecules, and conforms to the commonly known behaviors of molecules with larger N. Orthonormal transformations are performed so that the molecules can be arranged according to their numbers of electrons and to the differences of atomic numbers of the constituent atoms. These arrangements parallel the physical reality of atomic bonding and permit partial three-dimensional models of the systems to be constructed for molecules with as many as four atoms. We show how vast amounts of information have been, or can be, formulated into arrays with periodic and monotonic axes. For example, we propose a Periodic System of nuclei for the first time. We consider two cases where Periodic Systems in the natural world can be bootstrapped from objects of one size to objects of the next larger size. The mathematical methods in the two cases are essentially equivalent. We apply the methods to linguistics in an exploratory way. Then we construct a Periodic System of all the Periodic Systems previously discussed. The 50th Anniversary of work on molecular periodic systems: Broad scientific and human-interest aspects As the result of rapidly accelerating work begun 50 years ago, there now exists an understanding of the Periodic Law for Molecules, and there now exist numerous forms of Periodic Systems of Molecules. This work is descried in broad strokes, with attention to its human interest aspects. (We have since found that Grimm in 1935 was not the first to construct some sort of molecular classifications scheme) Periodic Systems of Molecules and their Relation to the Systematic Analysis of Molecular Data (Table of contents) Classification of Molecules and Group Theory We review the group-theoretical investigation into the periodicity of the elements and then the researches into the major and the minor periodicities of molecules. The results agree with the periodic law and allow building of periodic systems of molecules. (No abstract) Bosonic Symmetry and Periodic Systems of Molecules The phenomenological group-theoretical interpretation of the periodic system of chemical elements, given by Rumer and Fet (1971) and by Barut (1971), prompted us to work on development of the periodic systems of molecules based on the same interpretation [Zhuvikin, Hefferlin (1982), Hefferlin et al (1984), Hefferlin (1989)]. Our new concept, presented in this paper, is to join to this group-theoretical approach for molecular systems the formalism suitable for bosons. Thus, the periodic chart of the elements, instead of being multiplied by itself into higher-dimensional spaces, serves as a kind of template for multiplets of molecular state vectors created by Lie algebras. Matrix-product Periodic Systems of Molecules Direct products of the periodic chart of the elements, considered as a matrix, with itself produce 2N-dimensional periodic systems of N-atomic molecules. It is shown that these periodic systems subsume a large number of published molecular periodic systems. Symmetry Principles for Periodic Systems of Molecules Extensive research, most of it inspired by fundamental-particle physics,
has been done on the group-dynamic foundations of the classification
of atoms known as the periodic system. Also, a very great deal of work
has been carried out for a century on varieties of ways to classify
molecules and to predict the properties of new ones in a systematic
way. Much of this work has been motivated by the need for small-molecule
astrophysical data and for pharmaceutical data. It is the purpose of
this paper to employ the methods of group dynamics, as they have been
applied to atoms, for the molecular classification problem. We begin
with known bosonic creation and annihilation operators, since any number
of identical atoms may be present in a molecule. Then we define state
vectors in the space H(N) of N-atomic molecules.
