Potential energy surfaces

1. Potential energy surfaces Fernando Pirani Dipartimento di Chimica Universita’ degli studi di Perugia Erice 1-7 Agosto 2005

2. The detailed knowledge of the Interaction V(R) is still a challenge • Presented topics: • well assessed arguments • questions under investigation • future perspectives

3. The detailed characterization and modelling of the intermolecular interaction requires the combination of New experiments Development of empirical and semiempirical methods Extensive ab initio calculations

4. Absorption spectroscopy

5. diffraction oscillations rainbow scattering angle Differential cross section

6. Integral cross section the Lambert Beer law

7. average value glory oscillations Q(v)v2/5 Integral cross section, Q(v) v average value ~v-2/5 diffraction oscillations collision velocity , v glory Interaction potential , V intermolecular distance, R rainbow differential cross section average value rainbow diffractions Scattering investigations scattering angle

8. Perugia experimental setup for integral cross section measurements

9. cryostat entrance slit electron beam to the detector multiplier defining slit 60cm 50cm 12cm 38cm 32cm S cell IB / I0 Beam transmittance (paramagnetism) skimmers ionizer chopper I/ I0 Beam attenuation (intermolecular forces) supersonic beam source velocity scattering Stern-Gerlach quadrupole selector chamber magnet mass filter Experimental Apparatus velocity selection magnetic analysis N IB I0 scattering experiments I0 I

10. F.Pirani et al. JCP 75, 1042 (1981) • 1000 K V(R) (b) 10 K R O2-Kr Ar-Kr If the molecule rotate faster then the time required for a collision, an effective averaged interaction drives the collision (O2)=1.60 Å3 (Ar)=1.64 Å3

11. O2-Kr The scattering of aligned molecules: the anisotropy in van der Waals interactions V. Aquilanti et al., JCP, 109, 3898 (1998)

12. The glory shift: a signature of an embryonic H-bond αH2O=1.47 Ǻ3 αO2=1.60 Ǻ3 V. Aquilanti et al., Angew. Chem. Int. Ed.,117, 2408 (2005)

13. The glory shift and quenching: the role of additional components to vdW

14. The glory quenching and its modification with the controlled change in the sublevels of the Cl atoms provide information on the spherical component V0(vdW) and on the interaction anisotropy V2 Kr+Cl- V2 – configuration interaction Kr Cl

15. Supermolecule Approach VAB = EAB - EA - EB where EAB denotes the energy of the supermolecule and EA and EB the partners energies Perturbation Theory VAB = Vex.rep.+ Vch.tr.+ Vind+ Vdisp+ Velectr + … Ab initio methods

16. Identification of the leading interaction components VAB = Vex.rep.+ Vind+ Vdisp + Vch.tr.+ Velectr = VvdW + Vch.tr.+ Velectr Semiempirical and empirical methods Semiempirical: representation of each component by theoretical formulas where some quantities are identified with basic properties of involved partners Empirical: representation of each component by empirical formulas given in terms of fundamental physical properties of involved partners (polariz., charge, permanent multipole, ioniz. potential, electron affinity…)

17. The polarizability properly scales both attraction and repulsion When only van der Waals forces are operative! repulsion intermolecular distance a1/3 potential energy molecular volume ε attraction ~ R-6(n-n) || ~ R-4 (i-n) Rm well region molecular polarizability atomic radius Neutral-neutralJ. Chem. Phys., 95, 1852 (1991) Further applications: ion–neutral Chem.Phys.Lett. 183, 297 (1991) multicharged ion–neutraland ion–ion Chem.Phys. 209, 299 (1996) Atom (ion)-polyatomic molecule – Chem.Phys.Lett 350, 286 (2001); Chem.Phys.Lett. 394, 37 (2004)

18. van der Waals forces NEUTRAL A – NEUTRAL B (polarizabilities αA,αB) Models for the representation of intermolecular forces J. Chem. Phys., 95, 1852 (1991) ~100 systems investigated (Rm<3%  <15%) Closed shell-closed shell Other references: ion–neutral Chem.Phys.Lett. 183, 297 (1991) multicharged ion–neutral and ion–ion Chem.Phys. 209, 299 (1996) atom-polyatomic molecule – Chem.Phys.Lett. 350, 286 (2001) Chem.Phys.Lett. 397, 37 (2004)

19. (Ion charge Z and polarizabilities αI, αN)

20. + vdW

21. (repulsion + induction + dispersion)

22. non resonant (excimers, dications, …) resonant at crossing (harpooning, …) resonant at all R (H2+,Ar2+, …)

