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NBO Analysis

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Natural Bond Orbital Analysis

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NBO Analysis

  1. 1. Advance Natural Bond Orbital (NBO) Analysis D Setiawan Advance Computational Chemistry Laboratory Southern Methodist University dsetiawan@smu.edu November 11, 2015 D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 1 / 36
  2. 2. NBO: Brief Overview NBO is a calculated bonding orbital with maximum electron density. Hierarchical Atomic/Molecular Orbitals in the NBO analysis: AO → NAO → NHO → NBO → NLMO → MO NAO: Natural Atomic Orbitals NHO: Natural Hybrid Orbitals NBO: Natural Bond Orbitals NLMO: Natural (Semi-)Localized Molecular Orbitals D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 2 / 36
  3. 3. Natural Atomic Orbitals ”Natural” atomic orbitals are the optimal (maximum occupancy), effective AOs in the molecular environment, derived by: diagonalizing the localized block of the full density matrix of a given molecule, which is associated with basis functions on that atom Thus they meet simultaneous requirements of orthonormality and maximum occupancy. For isolated atoms: NAOs coincide with NOs. For a polyatomic molecule: the NAOs mostly retain one-centre character (in contrast to NOs that become delocalized over all nuclear centers). D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 3 / 36
  4. 4. NBO Output: Natural AO Occupancies Lists the atoms with their respective NAO types attached: angular momentum type, orbital type, and orbital occupancy D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 4 / 36
  5. 5. NBO Output: NPA Summary Population Inversion WARNING: occupancy ordering inconsistent with energy ordering; May occurs for Rydberg-type orbitals of very low occupancy or near-degeneracy in occupancy or energy, so that no significant physical effects are indicated. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 5 / 36
  6. 6. NBO Output: NPA Summary Gives natural atomic charges (or sometimes attributed as NBO charges) and total core, valence, and Rydberg populations on each atom; Atomic charges are the differences between the nuclear charge and the total (natural) electronic population. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 6 / 36
  7. 7. NBO Output: Natural Electron Configuration Given as “natural” electron configuration for each atom; Can be somewhat related (idealized) to the Lewis’ electron configuration. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 7 / 36
  8. 8. NBO Output: Wiberg Bond Index (NAO Basis) Bond Order: Originally, a quantitative net measure of electronic population occupying bonding (molecular) orbital. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 8 / 36
  9. 9. Wiberg BI in NAO Basis The original Wiberg’s BI was defined for close-shell semi-empirical wavefunctions with the orthonormal basis: WAB = µ∈A ν∈B |Dµν|2 (1) Dµν is the off-diagonal Density Matrix elements with NAO is an orthonormal orbital. For the “general” ab initio analysis, for which orthonormal basis sets is not used: Mayer’s Bond Index D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 9 / 36
  10. 10. Historical Perspective: Mayer’s BI Generalization of the original Wiberg’s BI for non-orthogonal basis functions, by taking into account also the Overlap Matrix S MAB = µ∈A ν∈B (DS)µν(DS)νµ (2) Nowadays one may instead use some orthogonalization techniques (e.g. Lowdin, OWSO analysis) OWSO: Occupancy-weighted Symmetric Orthogonalization, is used in the NBO analysis D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 10 / 36
  11. 11. Wiberg BI in NAO Basis: Spin Polarized Systems For spin polarized systems NBO analysis is automatically performed three times, yielding three different part of the outputs 1 Total Spin Orbitals 2 Alpha Spin Orbitals 3 Beta Spin Orbitals The spin-corrected bond order in the NAO basis will be: WAB = 2W (α) + 2W (β) (3) D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 11 / 36
  12. 12. NBO Output: Bond Valencies D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 12 / 36
  13. 13. NBO Output: Search for An Optimum Lewis Structure Check whether ”reasonable” Lewis structure is obtained, e.g. the occupancy of Lewis orbitals should not be lower than 1.90 and non-Lewis orbitals (e.g. anti-bonding, or Rydberg-types) should not higher than 0.10. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 13 / 36