We require that this space be decomposed into irreducible representations
(IR's) of a group with demonstrated applicability to the classification
of atoms; the basis vectors of these IR's form multiplets of molecules
which bear a great deal of similarity to multiplets of atoms. Finally,
we show how to formulate observable operators of various orders and
in several approximations; these operators provide expectation values
expressed as functions of state quantum numbers. (In a later paper we
show how tabulated experimental data for various properties, substituted
into these expectation values and plotted one multiplet at a time, produce
surfaces which are periodic, are often well-behaved, and allow estimation
of molecular data.) In the paper we list the symmetry groups to be treated
and describe the role which each of them plays in classifications of
atoms. We take up compact multiplets in conformal symmetry: SO(3),
SO(3)xSU(2)s , SO(3)xSU(2)d
, SO(3)xSU(2)s xSU(2)d , SO(4)xSU(2)s
, and Periodic Systems of Molecules: Physical and Chemical This paper is a review of research on molecular periodic systems, a developed field of research. The distinguishing characteristics of Physical Periodic Systems are that they include only molecules with a given number of atoms, e.g., diatomic molecules (N=2), and that all relevant molecules with that number of atoms are or can be included. Physical Periodic systems are defined as follows: a Physical Periodic System for N-atom molecules is the outer N-product of an originating atomic periodic table, or can be generated from such a product system by use of slicing or projection techniques to include only molecules with a given number of atoms, e.g., diatomic molecules (N=2); they include recent classifications based on group dynamics. The distinguishing characteristic of Chemical Periodic Systems is that they contain molecules with differing numbers of atoms. It is also a characteristic that they include only molecules stable under a well-known set of conditions (such as atmospheric-pressure wet chemistry). Work related to each kind of system is described chronologically, whether or not the work was identified as a periodic system by its author. All publications claiming to present molecular periodic systems (and of which the authors are aware) are listed, in an effort to achieve a complete review of the rapidly growing field. Finally, a recommendation is made that future classification systems be identified as Physical or Chemical periodic systems, in accordance with the distinguishing characteristics. Care should be taken to ensure that a system truly displays periodicity, and is not just an interesting lattice. Fizicheskie i khmimicheskie periodicheskie sistemy molekul This paper is a review of research on molecular periodic systems, a developed field of research. The distinguishing characteristics of physical periodic systems are that they include only molecules with a given number of atoms, e.g., diatomic molecules (N=2), and that all relevant molecules with that number of atoms are or can be included. Physical periodic systems are defined as follows: a phyical periodic system for N-atom molecules is the outer N-product of an originating atomic periodic table, or it can be generated from such a product system by the use of slicing or projection techniques to include only molecules with a given number of atoms, e.g., diatomic molecules (N=2); they include recent classifications based on group dynamics. The distinguishing characteristic of chemical periodic systems is that they contain molecules with differing numbers of atoms. It is also a characteristic that they include only molecules stable under a well-known set of conditions (such as atmospheric-pressure wet chemistry). Work related to each kind of system is described chronologically, whether or not the work was identified as a periodic system by its author. All publications claiming to present molecular periodic systems (and of which the authors are aware) are listed, in an effort to achieve a complete review of the raplidly growing field. Finally, a recommendation is made that future classification systems be identified as physical or chemical periodic systems in accordance with the distinguishing characteristics. Care should be taken to ensure that a system truly displays periodicity and is not just an interesting lattice. Analysis of Group Theoretical Periodic Systems of Molecules using Tabulated Data The second of a series, this paper substantiates the theory given previously by substituting tabulated data for observable operator expectation values of molecular-state-vector multiplets corresponding to the groups SO(3)xSU(2)s , SO(4)xSU(2)s , and SO(2,1). We plot the data on the principle axes of the multiplets using various orders of observable operators and expectation value identities whose particular merits are discussed. The generally well-behaved plots for the first and third symmetries demonstrate a similarity between various N-atomic species, one example of invariance for different properties, periodicity with respect to changes in the row numbers of the constituent atoms, and inclusive similarity in many cases where the independent variable ranges of one