scholarly journals Calculation of Five Thermodynamic Molecular Descriptors by Means of a General Computer Algorithm Based on the Group-Additivity Method: Standard Enthalpies of Vaporization, Sublimation and Solvation, and Entropy of Fusion of ordinary Organic Molecules and Total Phase-Change Entropy of Liquid Crystals

2017 ◽  
Author(s):  
Rudolf Naef ◽  
William E. Acree Jr.
Keyword(s):  
Liquid Crystals ◽  
Phase Change ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Organic Molecules ◽  
Enthalpy Of Fusion ◽  
Computer Algorithm ◽  
Group Additivity ◽  
Entropy Of Fusion ◽  
Total Phase

The calculation of the standard enthalpies of vaporization, sublimation and solvation of organic molecules is presented using a common computer algorithm on the basis of a group-additivity method. The same algorithm is also shown to enable the calculation of their entropy of fusion as well as the total phase-change entropy of liquid crystals. The present method is based on the complete break-down of the molecules into their constituting atoms and their immediate neighbourhood; the respective calculations of the contribution of the atomic groups by means of the Gauss-Seidel fitting method is based on experimental data collected from literature. The feasibility of the calculations for each of the mentioned descriptors was verified by means of a 10-fold cross-validation procedure proving the good to high quality of the predicted values for the three mentioned enthalpies and for the entropy of fusion, whereas the predictive quality for the total phase-change entropy of liquid crystals was poor. The goodness of fit (Q2) and the standard deviation (σ) of the cross-validation calculations for the five descriptors was as follows: 0.9641 and 4.56 kJ/mol (N=3386 test molecules) for the enthalpy of vaporization, 0.8657 and 11.39 kJ/mol (N=1791) for the enthalpy of sublimation, 0.9546 and 4.34 kJ/mol (N=373) for the enthalpy of solvation, 0.8727 and 17.93 J/mol/K (N=2637) for the entropy of fusion and 0.5804 and 32.79 J/mol/K (N=2643) for the total phase-change entropy of liquid crystals. The large discrepancy between the results of the two closely related entropies is discussed in detail. Molecules, for which both the standard enthalpies of vaporization and sublimation were calculable, enabled the estimation of their standard enthalpy of fusion by simple subtraction of the former from the latter enthalpy. For 990 of them the experimental enthalpy-of-fusion values are also known, allowing their comparison with predictions, yielding a correlation coefficient R2 of 0.6066.

scholarly journals Application of a General Computer Algorithm Based on the Group-Additivity Method for the Calculation of two Molecular Descriptors at both Ends of Dilution: Liquid Viscosity and Activity Coefficient in Water at infinite Dilution

2017 ◽  
Author(s):  
Rudolf Naef ◽  
William E. Acree
Keyword(s):  
Activity Coefficient ◽  
Infinite Dilution ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Viscosity Coefficient ◽  
Computer Algorithm ◽  
Group Additivity ◽  
Liquid Viscosity ◽  
Fitting Method ◽  
Complete Breakdown

The application of a commonly used computer algorithm based on the group-additivity method for the calculation of the liquid viscosity coefficient at 292.15K and the activity coefficient at infinite dilution in water at 298.15K of organic molecules is presented. The method is based on the complete breakdown of the molecules into their constituting atoms, further subdividing them by their immediate neighbourhood. A fast Gauss-Seidel fitting method using experimental data from literature is applied for the calculation of the atom groups’ contributions. Plausibility tests have been carried out on each of the calculations using a 10-fold cross-validation procedure which confirms the excellent predictive quality of the method. The goodness of fit (Q2) and the standard deviation (σ) of the cross-validation calculations for the viscosity coefficient, expressed as log(η), was 0.9728 and 0.11, respectively, for 413 test molecules, and for the activity coefficient log(γ)∞ the corresponding values were 0.9736 and 0.31, respectively, for 621 test compounds. The present approach has proven its versatility in that it enabled at once the evaluation of the liquid viscosity of normal organic compounds as well as of ionic liquids.

scholarly journals Calculation of the Isobaric Heat Capacities of the Liquid and Solid Phase of Organic Compounds at 298.15K by Means of a Generally Applicable Computer Algorithm Based on the Group-Additivity Method

2020 ◽  
Author(s):  
Rudolf Naef
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Solid Phase ◽  
Heat Capacities ◽  
Computer Algorithm ◽  
Molecular Volume ◽  
Complementary Method ◽  
Standard Deviations

The calculation of the isobaric heat capacities of the liquid and solid phase of molecules at 298.15 K is presented, applying a universal computer algorithm based on the atom-groups additivity method, using refined atom groups. The atom groups are defined as the molecules' constituting atoms and their immediate neighbourhood. In addition, the hydroxy group of alcohols are further subdivided to take account of the different intermolecular interactions of primary, secondary and tertiary alcohols. The evaluation of the groups' contributions has been carried out by means of a fast Gauss-Seidel fitting calculus using experimental data from literature. Plausibility has been tested immediately after each fitting calculation using a 10-fold cross-validation procedure. For the heat capacity of liquids, the respective goodness of fit of the direct (R2) and the cross-validation calculations (Q2) of 0.998 and 0.9975, and the respective standard deviations of 8.2 and 9.16 J/mol/K, together with a medium absolute percentage deviation (MAPD) of 2.69%, based on the experimental data of 1133 compounds, proves the excellent predictive applicability of the present method. The statistical values for the heat capacity of solids are only slightly inferior: for R2 and Q2, the respective values are 0.9915 and 0.9875, the respective standard deviations are 12.19 and 14.13 J/mol/K and the MAPD is 4.65%, based on 732 solids. The predicted heat capacities for a series of liquid and solid compounds has been directly compared to those received by a complementary method based on the "true" molecular volume [1] and their deviations elucidated.

