The Number of Isomeric Hydrocarbons of the Methane Series

Henze, Henry R.; Blair, Charles M.

doi:10.1021/ja01359a034

Cited by 88 publications

(37 citation statements)

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“…The enumeration (and canonization) of all possible constitutional isomers has been the focus of long standing graph-theoretical efforts. [8][9][10][11] The exponential scaling of their number is also evident for the recently published exhaustive list of small organic molecules. [12] This is the regime in which isomerism occurs through conventional ' 'chemistry,' ' that is, chemical reactions that lead from one constitutional isomer to another, usually under the influence of pressure, temperature, light, or some catalytic agent.…”

Section: Energy Hierarchymentioning

confidence: 79%

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Lilienfeld

2013

Int J of Quantum Chemistry

138

160

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A well‐defined notion of chemical compound space (CCS) is essential for gaining rigorous control of properties through variation of elemental composition and atomic configurations. Here, we give an introduction to an atomistic first principles perspective on CCS. First, CCS is discussed in terms of variational nuclear charges in the context of conceptual density functional and molecular grand‐canonical ensemble theory. Thereafter, we revisit the notion of compound pairs, related to each other via “alchemical” interpolations involving fractional nuclear charges in the electronic Hamiltonian. We address Taylor expansions in CCS, property nonlinearity, improved predictions using reference compound pairs, and the ounce‐of‐gold prize challenge to linearize CCS. Finally, we turn to machine learning of analytical structure property relationships in CCS. These relationships correspond to inferred, rather than derived through variational principle, solutions of the electronic Schrödinger equation. © 2013 Wiley Periodicals, Inc.

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Section: Energy Hierarchymentioning

confidence: 79%

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Lilienfeld

2013

Int J of Quantum Chemistry

138

160

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“…For example, it has been estimated that oligomers of 1-decene in the C 30 and C 40 range can have well over 6 × 10 13 isomer structures. 7 This large number of structures presents the lubricant formulator with two major problems: (1) Which of the countless PAO isomers produce a lubricant with superior performance properties? (2) Given a target isomer, how does one go about tailoring the reaction conditions such that the desired species is formed at high levels?…”

Section: Introductionmentioning

confidence: 99%

Molecular Simulation of Poly-α-olefin Synthetic Lubricants: Impact of Molecular Architecture on Performance Properties

and

Maginn

1999

J. Phys. Chem. B

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Equilibrium and nonequilibrium molecular dynamics simulations are performed at constant pressure and temperature on three structurally distinct poly-R-olefin (PAO) isomers representative of a major component in synthetic motor oil basestock. In agreement with empirical observations, the temperature dependence of viscosity, as characterized by the viscosity number (VN), is reduced as the degree of branching is lowered. A molecular-level explanation for this behavior is given in terms of the energy barriers for intramolecular reorientation. Other dynamic properties, such as the diffusivity and rate of tumbling, were also computed and found to have similar dependencies on temperature as the viscosity. Based on these calculations, it appears that PAO molecules with long, widely spaced branches should yield a higher VN than those with short, closely spaced branches. The impact of shear rate on PAO properties is also investigated. High shear rates and shear-thinning increases the VN because the behavior of the fluid is largely dominated by the flow field rather than by the thermodynamic state point. Contrary to what has been observed with linear alkanes, it is observed that molecular alignment with the flow field does not always correlate with enhanced shear-thinning. These observations are explained in terms of a competition between the shear forces responsible for aligning the molecules and intermolecular forces that resist shear-thinning. The results of the present work provide molecular-level explanations for the favorable lubricant properties exhibited by "star-like" molecules and suggest an important strategy for assisting in a more rational approach toward the development of improved lubricants and additives.

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“…20 As for a mathematical foundation for linking between rooted trees (or alcohols or monosubstituted alkanes) and trees (or alkanes), Jordan's work 21 on the dichotomy of centroidal and bicentroidal trees should be cited, because Cayley's accomplishments relied on this dichotomy. In addition, we should refer to a chemical approach conducted by Henze and Blair, 22,23 where aliphatic alcohols (rooted trees) and alkanes (trees) were enumerated after the development of recursive formulas. 22,23 Pólya, a mathematician developed a versatile theorem named after him (Pólya's theorem), 24 where a permutation group governing the symmetry of molecules was used to enumerate isomers as graphs.…”

Section: How Does Chemistry Link With Mathematics?mentioning

confidence: 99%

“…In addition, we should refer to a chemical approach conducted by Henze and Blair, 22,23 where aliphatic alcohols (rooted trees) and alkanes (trees) were enumerated after the development of recursive formulas. 22,23 Pólya, a mathematician developed a versatile theorem named after him (Pólya's theorem), 24 where a permutation group governing the symmetry of molecules was used to enumerate isomers as graphs. As an application of Pólya's theorem, Pólya himself enumerated trees (as mathematical objects) or alkanes (as chemical objects), which were regarded as graphs or constitutional isomers.…”

Section: How Does Chemistry Link With Mathematics?mentioning

confidence: 99%

Numbers of Alkanes and Monosubstituted Alkanes. A Long-Standing Interdisciplinary Problem over 130 Years

Fujita¹

2009

Bulletin of the Chemical Society of Japan

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Enumeration of alkanes and monosubstituted alkanes with given carbon contents has been investigated by chemists and mathematicians over 130 years and solved recently by the present author in agreement with stereochemical and mathematical requirements. In the present account, the advances of the methodologies for solving the problem are discussed from an interdisciplinary point of view between chemistry and mathematics. Historical backgrounds of the interdisciplinary problem are introduced by emphasizing three epochs, i.e., the first epoch marked by Cayley, a mathematician (the 1870s), the second epoch by Pólya, a mathematician (the 1930s), and the third epoch by Fujita, an organic chemist (the first decade of this century). Among them, the accomplishments of the second epoch and those of the third epoch are compared in detail, where graphs (trees, rooted trees, or planted trees) and three-dimensional (3D) objects as mathematical terms are correlated to constitutions (two-dimensional structures) and 3D structures as chemical terms.After an introduction to terminology on isomerism and stereoisomerism, alkanes and monosubstituted alkanes are enumerated as graphs or constitutional isomers by Pólya's theorem, while they are alternatively enumerated as 3D objects or 3D-structural isomers by Fujita's proligand method. The present account of the long-standing problem would provide readers with a hint or a motivation for pursuing a concrete route to "the Heavens of Fujita," which have caricatured stereochemical and mathematical barriers lying in wait for them.

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The Number of Isomeric Hydrocarbons of the Methane Series

Cited by 88 publications

References 0 publications

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Molecular Simulation of Poly-α-olefin Synthetic Lubricants: Impact of Molecular Architecture on Performance Properties

Numbers of Alkanes and Monosubstituted Alkanes. A Long-Standing Interdisciplinary Problem over 130 Years

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