Exploring chemical space using perturbation theory

We investigate the performance and limitations of perturbation theory applied to “alchemical” interpolations of nuclear charges and positions. The performance of first and second order estimates are examined for small molecules and crystalline systems within KS-DFT. Chemical accuracy can be achieved for some cases by first order estimate due to cancellations of higher order effects. In this case, the inclusion of second order correction gives worse results because the balance of error cancellation is disturbed. An empirical reference bond length is found for each bond type, which provides maximal error cancellation effects for first and second order estimates and is applicable across different chemical environments including σ-and π-bonding. We showed that if accurate density information is available, highly accurate first order estimates of potential energy surface is achievable. Results are presented for (i) covalent bonds to hydrogen in 12 molecules with 8 valence electrons (CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, GeH4 , AsH3 , H2Se, HBr); (ii) main-group single bonds in 9 molecules with 14 valence electrons (CH3F, CH3Cl, CH3Br, SiH3F, SiH3Cl, SiH3Br, GeH3F, GeH3Cl, GeH3Br); (iii) main-group double bonds in 9 molecules with 12 valence electrons (CH2O, CH2S, CH2Se, SiH2O, SiH2S, SiH2Se, GeH2O, GeH2S, GeH2Se); (iv) main-group triple bonds in 9 molecules with 10 valence electrons (HCN, HCP, HCAs, HSiN, HSiP, HSiAs, HGeN, HGeP, HGeAs). First order estimates are utilized to predict band structure of crystalline materials, including (i) III-V semiconductors AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb; (ii) IV-IV semiconductors Si, Ge, Sn, SiGe, GeSn, SnSi, where quantitative predictions is achieved with MAE = 0.05 eV for density changes less than 0.25 a.u./per atom. A hybrid gradient based genetic algorithm has been applied to design Al(x)Ga(1−x)As crystals with optimal band structure using first order alchemical estimates. Homogeneous Al 0.67 Ga 0.33 As crystals are identified to have the largest direct band gap of 2.1 eV. Alchemical perturbation to geometry variations is also studied, which proves that it is necessary to take the response of electron-electron interaction energy into account. The behavior of alchemical estimates is investigated up to fourth order for one-electron H2+ within Hartree-Fock theory. A finite radius of convergence is observed due to swapped order of Hamiltonian eigenvalues.