DFT-SAPT

Contrary to the previously described supermolecular approach, perturbation theory treatment allows for the partition of the interaction energy into physically interpretable components. The most frequently used method for this purpose is symmetry-adapted perturbation theory (SAPT) [13]. More recently, great effort has also been invested in the development of DFT-SAPT [14-16], In the present contribution, we use the variational-perturbational scheme [17-20], In this approach, the intermolecular interaction energy components are determined based on the wave functions of the subsystems evaluated in the dimer-centered basis set. Thus, both interaction energy and its components are BSSE-free. More details about this scheme can be found elsewhere [21-23]. The total intermolecular interaction energy at the MP2 level of theory can be expressed as follows ... 

To summarize, the primary findings of our systematic study (Parker et al., 2014) are as follows (1) low-order SAPTO provides fairly reliable interaction energies when used in conjunction with the jun-cc-pVDZ basis set, especially in the sSAPTO variant which uses exchange scaling (2) DFT-SAPT is quite reliable on average but exhibits errors for H-bonding systems that are perhaps larger... 

HeEelmann, A., Jansen, G., and Schiitz, M. (2005). DFT-SAPT with density fitting a new efficient method to study intermolecular interaction energies,/ Chem. Phys. 122, pp. 14103-14120. 

Perturbation theories such as the MP2 method (McWeeny 1992) (see Sect. 3.2) have been appreciated as ab initio wavefunction theories reproducing dispersion interactions with relatively short computational times. Therefore, dispersion interactions can be incorporated in the Kohn-Sham method by combining with such perturbation theories, in principle. One of the methods based on this concept is the DFT symmetry-adapted perturbation theory (DFT-SAPT), which uses Kohn-Sham orbitals to calculate the perturbation energies (Williams and Chabalowski 2001). In contrast to ab initio SAPT, in which both intermolecular and intramolecular electron correlations are calculated, only intermolecular electron correlations are calculated as a dispersion correction for the Kohn-Sham method in DFT-SAPT. Consequently, this drastically reduces the computational cost, typically by one or two orders of magnitude, compared to an ab initio SAPT calculation, with similar accuracies. 

One of the main advantages of the MB-SAPT method is that each term in the perturbation series can be meaningfully interpreted. In addition, the calculated INT is closer to the value as obtained from the CCSD(T) method. However, the application of the MB-SAPT is limited by its scaling behavior. For a chosen dimer, both CCSD(T) and MB-SAPT scale as A , where A is themeasnre of the size of the systems. Therefore, the computational demand of the MB-SAPT has been reduced by combining with the computationally less expensive DFT. Hessehnann et al. have provided the detailed account of the theory and applications of the DFT-SAPT method. In this approach, the first-order term provides exact electrostatic Coulomb interaction. The... 

Interaction energies calculated using the MP2/aug-cc-pvtz and DF-DFT-SAPT analysis are given in Table 15.4. 

It is possible to note that the dispersion interaction plays the major role in the stabilization of different complexes. The interplay of electrostatic forces is also clearly evident from the DF-DFT-SAPT results. The interaction of carbon dioxide with the organic linkers has significant contribution from electrostatic and induction terms in the stabilization of these complexes. It is also worth noting that the interaction energies obtained from DF-DFT-SAPT results are in very good quantitative agreement with the BSSE-corrected MP2/aug-cc-pVTZ level of theory. This clearly indicates the usefulness of the method to decompose weakly bound complexes. 

DF-DFT-SAPT Decomposition of Binding Energy (kcal/mol) for Complexes Formed by CO2 with Various Ligands in Metal-Organic Frameworks... 

Becke has proposed a novel approach that formulates the dispersion interaction in terms of the dipole moment that would be created when considering an electron and its exchange hole. " ° Like DFT-D, these methods appear to be more reliable than MP2 for noncovalent interactions. Alternatively, other workers " " have combined DFT with symmetry-adapted perturbation theory (SAPT) (discussed below). These DFT-SAPT approaches evaluate the dispersion term via the frequency-dependent density susceptibility functions of time-dependent DFT, an approach that appears to be theoretically sound. 