  14. 14. NBO Output: Natural Bond Orbitals Gives: Occupancies, Bond-types, Atomic/Bonding-center, and their respective Natural Hybrid Orbitals (NHOs) composition (i.e. “covalent” or “ionic” character). D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 14 / 36
  15. 15. Natural Bond Orbitals The NHOs part lists the orbital-hybridization (given in percentage, and also in a relative-scale, with lowest percentage orbital set as 1); For bonding and anti-bonding type orbitals, contribution of the NHOs (i.e. the polarization coefficient) are also given. Below each NHO label is the set of NAOs coefficients, ordered according to NAOs listed at the top part of the output (e.g. Carbon atom thus will have set of 9 coefficients if calculated using a double zeta basis sets). D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 15 / 36
  16. 16. NBO Output: NHO Directionality Summary of the angular properties of the NHOs; The ”direction” of a hybrid is specified in terms of the polar (θ) and azimuthal (φ) angles (in a polar coordinate system: θ = 90.0, means orbitals are on the XY plane; φ = 0.0, means orbitals are on the X axis). D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 16 / 36
  17. 17. NBO: 2nd Order Perturbation Analysis of Fock Matrix Summary of the 2nd -order perturbative estimates of donor-acceptor (bonding-antibonding) interactions in the NBO basis. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 17 / 36
  18. 18. NBO: 2nd Order Perturbation Analysis of Fock Matrix The purpose of this analysis is to give estimates of a “delocalization” corrections w.r.t the zeroth-order natural Lewis structure (i.e. charge transfer characteristic). These perturbations lead to donation of electron (occupancy) from the localized NBOs of the idealized Lewis structure into the (empty) non-Lewis orbitals (and thus, to departures from the idealized Lewis structure description): D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 18 / 36
  19. 19. NBO: 2nd Order Perturbation Analysis of Fock Matrix E(2) = ∆Eij = qi F(i, j)2 j − i (4) E(2) refers to the“(2-electron) stabilization energy” (see also the related Perturbational MO (PMO) Theory Models & Concepts Class) qi is the donor orbital occupancy; i , i are NBO orbital energies; and F(i, j) is the off-diagonal elements of the NBO Fock matrix. All possible interactions are considered. Default threshold for printing is 0.50 kcal/mol. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 19 / 36
  20. 20. NBO Output: NBO Summary The qualitative delocalization to non-Lewis orbitals: (i.e. the acceptor NBOs): corresponds to the “principal delocalization tails” of the natural localized molecular orbital (NLMO) associated with the parent donor NBO. D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 20 / 36
  21. 21. Natural (Semi-)Localized Molecular Orbitals (NLMO) Notes: NLMO summary table or plotting will require “NLMO” keyword in the NBO input file. Image Source: http://nbo6.chem.wisc.edu/ D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 21 / 36
  22. 22. MO vs. NLMO: H-Bond in HSSH Dimer Image Source: http://nbo6.chem.wisc.edu/ D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 22 / 36
  23. 23. NBO Orbitals: Sorting & Reordering NBO orbitals are sorted by type: BD, CR, RY*, and BD* (NBO3) NBO orbitals are sorted by type: CR, BD, BD*, and RY (NBO6) NBO programs will resorting these orbitals based on their occupancies, from lower to higher, which will go in this order: CR, BD, BD*, RY* (RY, NBO6) The numbering in the molecular viewer (e.g. GaussView, Avogadro) are thus not referring to the numbering used by the NBO program! D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 23 / 36
  24. 24. NBO Orbitals: Sorting & Reordering (NBO3) D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 24 / 36
  25. 25. NBO Orbitals: Sorting & Reordering (NBO3) D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 25 / 36
  26. 26. NBO Orbitals: Sorting & Reordering (NBO6) D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 26 / 36
  27. 27. Running NBO in Gaussian09 G09 Input File # METHOD/BasisSet Pop(NBO) G09 Input File: Read from Chk Files #P METHOD/BasisSet Geom(AllCheck) Guess=(Read,Only) Pop(NBO6read,SaveNBOs) NBO Keywords: At the end of file $nbo reson bndidx [other-keywords] $end D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 27 / 36