multiplet lie within those of another multiplet. We examine advantages and disadvantages of several expectation value identities and find that the group SO(4)xSU(2)s produces poorly behaved plots. Comment on "Periodicity and Peculiarity in 120 First- and Second-row Diatomic Molecules" (Part of first paragraph; no abstract) Complete, Verified, Group-dynamic Molecular Periodic Systems We present periodic systems of molecules which (1) agree with the periodicities observed in molecular data, (2) classify molecules so those with similar data are located "closer" together than those with dissimilar data, which (3) are analogous to the periodic chart of the elements, (4) are very much similar to it in form, (5) allow the estimation of data for some neutral, ground-state, gas-phase molecules, and (6) are rigorously based on group dynamics with boson operators. A complete wall-chart periodic system for all diatomic molecules in symmetry the SO(3)xSU(2)s is available on request from the third or fourth authors. The wall chart shows a schematic of the periodic system for triatomic molecules (also under the same symmetry). This presentation explains why the periodic systems are needed, refers to the earlier use of group dynamics as an alternate theoretical basis of the periodic chart of the elements using the symmetry SO(4,2)xSU(2)s, outlines the general approach used in the construction of the periodic systems of molecules, refers to instructions on reading the wall chart, presents some of the graphical evidence that the systems agree with tabulated molecular data, and alludes to the strategy we are employing to approach the construction of molecular periodic systems with the general symmetry, SO(4,2)xSU(2)s, of the chart of the elements. Periodic Systems of Molecular States from the Boson Group Dynamics of SO(3)xSU(2)s An overview of the principles of group-dynamic periodic systems is given. The process by which molecular multiplets are obtained is then described. Plots of observable operator expectation values for SO(3)xSU(2)s and SO(2,1) multiplets clearly demonstrate periodicity. To construct molecular periodic systems, these multiplets are situated in coordinates which are their chemical quantum numbers along with the principal quantum number coming from the SO(4,2)xSU(2)s group chain. Equivalence classes of substitutable (isomorphic) molecular multiplets are then defined for the two symmetry groups. The structures of the resulting molecular periodic systems are shown using plots of the number of multiplets located at given chemical-quantum-number coordinates. Molecular Multiplets of Alkaline Atoms Molecules formed from alkali-metal atoms are classified with the apparatus of group dynamics. The groups SO(1,2), SO(3), and SU(?) are used in turn. Ionization potentials (IP) of diatomic combinations of Li-Cs display symmetry-breaking consistent with the group chain SU(?)? SU(1). Known IP of triatomic combinations of Li-K are used to predict values of three unknown species: LiLiK, LiNaK, and LiKK have IP of 3.9, 3.8, and 3.6 eV, respectively. The Concepts of Periodicity and Hyper-periodicity: from Atoms to Molecules (Table of contents) Periodic Systems of Molecules as Elements of Shchukarev's "Supermatrix", i.e. the Chemical Element Periodic System Generations of Soviet scientists contributed invaluable insights into molecular classification. Unfortunately, this research is little appreciated in much of the world. Among these workers S. A. Shchukarev was of great importance. His and his followers’ legacy includes a host of graphical displays showing enthalpies of formation of gaseous molecules from free atoms Delta Ha, and standard enthalpies of formation of substances ?Hfo plotted on the atomic number of the central elements, on their oxidation states, their internuclear separations, and other variables for a wide range of molecules. These graphs serve as databases, from which data can be extracted, to moderate precision, visually. We discuss graphs for one very limited set, or “pleiade” (gas- phase oxides of nitrogen), and for three much broader sets, or subsystems, (gas-phase fluorides of all main subgroup atoms, and oxides of transition-metal atoms in gas-phase and in STP conditions). When dissolved in water, molecules lose their identities but periodicity is echoed in the acids and aquocations that are formed. We show, as an example in tabular form, that redox potentials of high-oxygen acids containing S, Se, and Te change concomitantly with Delta Ha and Delta Hao of their hexafluorides. We present graphical evidence that three properties for cations of groups 1 to 3 (in the short version of the periodic chart) behave similarly and share the periodicity of the elements. One of the properties is related to the ionization potential, which is shown in a tabular example to vary concomitantly with energy of hydration. It was the ultimate goal of S. A. Shchukarev that the transformation of any one graphical database into any other, having different molecules under different conditions, would be made mathematically. Adjacent-DIM-isoelectronic Molecules and Chemical Similarity among Triatomics Isoelectronic molecules and isovalent molecules commonly have chemical
