Comparison of density functional theory predictions of gas-phase deprotonation data

The SVWN, BVWN, BP86, BLYP, BPW91, B3P86, B3LYP, B3PW91, B1LYP, mPW1PW, and PBE1PBE density functionals, as implemented in Gaussian 98 and Gaussian 03, were used to calculate ΔG0 and ΔH0 values for 17 deprotonation reactions where the experimental values are accurately known. The PBE1PBE and B3P86 functionals are shown to compute results with accuracy comparable to more computationally intensive compound model chemistries. A rationale for the relative performance of various functionals is explored.

CCSD(T), W1, and other model chemistry predictions for gas-phase deprotonation reactions

A series of CCSD(T) single-point calculations on MP4(SDQ) geometries and the W1 model chemistry method have been used to calculate ΔH° and ΔG° values for the deprotonation of 17 gas-phase reactions where the experimental values have reported accuracies within 1 kcal/mol. These values have been compared with previous calculations using the G3 and CBS model chemistries and two DFT methods. The most accurate CCSD(T) method uses the aug-cc-pVQZ basis set. Extrapolation of the aug-cc-pVTZ and aug-cc-pVQZ results yields the most accurate agreement with experiment, with a standard deviation of 0.58 kcal/mol for ΔG° and 0.70 kcal/mol for ΔH°. Standard deviations from experiment for ΔG° and ΔH° for the W1 method are 0.95 and 0.83 kcal/mol, respectively. The G3 and CBS-APNO results are competitive with W1 and are much less expensive. Any of the model chemistry methods or the CCSD(T)/aug-cc-pVQZ method can serve as a valuable check on the accuracy of experimental data reported in the National Institutes of Standards and Technology (NIST) database.

Comparison of Model Chemistry and Density Functional Theory Thermochemical Predictions with Experiment for Formation of Ionic Clusters of the Ammonium Cation Complexed with Water and Ammonia; Atmospheric Implications

The G2, G3, CBS-QB3, and CBS-APNO model chemistry methods and the B3LYP, B3P86, mPW1PW, and PBE1PBE density functional theory (DFT) methods have been used to calculate ΔH° and ΔG° values for ionic clusters of the ammonium ion complexed with water and ammonia. Results for the clusters NH4+(NH3)n and NH4+(H2O)n, where n = 1−4, are reported in this paper and compared against experimental values. Agreement with the experimental values for ΔH° and ΔG° for formation of NH4+(NH3)n clusters is excellent. Comparison between experiment and theory for formation of the NH4+(H2O)n clusters is quite good considering the uncertainty in the experimental values. The four DFT methods yield excellent agreement with experiment and the model chemistry methods when the aug-cc-pVTZ basis set is used for energetic calculations and the 6-31G* basis set is used for geometries and frequencies. On the basis of these results, we predict that all ions in the lower troposphere will be saturated with at least one complete first hydration shell of water molecules.

Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

The performance of the parallel vector implementation of the one- and two-dimensional orthogonal transforms is evaluated. The orthogonal transforms are computed using actual or modified fast Fourier transform (FFT) kernels. The factors considered in comparing the speed-up of these vectorized digital signal processing algorithms are discussed and it is shown that the traditional way of comparing th execution speed of digital signal processing algorithms by the ratios of the number of multiplications and additions is no longer effective for vector implementation; the structure of the algorithm must also be considered as a factor when comparing the execution speed of vectorized digital signal processing algorithms. Simulation results on the Cray X/MP with the following orthogonal transforms are presented: discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), discrete Walsh transform (DWHT), and discrete Hadamard transform (DHDT). A comparison between the DHT and the fast Hartley transform is also included.(34 refs)