Novel density functional methodology for the computation of accurate electronic and thermodynamic properties of molecular systems and improved long-range behavior

A novel general purpose density functional methodology for the computation of accurate electronic and thermodynamic properties of molecules and improv ed long-range behavior is reported. Assuming the separability of the exchan ge (E-x) and correlation (E-c) contributions to the total exchange-correlat ion energy functional (E-xc), the E-x term consists of a hybrid mixture of 37.5% Hartree-Fock exchange and the appropriate local spin density exchange using the adiabatic connection formula. We demonstrated that E-x and its c orresponding potential V-x [=dE(x)/d rho(r)] have the proper asymptotic lim its at r = 0 and r --> infinity. E-c consists of the Vosko, Wilk, and Nusai r formula for the free-electron gas correlation energy and a generalized gr adient approximation term with one adjustable parameter. V-c [=dE(c)/d rho( r)] was shown to obey the r --> infinity limit of the corresponding potenti al derived from exact atomic exchange-correlation computations; namely, V-c is proportional to r(-4). Most importantly, we demonstrated that, at r val ues where dispersion forces are operating, V-c is proportional to 1/r(n) (n = 4, 6, 8,...). The reported method was denoted by K2-BVWN because it used two adjustable parameters in its formulation. The K2-BVWN scheme scales as N-3, where N is the number of basis functions, compared to similar to N-7 for Gaussian-2 (G2) ab initio theory and related methods, similar to N-5 fo r Barone's mPW1,3PW, and similar to N-4 for Becke's three-parameter density functional approaches. The K2-BVWN/6-311g-(d) model predicted the structur es of numerous molecular systems with remarkable accuracy. The results of K 2-BVWN/6-311 + g(df), K2-BVWN/6-311 + g(2df), and K2-BVWN/6-311 +g(3df) com putations on Li through Ar atoms showed that the calculated energies at all three levels of theory are comparable to within 0.1 kcal/ mel, thus demons trating the fast convergence of atomic energies as the size of basis sets i ncreased. Accordingly, the thermochemical properties of molecular systems c ould, in principle, be calculated to increasing levels of accuracy dependin g on the size of the basis sets used, in accordance with the usual practice in Hartree-Fock theory. In a data set comprised of 350 atomic and molecula r systems, which included the G2 data set, we demonstrated that the K2-BVWN /6-311 + g(2df) level of theory is a reliable model for the computation of room-temperature heats of formation, ionization potentials, and electron an d proton affinities of normal valent compounds with average errors of 1.4 k cal/mol, 0.07, 0.07, and 0.05 eV, respectively. The outliers in calculated heats of formation consisted mainly of hypervalent compounds, nonhydrides c ontaining multiple chlorine atoms, H2O, and HF. Enthalpies of formation of these outliers were computed using the K2-BVWN/6-311 + g(3df,p) level of th eory. Further refinement of calculated heats of formation of outliers was a chieved through the use of atom equivalent corrections instead of increasin g the size of basis sets beyond 6-311+g(3df,p). Interestingly, the only ato ms that required a correction for the latter step were oxygen (0.6 kcal/mol ), aluminum (0.60 kcal/mol), silicon (0.60 kcal/mol), phosphorus (0.60 kcal /mol), sulfur (0.60 kcal/mol), and chlorine (0.60 kcal/mol). Comparison of the results obtained from the K2-BVWN method and correspondin g ones from G2/6-311+g(3df,2p) ab initio theory, HFS-BVWN/6-311 + g(3df,p), bond additivity correction BAC-G2/6-311 ++ g(3df,2pd), G2(MP2)/6-311 +g(3d f,2p), G2(MP2, SVP)/6-311 Sg(3df,2p), B3LYP/6-311+g(3df,2p), and mPW1,3PW/6 -311 ++g(3df,3pd) demonstrated that G2 ab initio theory and the K2-BVWN den sity functional scheme have comparable average errors in computed heats of formation, ionization potentials, and electron and proton affinities of mol ecules and are superior to all other approaches. Furthermore, we showed tha t the interaction energies of nine noble gas dimers were remarkably well re produced using K2-BVWN/ 3-21+g(d,p) and K2-BVWN/3-21g levels of theory. Mor eover, binding energies of the hydrogen-bonded isoelectronic systems (H2O)( 2) and (HF)(2) and the interaction energy of the charge-transfer complex fo rmed between Cl-2 and ethylene were also reliably predicted to within less than 0.5 kcal/mol from corresponding experimental values. The G2 data set c omplemented by the reported molecular systems investigated in this work was recommended as a critical test for evaluating novel ab initio and density functional methodologies. The K2-BVWN method has been implemented in the Ga ussian series of programs.