similarity. This paper adds a third distribution of molecules and demonstrates
that it exhibits chemical similarity in the case of linear/bent triatomics:
the similarities of same-period triatomics which have equal C1
+ 2C2 + C3 The Learning and Prediction of Triatomic Molecular Data with Neural Networks (First section; no abstract) Global Forecasting of Data Using Least-squares Methods and Molecular Databases: a Feasibility Study Using Triatomic Molecules This paper shows that it is feasible to make rapid forecasts of data for large numbers of molecules by using least-squares smoothing of tabulated data, though the forecasts are not as precise as those from quantum-chemical computation packages which deal with one molecule at a time. The molecules' properties were chosen to be of value in plasma and astronomical physics. The work begins with the graphical analysis of critically-analyzed data for ground states of neutral, acyclic, main-group, row 2 to row 6, triatomic molecules to infer a least-squares smoothing equation. The equation is quadratic in a function (R1R2 + R2R3) of the atomic period numbers, quadratic in the group number of the central atom, and cubic in the total number of valence electrons. The coefficients of the equation (some of them zero for some properties) were obtained from high-quality tabulated data for heat of atomization, ionization potential, log of the partition function at 1000K, and log of the partial-pressure equilibrium constant for the constituent atoms over the diatomic molecules at 1000K. The equation with its coefficients were tested by comparison with data, from the same tabulations, for a few molecules not in the original set. Finally, values were forecasted for 164, 145, 107, and 164 additional molecules, for four the properties listed above and in order the same order. Least-squares and Neural-network Forecasting from Critical Data: Diatomic Molecular re and Triatomic DeltaHa and IP Multiple regression was used to predict 299 diatomic internuclear separations using atomic period and group numbers as a basis. Van der Waals molecules were excluded. The standard deviation of the differences of predictions from 150 tabulated data is 4.128%. Neural networks, one with van der Waals molecules in the learning set and one without, each predicted the property for 2,145 real and non-redundant molecules; of the differences of the predictions from 342 and 316 tabulated data are 25.00% and 8.63%. For comparable cases, the least-squares technique was more accurate. Multiple regression has been used to predict 205 triatomic ionization potentials using a 3-d basis consisting of combinations of atomic period and group numbers. The of differences from 80 tabulated data is 14.65%. Neural networks using the same 3-d basis and using a 6-d period and group number basis have predicted the IP for 2,596 and for 5,148 molecules; the of the differences from 69 and 92 tabulated data are 12.35% and 10.97%. The neural network method was more accurate than the least-squares technique. Neural networks using the same two bases have predicted the bonding energies for 16,324 and for 5,418 molecules; the of the differences from 79 and 117 tabulated data are 22.67% and 15.13%. Field Theory for Chemical Spaces The periodic chart of the elements, and periodic systems of molecule,
are constructed in what are known as chemical spaces. Properties of
target atoms or molecules can be interpolated one by one (the triad
principle) or they can be iteratively interpolated all at once for points
inside well-selected boundaries (the numeric solution to Laplace's equation).
Examples will be shown for both atomic and molecular data. The second
derivatives in the Laplace equation describe the curvatures of the data
along the appropriate axes, and so if the curvature is known in along
one or more axes, then the curvature along the remaining axis may be
predicted. Examples of this phenomenon will be presented. This connection
of the triad principle with Laplacian field theory is not only interesting
in that it connects a simple concept in two disparate disciplines, but
also it is useful in the important tasks of molecular data analysis
and molecular design. Systematics of Diatomic Molecular Transition Moments Highly accurate intensity constants for bands in diatomic-molecular spectra are now available in the RADEN data bank. This paper uses them to improve earlier systematics of D(<R>) for A-X and related (0,0) bands. The data are plotted to determine trends and wherever possible a heuristic equation is used to smooth them. Isoelectronic, dimer, hydride, and halide molecules are considered. Isoelectronic series containing a total of 28 molecules are plotted on Z1-Z2|, the absolute difference of the atomic numbers of the two atoms in the molecules. The data become rapidly larger as rare-gas molecules are approached, behaving in a qualitative way like the internuclear separation re. Dimers from periods R = 2 and 3 behave similarly to each other, which is evidence for periodicity in diatomic data. The ad hoc function D0(<R>) = 0.33+0.054Cosh[1.5(C-4.2)], where 1<= C <= 6 or 7 is the group number of either atom, describes their behavior reasonably well (C = 1, 2, 13, ... 