A New Sets of Accurate Multi-level Methods Including Parameterization for Heavy Elements 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 new series of multi-coefficient electronic structure methods that including parameterization for heavy elements. New database was taken from our last MLSE(Cn)-DFT method and added 10 atomization energies of Br and I containing molecules (Br 2, I 2, HI, IBr, HBr, ICl, NOBr CH 3 I, CH 3 Br, C 2 H 5 I ), ionization potentials and electron affinities of Br and I. Several methods have been developed this time, we called them MLSE(HA-n) methods. The most important correction term was SCS-MP2(spin component scaled MP2) correction. The best method MLSE(HA-1) gave an average mean unsigned error (MUE) 0.57 kcal/mol on 225 thermochemical kinetics data. It also gave average error less than 1.0 kcal/mol for 10 AEs of Br and I containing molecules. In comparison, the MLSE(C1)-DFT gave an MUE of 1.77 kcal/mol on the same test set. The new methods MLSE(HA-1) takes 60% more computer time than MLSE(C1)-DFT method. This new method is suitable for thermochemical kinetics study on systems containing heavy halogens. This is also the first developed Multi-Level methods for 4- and 5- row elements Introduction Traditionally, the accuracy of quantum chemical calculation is a very important goal in comparison with experiment. To approach the high accuracy, we can use very high-level theories, such as QCISD(T) and CCSD(T), with large basis sets. However, the costs of these methods are prohibitively high except for very small molecules. Finding high accuracy and economic methods is the most important goal in the quantum chemical calculation area. In the past two decades, this goal had been realized by the so-called multi-level methods or multi-coefficient methods. Our group had also published MLSE(n)+d, MLSE-DFT and MLSE(Cn)-DFT methods in the last five years. However, these methods are all designed for the first to third rows main group elements. This time, the MLSE(HA-n) method is our first and the worldly first published multi-coefficient methods for heavy halogens. 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. Two developed methods MLSE(HA-n)(n=1,2) are shows right(Eq.1), 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. E2aa means the alpha-alpha spin component E2 energy in the MP2 calculation, the same abbreviation for bb(beta-beta) and ab(alpha-beta). For elements not in the second row, the original cc-pVnZ and aug- cc-pVnZ (n = D, T) basis sets were used. For iodine, we used cc-pVnZ-pp and aug-cc- pVnZ-pp (n = D, T) basis sets instead of the inexistent Dunning’s basis sets. The training set is the same with test set that including 109 main-group atomization energies (AEs), 38 hydrogen-transfer barrier heights (HTBHs), 38 non- hydrogen-transfer barrier heights (NHTBHs), 13 ionization potential (IPs) energies and 13 electron affinity (EAs) energies, respectively, that originally used in the MLSE(Cn)-DFT method, totally 211 energies. And additional ten heavy atom atomization energies(HAAEs) containing Br and I atoms, two IPs and two EAs of Br and I(HAIP and HAEA) that added this time in MLSE(HA-n) method, totally 225 energies. New added training set are listed in table 1. The MLSE(HA-1) method consists of several ab initio energy components and MPW1PW91/aptz+apdz terms. The MLSE(HA-2) method omits QCISD(T)/apdz Results Figure 1 shows the MUE(225), HASE(10) and costs comparison of these methods. The cost and MUE of in Figure 1 shows MLSE(HA-n) method get large improvement to MLSE(Cn)-DFT methods in the HAAE(10). Table 2 shows the comparison of our new methods and several related methods. MLSE(C1)- M062X (Eso) is the original version only added Eso and re-optimized aim MUE(211). MLSE(C1)- M062X-HA is the same method that optimized aim MUE(225). By our testing, the SCS-MP2 correction term play a very important rule in our new method. However, the effect of SCS-MP2 is not very clear in the MLSE(Cn)-DFT method. Reference 1.Sun, Y.-L, Li, T.-H., Chen, J.-L., Hu, Chen, W.-P. Chem. Phys. Lett. 2009, 475, Grimme, S. J. Chem. Phys. 2003, 118, Szabados, A. J. Chem. Phys. 2006, 125, Kozuch, S.; Gruzman, D.; Martin, J. M. L. J. Phys. Chem. C 2010, 114, 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 that are widely useful for the main group elements. These two methods provided the overall MUE of 0.58~0.64 kcal/mol, which also are very accurate for the heavy halogens that the overall MUE is less than 1.0 kcal/mol. We expect that the new MLSE(HA-n) methods can easily be applied to many types of interesting chemical systems with heavy atoms, and they will be invaluable for accurate study of thermochemistry and kinetics. Table 2 Mean unsigned errors (kcal/mol) obtained using the MLSE(HA-n) methods and other related methods. E(MLSE(HA-1)) and E(MLSE(HA-2))= C WF { E(HF/pdz) + C HF+ [E(HF/apdz) – E(HF/pdz]) + C B1HF [E(HF/ptz) – E(HF/pdz]) + C B2HF [E(HF/aptz) – E(HF/ptz]) + C E2S [(E2aa+E2bb)/pdz] + C E2O [(E2ab)/pdz] + C E2+S [(E2aa+E2bb)/apdz] + C E2+O [(E2ab)/apdz] + C B1E2S [(E2aa+E2bb)/ptz] + C B1E2O [(E2ab)/ptz] + C B2E2S [(E2aa+E2bb)/aptz] + C B2E2O [(E2ab)/aptz] + C E34D [E(MP4D/pdz) – E(MP2/pdz)] } + C E34D+ [E(MP4D/apdz) – E(MP4D/pdz)] } + C B1E34D [E(MP4D/ptz) – E(MP4D/pdz)] } + C E34 [E(MP4SDQ/pdz) – E(MP4D/pdz)] } + C E34+ [E(MP4SDQ/apdz) – E(MP4SDQ/pdz)] } + C B1E34D [E(MP4MP4SDQ/ptz) – E(MP4SDQ/pdz)] } + C QCID [E(QCISD/pdz) – E(MP4SDQ/pdz)] + C QCID+ [E(QCISD/apdz) – E(QCISD/pdz)] + C QCI [E(QCISD(T)/pdz) – E(QCISD/pdz)] + C QCI+ [E(QCISD(T)/apdz) – E(QCISD(T)/pdz)] + (1  C WF ) { E(DFT/pdz) + C DFT+ [E(DFT/apdz – DFT/pdz] } + Eso –(1) Figure 1 Comparisons of the MUEs and costs of MLSE(HA-n) methods and MLSE(C1)-M062X-HA method. AE I2I HI73.79 IBr42.27 ICl50.19 Br HBr90.51 NOBr CH 3 I CH 3 Br C2H5IC2H5I IP I Br EA I70.54 Br77.60 calculation, and changes the DFT calculation to B3LYP/apdz+pdz. The MLSE(HA-1) includes additional SCS-MP2 correction terms and QCISD(T)/apdz calculation compared with our previous MLSE(Cn)-DFT method. The spin-orbital correct energies(Eso) were also used in the MLSE(HA-n) methods be cause of the large spin-orbital effect sof Br and I atoms. MLSE(HA-2) is a economic method with costs similar to the MLSE(Cn)-DFT method but suitable for the 4- and 5- row elements. Table 1 New data (kcal/mol) AE(109)IP(13)EA(13)HTBHNHTBHMUE(211) MCG3-MPWB G3SX MLSE(C1)-M062X AE(119)IP(15)EA(15)HTBHNHTBHMUE(211)HAAEHAIPHAEAMUE(255) MLSE(C1)-M062X (Eso) MLSE(C1)-M062X-HA MLSE(HA-1) MLSE(HA-2)