Evaluation of Safety Performance Functions Based on Experimental Design Using a Cross-Validation Method

2017 ◽  
Vol 2636 (1) ◽  
pp. 62-72 ◽  
Author(s):  
Jung-Han Wang ◽  
Mohamed A. Abdel-Aty ◽  
Jaeyoung Lee
Keyword(s):  
Goodness Of Fit ◽  
Cross Validation ◽  
Safety Performance ◽  
Major Road ◽  
Highway Safety Manual ◽  
Annual Average Daily Traffic ◽  
Minor Road ◽  
Safety Performance Functions ◽  
The One ◽  
Leave One Out

The Highway Safety Manual (HSM) Part C provides a series of safety performance functions (SPFs) for different roadway conditions. The SPFs suggested in the HSM are formulated on the basis of exposure variables: the logarithms of the annual average daily traffic (AADT) on the major road and on the minor road under the base condition. In this research, data from 7,802 intersections in Florida were collected and processed. These intersections were categorized into seven types based on area type (rural or urban), number of legs (three or four), and number of approaches controlled by stop signs. Twenty-two SPF formulations, including the one suggested by the HSM, were developed for each intersection type for examination of the goodness-of-fit measures of the SPFs. In addition, the goodness of fit of each model of the 22 SPFs in each category was examined with 10-fold leave-one-out cross-validation (LOOCV). With a comparison of the delta values generated with the LOOCV method, it is suggested that the SPF with the logarithm of the total entering vehicle volume and the ratio of the AADT on the minor road and the AADT on the major road are important. In addition, the SPFs with the AADT on the major road and the AADT on the minor road and their logarithmic transformations are also important. Therefore, it is suggested that the future HSM compare these two SPF formulations—as suggested in the current research, along with the original SPF formulation in the manual—and select the one with the best model fit on the basis of the delta value using LOOCV.

scholarly journals Calculation of the Isobaric Heat Capacities of the Liquid and Solid Phase of Organic Compounds at 298.15K by Means of the Group-Additivity Method

Molecules ◽  
2020 ◽  
Vol 25 (5) ◽  
pp. 1147
Author(s):  
Rudolf Naef
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Solid Phase ◽  
Linear Equations ◽  
Heat Capacities ◽  
Molecular Volume ◽  
Complementary Method ◽  
Standard Deviations

The calculation of the isobaric heat capacities of the liquid and solid phase of molecules at 298.15 K is presented, applying a universal computer algorithm based on the atom-groups additivity method, using refined atom groups. The atom groups are defined as the molecules’ constituting atoms and their immediate neighbourhood. In addition, the hydroxy group of alcohols are further subdivided to take account of the different intermolecular interactions of primary, secondary, and tertiary alcohols. The evaluation of the groups’ contributions has been carried out by solving a matrix of simultaneous linear equations by means of the iterative Gauss–Seidel balancing calculus using experimental data from literature. Plausibility has been tested immediately after each fitting calculation using a 10-fold cross-validation procedure. For the heat capacity of liquids, the respective goodness of fit of the direct (r2) and the cross-validation calculations (q2) of 0.998 and 0.9975, and the respective standard deviations of 8.24 and 9.19 J/mol/K, together with a mean absolute percentage deviation (MAPD) of 2.66%, based on the experimental data of 1111 compounds, proves the excellent predictive applicability of the present method. The statistical values for the heat capacity of solids are only slightly inferior: for r2 and q2, the respective values are 0.9915 and 0.9874, the respective standard deviations are 12.21 and 14.23 J/mol/K, and the MAPD is 4.74%, based on 734 solids. The predicted heat capacities for a series of liquid and solid compounds have been directly compared to those received by a complementary method based on the "true" molecular volume and their deviations have been elucidated.

Electric-Field-Induced Phase Change in Cholesteric Liquid Crystals

1968 ◽  
Vol 20 (19) ◽  
pp. 1024-1025 ◽  
Author(s):  
J. J. Wysocki ◽  
J. Adams ◽  
W. Haas
Keyword(s):  
Liquid Crystals ◽  
Electric Field ◽  
Phase Change ◽  
Cholesteric Liquid Crystals

scholarly journals Cross-Validation, Bootstrap, and Support Vector Machines

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Masaaki Tsujitani ◽  
Yusuke Tanaka
Keyword(s):  
Support Vector Machines ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Prediction Rule ◽  
Support Vector ◽  
Resampling Methods ◽  
Tuning Parameters ◽  
Training Samples ◽  
Vector Machines ◽  
Disease Study

This paper considers the applications of resampling methods to support vector machines (SVMs). We take into account the leaving-one-out cross-validation (CV) when determining the optimum tuning parameters and bootstrapping the deviance in order to summarize the measure of goodness-of-fit in SVMs. The leaving-one-out CV is also adapted in order to provide estimates of the bias of the excess error in a prediction rule constructed with training samples. We analyze the data from a mackerel-egg survey and a liver-disease study.

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