16 or 17 in the IUPAC scheme). For unipositive dimers, D+(<R>) = 0.25+0.016Cosh[(1.5(C-5)] tracks the behavior as well but with one outlier (C). 15 neutral hydride and 11 unipositive hydride molecular data show clear periodicity when plotted versus Z1+Z2. The hydride data have nearly linear behavior, with increasing slopes for R = 2 to 4, when plotted on a function suggested by the 1/Z dependence of atomic oscillator strengths, with one major exception (CaH). The function is F0 = [1/(ne1+ne2)]-0.14, where nei is the valence-electron count in atom i. The unipositive hydride data have close to linear behavior, with increasing slopes for R = 2 and 3, when plotted on the similar function F+=[1/(ne1+ne2)]-0.10, also with one major exception (BeH+). Clearly evident trends for halide molecules allow making qualitative estimates for two unknown transition strengths. Numerical Solutions of the Laplace Equation in Chemical Space The triad principle states that numerical values of properties of atoms and molecules can be obtained by interpolation in their chemical spaces. This principle is associated with the numerical solution to the Laplace equation. The Textures of Chemical Spaces The classification of small molecules and the forecasting of small-molecular data has advanced far in recent years, stimulated by needs in astrophysical and laboratory plasmas. The systematization of larger species has also progressed, prompted by the demands of environmental, toxicological, and pharmaceutical chemistry. Here is presented a first known thorough analysis of the chemical spaces in which molecules are placed in the course of these systematizations. The approach is to ask "What can we learn about the chemical spaces on the basis of the gas-phase spectroscopic and thermodynamic data displayed by the molecules placed in them?" In other words, this paper is a first attempt to look heuristically at data as if derived from the properties of chemical spaces rather than as descended from quantum mechanics or group dynamics. It is found that there are in some spaces salient lines, planes, and hyperplanes on which molecules become homonuclear and homovalent; on which species become isoelectronic or at least have the same numbers of valence electrons; and on which molecules take on extreme and least-descent intermediate data values. The spaces have certain symmetries or broken symmetries with respect to the first of these loci. An algebraic formulation of Lewis-bond structures leads to the discovery of salient lines, planes, and hyperplanes on which molecules assume closed-shell covalent or ionic structures. A field theory of chemical spaces is reviewed, it being pointed out the extent to which the discretized Laplace equation applies. New data have been forecasted by this equation. Molecular ions, and alloys and Bertheloids, lie at non-integer positions in chemical spaces. Molecular Similarity for Small Species: Refining the Isoelectronic Index This paper tests a chemical-similarity model against properties of gas-phase neutral triatomic and four-atom molecules. The model is a variant of the Diatomics-in-Molecules (DIM) picture, which considers a molecule to be the superposition of all diatomic molecules that could be formed from adjacent atoms in the molecule. The variant is that adjacent atoms are counted as a diatomic molecule only if they are bonded. The tests consist of investigating whether molecules with the same number of electrons, computed by the adjacent-DIM model, have data more similar than do molecules selected at random. The tests vindicate the model for the heat of atomization and for the equilibrium constant for formation, they agree with the model with lesser confidence for the entropy and the partition function, and they show that the model fails for the ionization potential. The model applies with most confidence to molecules with the more electronegative atoms from rows 2 or 3 (those of greatest interest in organic chemistry), and with lesser confidence otherwise. For these properties and these molecules, the model passes graphical and statistical tests at least as well as does the traditional isoelectronic model. Thus, this work refines what may be called the isoelectronic index. On the Use of Laplace's Equation for Global Predictions of Internuclear Separation and Dissociation Energy Properties of target species can be estimated by various means including interpolations in periodic charts. Interpolation is equivalent to numerical solution of the Laplace equation. A test of this equivalence, within some confidence level, for any N-atomic molecule surrounded by 4N nearest neighbors: the sum of the second differences of the data in all directions must be zero. Since very few molecules have 4N neighbors with known data, the test becomes: the sum of the averages of the second differences must be zero. The validity of these tests is explored. For radii of main-group atoms, and for internuclear separations of their diatomic combinations, the averages are different from zero and the sums of the averages are zero to within one if second-nearest neighbors are used. Dissociation potentials pass the tests but with larger scatter. Predictions for dissociation potentials, using iterative interpolation within