  28. 28. Running NBO in the cluster Maneframe module load gaussian module load nbo SMUHPC export PATH=/data/share/software/NBO6/nbo6/bin:$PATH D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 28 / 36
  29. 29. Some Important NBO Keywords NBOSUM, requests printing of the NBO summary table. RESON, requests search for highly delocalized structures. NOBOND, requests that no bonds (2-center NBOs) are to be formed in the NBO procedure; This is useful for highly ionic species. 3CBOND, requests search for 3-center bonds; This is useful for diborane and other electron-deficient ’bridged’ species. NLMO computes and prints out the summary table of Natural Localized Molecular Orbitals (NLMOs). BNDIDX, calculates and prints Wiberg bond indices. NRT, calculates and prints Natural Resonance Theory analysis and bond indices. E2PERT=N, increase/decrease the printing threshold for the 2nd Order Perturbation stabilization energies (in kcal/mol). D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 29 / 36
  30. 30. Questions? D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 30 / 36
  31. 31. Tasks: Fluoroamines H N H H F N H F F N F F H N F H C N F H H N N F H N N F F Input Files can be found in SMUHPC:/users/chem/Temp/NBOLab D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 31 / 36
  32. 32. Tasks: Fluoroamines How does different fluorination affect the charge distributions and NF bond order? How does different substituents affect the charge delocalizations? Which orbitals might be involved in this? What are the characteristics of the bonds? Can there be more than one possible (resonance) structures? Bonus: Sum up the total 2pz (oop, ⊥ w.r.t. the molecular plane) orbital occupancies. How do these electron population might affect NF bond order upon planarization? D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 32 / 36
  33. 33. NBO Analysis: Fluoroamines H N H H F N H F F N F F H N F H -1022 -358 +169 +571 -190-265 -232+341 +312 +296 C N F H H +14 -258 +187 -106 +192 N N F H N N F F +215 +192 -193-258 +336 -294 D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 33 / 36
  34. 34. NBO Analysis: Fluoroamines D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 34 / 36
  35. 35. NBO Analysis: Fluoroamines D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 35 / 36
  36. 36. NBO Analysis: Fluoroamines # Molecule Central PYR PLA ∆Pop Substituent PYR PLA ∆Pop ∆Pop PYR-∆E PLA-∆E Atom (E) Pop[LP(E)] Pop[LP(E)] [LP(E)] Atom (X) Pop[LP(X)] Pop[LP(X)] [LP(X)] TOTAL (lpE−lpX) (lpE−lpX) 4 H2N-H(1A1), C3v N 1996.60 1994.97 -1.63 H -1.63 5 H2N-F(1A ), Cs N 1995.13 1989.10 -6.03 F 1995.79 1996.81 1.02 -5.01 3.18 128.82 6 H(F)N-F(1A ), Cs N 1996.46 1987.39 -9.07 F 1994.08 1996.70 2.62 -6.45 41.15 126.33 7 F2N-F(1A1), C3v N 1996.19 1994.40 -1.79 F 1980.43 1997.78 17.35 15.56 61.91 125.36 31 H2N-Cl(1A ), Cs N 1994.59 1986.82 -7.77 Cl 1995.60 1997.18 1.58 -6.19 85.23 17.38 32 H(Cl)N-Cl(1A ), Cs N 1993.53 1981.33 -12.20 Cl 1994.24 1997.79 3.55 -8.65 113.50 4.27 33 Cl2N-Cl(1A1), C3v N 1992.60 1978.22 -14.38 Cl 1982.25 1998.25 16.00 1.62 61.81 9.60 34 H2P-H(1A1), C3v P 1998.48 1993.37 -5.11 H -5.11 35 H2P-F(1A ), Cs P 1996.75 1979.41 -17.34 F 1984.21 1991.55 7.34 -10.00 42.85 225.13 36 H(F)P-F(1A ), Cs P 1996.46 1964.46 -32.00 F 1981.29 1990.22 8.93 -23.07 42.95 241.25 37 F2P-F(1A1), C3v P 1997.11 1994.61 -2.50 F 1971.21 1921.90 -49.31 -51.81 40.64 22.00 38 H2As-H(1A1), C3v As 1998.22 1993.15 -5.07 H -5.07 39 H2As-F(1A ), Cs As 1996.60 1976.73 -19.87 F 1989.36 1995.09 5.73 -14.14 2.03 216.84 40 H(F)As-F(1A ), Cs As 1996.58 1967.08 -29.50 F 1987.55 1993.80 6.25 -23.25 3.07 234.70 41 F2As-F(1A1), C3v As 1997.14 1998.03 0.89 F 1978.60 1938.76 -39.84 -38.95 0.73 53.83 Table 1: Lone pair orbital population based on Natural Bond Orbital Analysis on the central E = N, P, or As atoms and on substituent atoms X = F or Cl of molecule 4-7 and 31-41. The electron occupancies and differences are given in me. It is shown that the lone pair occupancies at central atoms are decreasing at the planar form, with exception of atom As of molecule 41, while for substituent atoms, lone pair densities gaining electrons, except for molecule 37 and 41. ∆Pop TOTAL shows how many (partial) electrons gain/loss by the lone pair orbitals of E and X as results of planarization. The ∆E(lpE-lpX) shows the energy differences between the lone pair orbitals in kcal/mol. All values are based on CCSD(T)/aug-cc-pVTZ calculations. 1 D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 36 / 36

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