CBS Model Research Articles

A complete basis set model chemistry. V. Extensions to six or more heavy atoms

The major source of error in most ab initio calculations of molecular energies is the truncation of the one-electron basis set. Extrapolation to the complete basis set second-order (CBS2) limit using the N−1 asymptotic convergence of N-configuration pair natural orbital (PNO) expansions can be combined with the use of relatively small basis sets for the higher-order (i.e., MP3, MP4, and QCI) correlation energy to develop cost effective computational models. Following this strategy, three new computational models denoted CBS-4, CBS-q, and CBS-Q, are introduced. The mean absolute deviations (MAD) from experiment for the 125 energies of the G2 test set are 2.0, 1.7, and 1.0 kcal/mol, respectively. These results compare favorably with the MAD for the more costly G2(MP2), G2, and CBS-QCI/APNO models (1.6, 1.2, and 0.5 kcal/mol, respectively). The error distributions over the G2 test set are indistinguishable from Gaussian distribution functions for all six models, indicating that the rms errors can be interpreted in the same way that experimental uncertainties are used to assess reliability. However, a broader range of examples reveals special difficulties presented by spin contamination, high molecular symmetry, and localization problems in molecules with multiple lone pairs on the same atom. These characteristics can occasionally result in errors several times the size expected from the Gaussian distributions. Each of the CBS models has a range of molecular size for which it is the most accurate computational model currently available. The largest calculations reported for these models include: The CBS-4 heat of formation of tetranitrohydrazine (91.5±5 kcal/mol), the CBS-4 and CBS-q isomerization energies for the conversion of azulene to naphthalene (ΔHcalc=−35.2±1.0 kcal/mol, ΔHexp=−35.3±2.2 kcal/mol), and the CBS-Q heat of formation of SF6 (ΔHcalc=−286.6±1.3 kcal/mol, ΔHexp=−288.3±0.2 kcal/mol). The CBS-Q value for the dissociation energy of a C–H bond in benzene (113.1±1.3 kcal/mol) is also in agreement with the most recent experimental result (112.0±0.6 kcal/mol). The CBS-QCI/APNO model is applicable to the prediction of the C–H bond dissociation energies for the primary (100.7±0.7 kcal/mol calc.) and secondary (97.7±0.7 kcal/mol calc., 97.1±0.4 kcal/mol exp.) hydrogens of propane.

Advertising and US alcoholic beverage demand: system-wide estimates

The effects of advertising on consumption of alcoholic beverages in the US are analysed. The goal is to obtain evidence on the importance of advertising at the level of beverage demand(beer, wine, spirits) and for total consumption of alcohol (per capita gallons of ethanol). A three-equation conditional demand system is estimated that includes own- and cros-beverage advertising as explanatory variables. Four models of the differential demand system are estimated, including the Rotterdam, AID, CBS, and NBR models, using annual US data for the period 1964-90 on beverage consumption, prices, expednitures, and real advertising. Estimates are obtained of the complete matrix of own- and cross-elascities for each beverage’ price and advertising. At the beverage level, the results indicate a positive butr very small effect of advertising on beverage consumption, with most of the impact due to wine advertising and non due to beer advertising. There is no efect of advertising in the composite demand function for al...

A class of differential demand systems

The Rotterdam, Almost Ideal Demand System, CBS, and NBR models constitute a class of differential demand systems. They correspond to alternative assumptions made concerning the constancy of certain parameters. This paper discusses the restrictions that they impose on the evolution of demand elasticities over time.

Estimation of demand systems using both time series and cross section data

This article deals with three models of complete systems of demand equations (Rotterdam model, AIDS and CBS model). After the models and the theoretical restrictions have been described the parameters are estimated subject to an increasing number of restrictions and using aggregate time series for the Netherlands on five commodity groups.