Dispersion B3LYP

The ab initio methods used by most investigators include Hartree-Fock (FFF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide reliable molecular structures and are considerably faster than FFF methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. FFowever, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

We now compare the PM3-D method with previous uncorrected DFT calculations on the S22 complexes [130], For the dispersion-bonded complexes the errors in the interaction distances for the PBE, B3LYP and TPSS functionals are reported to be 0.63, 1.16 and 0.69 A which are reduced to 0.17, 0.00 and 0.02 A when appropriate dispersive corrections are included. We see in Table 5-9 that the PM3-D method is capable of predicting the structures of dispersion-bonded complexes with greater accuracy than some uncorrected DFT functionals and with an accuracy comparable to that for the dispersion corrected PBE functional [130],... 

The intrinsic atom-in-molecule polarizabilities were tested by us [99] for their performance in the calculation of the dispersion energy for a set of Van der Waals complexes, at their equilibrium geometry using a DFT- B3LYP computational ansatz combined with an aug-cc-pVTZ basis set for the calculation of the (Mf) values using Van Alsenoy s STOCK program, also used to partition the polarizabilities [100]. 

Table 3.1 Electrostatic contribution (Ge/e kcal moC1) to the solvation free energy and dipole moment (p Debye) for a series of representative neutral compounds in water (determined from QM-SCRF B3LYP/ aug-cc-pVDZ calculations with and without coupling between electrostatic and dispersion-repulsion components...

The authors explain that there is a slight equilibrium between attractive (electrostatic and dispersive) and repulsive (steric) forces in the fundamental and excited state of the adducts, depending on solvent configuration and the chromophore structure. The homochiral complexes have been found to be more stable than their heterochiral counterparts. Another R2PI study by Speranza [113] used R-(+)-l-phenyl-1-propanol as model, to study the interaction with several solvents as methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, S-(+)-2-butanol, R-(—)-2-butanol, 1-pentanol, S-(+)-2-pentanol, R-(—)-2-pentanol, and 3-pentanol. The experimental results had the support of theoretical calculations at the B3LYP/6-31G level. In all cases studied, the homochiral complexes were found to be more stable than the heterochiral ones, both in fundamental and excited states, as well as for the corresponding ionic adducts. 

Figure 14-3. Comparison of different structures of model E from different calculations (the number below each superposition is the backbone RMSD) (a) SCC-DFTB-optimized structure (CPK color) vs ideal 14-helix (purple) (b) SCC-DFTB-optimized structure (CPK color) vs B3LYP/6-31G -optimized structure (yellow) (c) SCC-DFTB-optimized structure (CPK color) vs SCC-DFTB+dispersion optimized structure (green) (d) SCC-DFTB+dispersion optimized structure (green) vs ideal 14-helix (purple)...

Fig. 2. Activation parameters vs number of HFIP molecules for the epoxidation of Z-butene within a solution model at 298K (RB3LYP/6-311++G(d,p)//RB3LYP/6-31+G(d,p)). Dashed lines refer to values in parentheses which include a correction for the dispersion interaction from a BSSE-corrected MP2/6-31+G(2d,p)//B3LYP/6-31+G(d,p) single-point calculation on the corresponding initial aggregates. AG (cyclooctene) and -TAS (cyclooctene) correspond to the experimentally determined activation parameters for the epoxidation of Z-cyclooctene at 298 K...

One can even combine this damped atom-atom dispersion correction to the LC hybrid functionals. The (oB97X functional has been modified to include dispersion correction to create the (j)B97X-D functional. Performance of this functional is significantly better than dispersion-corrected standard functionals, like B3LYP-D, and improves performance in the G3/05 thermodynamic data set by 0.6 kcalmol over (OB97-X. 

It was recognized early on that the binding energy of the benzene dimer is quite sensitive to computational method. The potential energy surface of 77 is completely repulsive at the HF level, as well as with any DFT that does not include a dispersion correction, such as B3LYP. " Furthermore, the weakly bound benzene dimer is susceptible to basis set superposition error and counterpoise corrections are likely to be necessary. ... 

B3LYP and B3P86 fail to locate a face-to-face dimer of benzene, leading to the standard thought that DPT fails to appropriately treat dispersion. This would make DFT unsuitable for computing the stacked nucleic acid bases. In fact, both B3LYP/6-31+G(d,p) and X3LYP/cc-pVTZ fail to locate any stacked A-T, C-G, C-C, or U-U pairs. 

Since these interactions only rarely are discussed, we list t5q>ical results from their work in Table 4. It is seen that fairly large basis sets are needed in order to obtain results that can be considered close to converged. Moreover, the density-functional B3LYP method yields larger absolute values than does the Hartree-Fock method. Finally, the repulsion contribution amounts to only some 10-20% of the dispersion contribution. 

Using the B3LYP method for reference they compared subsequently the performance of four force-field methods for reproducing the B3LYP results for the dispersion and repulsive contributions to the free energy of solvation for 22 neutral molecules in four solvents. The results, Table 5, show that in most cases the force fields do not perform very well with the MST being an exception. 

Insufficient description of dispersion in B3LYP and large basis set superposition errors in MP2 calculations can hide peptide conformers ... 

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