# A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

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### "A new hybrid exchange–correlation f..." refers background or methods in this paper

...Tsuneda and co-workers have demonstrated that their LC method for the Becke 1988 [14] or PBE [15] generalized-gradient approximation (GGA) exchange functionals in conjunction with their one-parameter progressive (OP) correlation functional [16] can address the above notorious problems in DFT....

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...The CAM-B3LYP functional comprises of 0.19 Hartree–Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range....

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...We consider that due to the prevalence of hydrogen in chemical systems, the good reproduction of the total atomic energies, hydrogen in particular, is more important than the slight loss in quality of the atomization and ionization energies. molecules) with aug-cc-pVQZ Gaussian basis sets les) with aug-cc-pVQZ Gaussian basis sets Table 4 Statistical data for total atomic energies (hartree) of H–Ne with aug-cc-pVQZ Gaussian basis sets a aþ b MAE RMS Maximum deviation ( ) Maximum deviation (+) Deviation H LC-BOP 0.0 1.0 0.084 0.093 – 0.134 (Ne) 0.0091 LC-BLYP 0.0 1.0 0.085 0.128 – 0.128 (Ne) 0.0091 CAM-BOP 0.2 1.0 0.068 0.075 – 0.112 (Ne) 0.0075 0.8 0.049 0.054 – 0.080 (Ne) 0.0061 0.6 0.030 0.049 – 0.049 (Be) 0.0047 CAM-BLYP 0.2 1.0 0.069 0.075 – 0.107 (Ne) 0.0075 0.8 0.050 0.054 – 0.075 (Ne) 0.0061 0.6 0.031 0.034 – 0.043 (Ne) 0.0047 CAM-B3LYP 0.2 1.0 0.033 0.035 – 0.045 (Be) 0.0034 0.8 0.014 0.017 – 0.029 (Be) 0.0019 0.6 0.009 0.013 )0.025 (Ne) 0.013 (Be) 0.0005 B3LYP(G) 0.2 0.2 0.019 0.023 )0.040 (Ne) – )0.0024 B3LYP 0.2 0.2 0.005 0.005 )0.006 (F) 0.009 (Be) 0.0010 BLYP 0.0 0.0 0.011 0.016 )0.031 (F) 0.007 (Be) 0.0021 HCTH 0.0 0.0 0.008 0.010 )0.019 (Ne) 0.004 (C) )0.0064 Increasing the ratio of the Becke 88 exchange contribution at long-range reduces the errors of the atomization, ionization and the total atomic energies....

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...…0.005 )0.006 (F) 0.009 (Be) 0.0010 BLYP 0.0 0.0 0.011 0.016 )0.031 (F) 0.007 (Be) 0.0021 HCTH 0.0 0.0 0.008 0.010 )0.019 (Ne) 0.004 (C) )0.0064 Increasing the ratio of the Becke 88 exchange contribution at long-range reduces the errors of the atomization, ionization and the total atomic energies....

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...In the CAM-B3LYP functional, we have replaced the Becke parameter a by two parameters a, b for mixing Becke 1988 exchange and HF exchange, with l describing the conversion from one to the other through Eq....

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