boundaries on which there are known data, are reviewed. The Periodic Systems of Molecules: Presuppositions, Problems, and Prospects A taste of the philosophical and historical aspects of the scientific enterprise for professional chemists, and a glimpse of scientists’ ontology and epistemology for philosophers and historians. The narrative is based on a limited endeavor with most of whose living participants the author has a personal acquaintance. The endeavor consists of creating, testing, and utilizing organizations of molecular symbols in architectures of two or more dimensions. These periodic systems play the same role for molecules as the chart of the elements does for individual atoms. The presuppositions, on several levels, that contributed to the creation of molecular periodic systems are explored. Problems faced by some systems are exposed, including the difficulty of visualizing them in multiple dimensions and the challenge of finding not molecular symbols, but linear combinations of symbols, in the compartments. Prospects for further maturation and usefulness of the periodic systems are presented. Global Molecular Identification from Graphs. Neutral and Ionized Main-Group Diatomic Molecules Diophantine equations and inequalities are presented for main-group closed-shell diatomic molecules. Specifying various bond types (covalent, dative, ionic, van der Waals) and multiplicities, it becomes possible to identify all possible molecules. While many of the identified species are probably unstable under normal conditions, they are interesting and present a challenge for computational or experimental analysis. Ionized molecules with net charges of -1, 1, and 2 are also identified. The analysis applies to molecules with atoms from periods 2 and 3 but can generalized by substituting isovalent atoms. When closed-shell neutral diatomics are positioned in the chemical space (with axes enumerating the numbers of valence electrons of the free atoms), it is seen that they lie on a few parallel isoelectronic series. Global Molecular Identification from Graphs. Main-Group Triatomic Molecules It is required that molecules with a given graph and with covalent, coordinate-covalent, and ionic bonding contain closed-shell atoms. This requirement results in an equation for each atom, which states that the number of valence electrons pertaining to it before bonding, plus those made available to it in the bonding processes, close its valence shell. Solving the equations results in identifying the atoms and the bond orders of the Lewis diagrams. The algebraic procedure can identify new species. Some of them may be considered impossible (for instance, with high steric strain), or may be transitory, or may be found only under the most unusual conditions. Lists of triatomic molecules, clusters, and resonances found by solving the equations is presented. The code for the computer program that identifies the species is listed. Closed-shell molecules lie on parallel planes in their chemical spaces, namely those on which isoelectronic molecules are located. Global Molecular Identification from Graphs. IV. Molecules with Four Closed p-Shell Atoms and Beyond The identification of main-group molecules having atoms with closed valence p shells, i.e., having atoms with eight valence electrons, is continued into the realm of four-atom molecules. All possible covalently-bonded species, obtained from two independent computer programs, are shown. The method for generalizing to molecules in which some or all atoms have closed valence s shells, i.e., having atoms with two valence electrons, is recalled. A list of all prototype linear/bent four-atom molecules, with dative bonds in addition to covalent and/or van der Waals bonds, is presented (permutations having been culled out). A program code, lists of molecules based on other graphs, and lists of five- and covalently-bonded six- atom species, are available on the Web. For molecules derived from the two other four-vertex graphs, their vast numbers require extensive indexing schemes for the results to be useful. The paper concludes with some preliminary observations concerning the stabilities of four-atom molecules having atoms with closed shells. An Atlas of Forecasted Molecular Data I: 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 Herzberg1 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 so that the neural network software might train well throughout the range of magnitudes. Internuclear separations for 1001 species not found in Huber & Herzberg are presented, and least-squares predictions supplement some of them. The results, i.e., the Atlas, are presented as an appendix in Table A. 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 Ĺ; 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 21 "questionable" data from the 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 the stated errors and five more agree to within twice the stated errors. Additional atlases for other properties of diatomic molecules are in preparation. 