Yi-Lun Sun, Wei-Ping Hu*

1. Accurate Multi-Level Electronic Structure Methods, MLSE(Cn)-DFT for Atomization Energies and Reaction Energy Barriers Yi-Lun Sun, Wei-Ping Hu* Department of Chemistry and Biochemistry, National Chung Cheng University,Chia-Yi County, Taiwan, Republic of China Abstract We have developed a series of new multi-coefficient electronic structure methods, MLSE(Cn)-DFT, that performed equally well on both neutral and charged systems. The lowest average mean unsigned error on 211 thermochemical kinetics data is 0.56 kcal/mol using the MLSE(C1)-M06-2X method. The simplified MLSE(C2)-M06-2X method can achieve similar accuracy at 54% of the computational cost. Therefore, it is the most recommended method. The highly simplified, but reasonably accurate, MLSE(C3)-B3LYP method is an economical alternative for larger systems. Introduction A traditional goal in developing quantum chemical methods is to obtain relative molecular energies to within a so-called “chemical accuracy” of ~1 kcal/mol. Such accuracy can sometimes be achieved using very high-level theories with larger basis sets. However, the computational costs for applying these methods are prohibitively high, except when modeling very small molecules. Alternatively, this goal can also be achieved more economically by using the so-called “multi-level methods” and “multi-coefficient methods. The addition of hybrid DFT energies into the multi-coefficient methods can substantially increase the accuracy. So, we present a new set of all-purpose, improved MLSE-DFT methods that include or approximate the two additional theoretical levels with very good performance. Methods In the so-called “multi-coefficient methods”, we used scaled energy components in the multi-level methods, all of the scaling coefficients for the various energy components were optimized against databases of experimentally derived or high-level theoretical energies. Three developed methods are shows following , pdz means cc-pV(D+d)Z, apdz means aug-cc-pV(D+d)Z, ptz means cc-pV(T+d)Z, and aptz means aug-cc-pV(T+d)Z. The “+d” signifies that an additional set of d functions are added to the original correlation-consistent basis sets for the second-row elements. For elements not in the second row, the original cc-pVnZ and aug-cc-pVnZ (n = D, T) basis sets were used. The only difference of MLSE(C1)-DFT and MLSE(C2)-DFT is the simplification of aug-cc-pVTZ basis set. The expensive computational cost of MLSE(C1)-DFT is cause of the MP2/aug-cc-pVTZ calculation. The second method simplified the aug-cc-pVTZ basis sets by omitting the f diffuse functions for the second-row elements, omitting the d and f diffuse functions for the first-row elements, and omitting all diffuse functions for hydrogen. The resulting basis set is abbreviated as aptzs. The MLSE(C2)-DFT method significantly reduce the computation cost. However, two large basis sets, ptz and aptzs, are still required for the MP2 calculation. Moreover, the MP4D/ptz calculation is also very expensive. To make the method even more computationally affordable, we completely eliminate the calculation using the ptz basis set in the MLSE(C3)-DFT method. Among the choices of the density functionals, for n = 1 and 2, the methods using the M06-2X functional performed best, while for n = 3, the method using the B3LYP functional performed best. Results Table 1 Mean unsigned errors (kcal/mol) obtained using the MLSE(Cn)-DFT methods Table 2 The computational cost (CPU time) relative to an MP2/6-31+G(d,p) calculation for 7 middle-size molecules. a MLSE-Full-M062X is a new Multi-Level method developed by our group member Chong-Yu Yang ,that used completed combination up to the highest QCISD(T)/aug-cc-pVTZ calculation. MLSE-Full-M062X method get 0.07 kcal/mol improvement in accuracy than the MLSE(C1)-M06-2X method, but also costs more ten times than it. These data include 109 main-group atomization energies (AEs) from the MGAE109/05 database, 38 hydrogen-transfer barrier heights (HTBHs), 38 non-hydrogen-transfer barrier heights (NHTBHs) from the HTBH38/04 and NHTBH38/04 databases, 13 ionization potential (IPs) energies and 13 electron affinity (EAs) energies from the IP13/3 and EA13/3 databases, respectively. The cost and MUE of in Table 2 shows multi-level methods get large improvement to single-level methods such as QCISD(T)/aug-cc-pVTZ. The cost of QCISD(T)/aug-cc-pVTZ is more than MLSE(Cn)-DFT methods with low accuracy. DFT methods such as M06-2X/MG3Sis very cheap, however, it cannot achieve the “chemical accuracy” of ~1 kcal/mol. Our MLSE(Cn)-DFT methods are the most efficient methods that get higher accuracy with applicable cost. Reference Y.-L. Sun, T.-H. Li, J.-L. Chen, K.-J. Wu, W.-P. Hu, Chem. Phys. Lett. 442 (2007) 220. B.J. Lynch, D.G. Truhlar, J. Phys. Chem. A 107 (2003) 3898. Y. Zhao, B.J. Lynch, D.G.. Truhlar, Phys. Chem. Chem. Phys. 7 (2005) 43. L.A. Curtiss, P.C. Redfern, K. Raghavachari, J.A. Pople, J. Chem. Phys. 114 (2001) 108. Conclusions The aim of the current study was to develop a set of accurate and economical hybrid multi-coefficient methods for the study of thermochemical kinetics. These three methods provided the excellent overall MUE of 0.56~0.62 kcal/mol. We expect that the new MLSE(Cn)-DFT methods can easily be applied to many types of interesting chemical systems with 10-15 heavy atoms, and they will be invaluable for accurate study of thermochemistry and kinetics. In Future, we prepare to develop a new method that including 4th and 5throw element molecules.