With the density-fitted formulation of SAPT(DFT), commonly called DF-SAPT(DFT) or DF-DFT-SAPT, the computational cost of the second-order interaction energy scales as only O(N ) ifhybrid functionals are used (Bukowski et al. 2005 Podeszwa et al. 2006b). In the DFT-SAPT implementation the FDDS is calculated without a contribution from CHF theory. This reduces the computational scaling for evaluating the FDDS to but the overall scaling... 

Subsequently, applications were made to larger systems such as the ethyne and benzene dimers (Hesselmann et al. 2005 Podeszwa and Szalewicz 2005) where, once again, the accuracy of the method was demonstrated. More recently, the DFT-SAPT implementation has been used to study the interaction of water on graphene (Jenness and Jordan 2009), DNA base pairs (Hesselmann et al. 2006), and DNA base pair tetramers (Fiethen et al. 2008). Calculations of such accuracy are simply not possible using conventional electronic structure methods in the supermolecular approach, particularly as the only correlated ab initio method with a reasonable computational scaling is MP2, and MP2 is not suitable for the interactions of systems with 7T-bonding (Sinnokrot et al. 2002). 

Molpro 2008 (commercial, source available, parallel) The Molpro 2008 program (Werner et al. 2008) contains a number of state-of-the-art electronic structure methods including DF-DFT-SAPT. This program is probably the most computationally efficient implementation of SAPT(DFT), though the FDDS cannot include any fraction ot CHF (see O section Symmetry-Adapted Perturbation Theory ). 

SAPT The review articles by Jeziorski, Szalewicz, and others (Jeziorski and Szalewicz 1998, 2002 Jeziorski et al. 1994 Szalewicz 2002 Szalewicz et al. 2005) are probably the most comprehensive articles on symmetry-adapted perturbation theory. See also the discussion of these theories in Stone (1996). For a detailed examination of symmetry-forcing techniques and the convergence of intermolecular perturbation theories see Szalewicz et al. (2005). SAPT(DFT) The theory of the SAPT(DFT) method is described in Misquitta et al. (2005b) and DF-SAPT(DFT) in Podeszwa et al. (2006b). The DF-DFT-SAPT method is described in Hesselmann et al. (2005). 

Jenness, G. R., Jordan, K. D. (2009). Df-dft-sapt investigation of the interaction of a water molecule to coronene and dodecabenzo-coronene Implications for the water-graphite interaction. Journal of Physical Chemistry C, 113, 10242-10248. 

Hesseimann A, Korona T (2011) On the accuracy of DFT-SAPT, MP2, SCS-MP2, MP2C, and DFT plus Disp methods for the interaction energies of endohedral complexes of the Cgo fullerene with a rare gas atom. Phys Chem Chem Phys 13 732-743... 

Zgarbova M et al (2010) Large-scale compensation of errors in pairwise-additive empirical force fields comparison of AMBER intermolecular terms with rigorous DFT-SAPT calculations. Phys Chem Chem Phys 12 10476-10493... 

The SAPT method [19] provides an exact decomposition of the total interaction energies into various components of the first and secrnid perturbation order. The DPT version of the SAPT (DFT-SAPT) [20-28] allows for the treatment of extended complexes (up to about 40 atoms) and the total interaction energy is decomposed into polarisation/electrostatic inductirm (E ), dispersion (Ep)... 

The greatest improvement of the DFT-SAPT method over the original SAPT is the acceleration of the calculations by one order of magnitude. The intramolecular treatment is conducted using the DPT and therefore suffers from inaccurate energies of the virtual orbitals. This drawback is corrected for in advance of the actual SAPT treatment by a gradient-controlled shift procedure, which uses the difference between the exact vertical ionisation potential (IP) and the energy of the (HOMO) [24]. In this work, PBEO/aug-cc-pVTZ and PBEO/aug-cc-pVDZ calculations were carried out to obtain the IP respective HOMO values and intermolecular terms were described by aug-cc-pVDZ and aug-cc-pVTZ basis sets. Bromine and iodine atoms were treated by pseudopotentials to describe relativistic effects of inner-core electrons correctly. 

All the post Hartree-Eock calculations (including DFT-SAPT) were carried out using the Molpro 2010 package [29]. The DPT calculations were done utilising the Turbomole 6.3 package [30]. 

Table 2 DFT-SAPT interaction energies (in kcal/mol) and Y- -D/Ar distances (A) for halogen-bonded complexes from the X40 dataset [6]... 

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