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). Neural Networks in Mining Molecular Properties from Tabulated Data The use of neural networks for the study of molecular data is not new, however the protocols are still imperfect. We discuss frequency compensation, choice of error measure, and use of a genetic algorithm for variable selection. We show how the determination of an optimal number of models was made both by culling from a greater set those with large errors and by starting from models with low error and few nodes and adding more models until the average, over all molecules, of the error standard deviation reached a minimum. 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. A Periodicity-Sensitive Vector Index for Small Molecules In the vastness of molecular space there are many series X, XY, …, XYn…XYN, where N is lies between 3 and less than say 50, whose data for a given property and phase are approximately linear with respect to n. We develop a vectorial representation of the tabulated data in a series, and a vector index to describe the series. We start with X as a metallic atom and with the property as heat of atomization, and show that the vector index manifests periodicity. We then move to cases where X is itself a molecule and where the properties are enthalpies of formation, entropy, retention index, hydrophobility, and boiling point. The vector index is a two-dimensional vector whose upper element describes the value of the property for the atom or molecule X and whose lower element describes the abscissa difference of any two members of the series after the data have been fitted, in least-squares fashion, to a standard, linear with n, series A, AL, … ALn, … ALN. Matrices can transform the data vectors of any series of species whatsoever to any other series of the same imensionality. Matrices can also transform the vector index for property data of any approximately linear series, in any phase, to the vector index for any other approximately linear series. Hasse Diagrams and their Relation to Molecular Periodicity Hasse diagrams are applied to molecules and radiation phenomena. Then the relation of these diagrams to periodicity in atoms is noted. The possibility is raised that Hasse diagrams can also be related to the growing body of evidence that periodicity exists in molecules with two, three, and four atoms; in binary inorganic molecules; and in some organic molecules. A Moebius-Strip Representation of the Matrix-Product Periodic System of DiatomicMolecules Hasse diagrams are applied to molecules and radiation phenomena. Then the relation of these diagrams to periodicity in atoms is noted. The possibility is raised that Hasse diagrams can also be related to the growing body of evidence that periodicity exists in molecules with two, three, and four atoms; in binary inorganic molecules; and in some organic molecules. Algebraic Characterization of Simple Transition-Metal Molecules This work extends previous studies of molecules with main-group atoms to those also containing transition-metal atoms. The maximum oxidation states of group 3 to 7 atoms are succinctly described by the same algebraic equation that applies to ionically-bonded main-group atoms in molecules. Covalently bonded transition-metal molecules are characterized by the same equations that apply to main-group species, except that the octet rule is supplemented by the rule of 18, and a proposed rule of 12. Examples are given of organo-metallics with simple ligands and of transition-metal atoms in p-ring sandwiches. The solutions for a special case of the same equations apply to the gas-phase diatomic species which are of such importance in stellar and planetary atmospheres and in combustion devices. 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. A Periodicity-Sensitive Vector Index for Small Molecules 2. Simplifications and additional evidence of periodicity In a previous paper, a “Periodicity-Sensitive Vector Index for Small Molecules” was defined to characterize a central atom (or molecule) and a progressively larger number (n) of identical atomic (or molecular) ligands or substituents which have some property varying (approximately) linearly with n. A significant simplification of the mathematical methods is presented in this paper. The lower component of the index is demonstrated to be periodic for transition-metal atom oxides. Very recent work by Zenkevich is shown to provide at least one of the two vector-index elements.
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Last Updated 09/04/2007 By Ray Hefferlin. © 2007 Physics at Southern |
@ 3%. 254 predicted re
are given, some of laser interest, some of superheavy (quasi) molecules,
and some for molecules with superheavy atoms.
P/
g(C) where Ci is the number of valence
electrons of atom i and where i = 2 is the middle atom.
It is shown, by graphical and statistical analyses of critically analyzed
data for several observables of main-group molecules, that molecules
with constant g(C) are at least as similar as isoelectronic
molecules and are vastly more similar than are molecules chosen at random.
It is suggested that since g(C) can be written additively
as (C1 + C2) + (C2
+ C3) a theoretical basis for the new tool might be
constructed using a "diatomics-in-molecules" (DIM or similar
theory in which the 1-3 bond is ignored. The generalization to molecules
with more than three atoms is presented.