23. The configuration interaction in rare gas-oxides, RgO and in rare gas-halides, RgX

24. Rare gas sulfides: the interaction anisotropy van der Waals +charge transfer

25. The electrostatic component is important in systems, such as: • Alkali halides • Na+ + Cl-(charge—charge) V. Aquilanti, D. Cappelletti, F. Pirani • Chem. Phys.,209, 299 (1996) • Excimers • Kr+ + Cl-(charge—charge) M. Krauss, J. Chem. Phys.,67, 1712 (1977) • (charge--quadrupole)

26. electron transfer coupling H H+ X+(3P) X2+(4S) + proton-induced dipole proton-quadrupole Coulomb dispersion induction exchange repulsion HX+2- Double photoionization of HX (X=Cl,Br,I)

27. 1 Low lying states of molecular dications HX++

28. HCl2+ 42 40 HBr2+ 1 38 1 HI2+ 36 POTENTIAL ENERGY (eV) 1 3 34 1 3 32 1 1 30 3 28 0 2 4 6 0 2 4 6 0 2 4 6 INTERNUCLEAR DISTANCE (Å)

29. He*(21S) + N2O He*… NNO NNO … He*

30. VAB = Vex.rep.+ Vind + Vdisp + Vch.tr + Velectr = VvdW + Vch.tr. + Velectr As usual The atom (ion) — molecule case Prototypical examples are: F, Cl – H2V. Aquilanti et al, JPC A, 105, 2401 (2001) Ar+ - N2R. Candori et al, JCP, 115, 8888 (2001) Vch.tr.depends on the overlap between orbitals which exchange the electron (exponentially decreasing with R and varying with the relative orientation of orbitals involved in the exchange) Velectr relates to the charge distribution on the molecular frame (obtainable from ab initio calculations) VvdW arises from the combination of size repulsion effects (short range) with dispersion and induction attraction (long range). It is very difficult to assess and to model such component

31. Atom: Vvdw + Vch.tr. Ion: Vvdw + Velectr + Vchtr + 2- + 3a1 (sp2 lone pair orbital) 1b1 (2p non bonding orbital) Atom (ion) - water

32. Atom (ion) - benzene

33. The atom (ion) — molecule case The assessment of the strength of the van der Waals component involves again the characterization of its dependence on the molecular polarizability (related to features of the electronic distribution in the HOMO and LUMO orbitals). For small and homonuclear diatoms (H2 , N2 …) the electronic distribution is approximately representable through an ellipsoid whose dimensions depend on the tensor components of the polarizability (a single dispersion-inductioncenter). For big and homonuclear diatoms (I2 , Br2 …)the electronic distribution isbetter represented by a combination of ellipsoids defined in terms of molecular polarizability contributions: one associated to the bond and the other to the lone pairs (multiple dispersion-induction centers). Heteronulear diatoms (HCl, HBr …) fall in the two previous cases. A polyatomic molecule can be considered as the combination of bond and lone pair components (multiple dispersion-induction centers). For the separability of molecular polarizability into several tensor components see JCP, 32, 502 (1960)

34. The atom (ion) — molecule case The proper modelling of the van der Waals component requires the development of atom (ion)—bond and atom (ion)—lone pairpotential models exhibiting two basic features: • they must involve an unique potential function, defined in terms of • few parameters, each one having a specific meaning; • they must remove, totally or partially, the inadequacies, both at short • and at long range, of the “venerable” LJ models

35. C r  B A Atom(ion)-bond formulation of the potential energy function (1) CPL, 394, 37 (2004) m= 6 atom m= 4 ion

36. Two-body interactions Three body interactions Potential energy function: Atom-bz

37. Atom(ion)-bond formulation of the potential energy function (2)

38. Benzene-Ar system

39. Benzene-Cl- and Benzene-K+clusters

40. Atom-bond formulation vs ab initio calculations: the case of K+ – C6H6

41. (Benzene)m-ion-Atomn clusters

42. Ar-Bz-Cl- and Ar-Bz-K+clusters: Potential energy surfaces Only one isomer Two isomers

43. Ar-Bz-Cl- Ar-Bz-K+ Ar-Bz-Cl- and Ar-Bz-K+clusters

44. The PES’s and related force fields have been extensively exploited in molecular dynamics simulations DL-POLY programs Cluster configuration energy (function of Etotal) defined, using the present method, as a sum of fragment contributions beginning of dissociation opening of isomerization channels

45. Conclusions and perspectives • Present investigations open new questions and further perspectives: • Molecule considered as non-rigid body • crucial is the dependence of VAB on the internal coordinates ri • the basic point is the characterization of the dependence of the polarizability α • on ri • - Molecule-Molecule systems

46. α = non bonding electron + bonding electron  effective bond  excitation contributions contributions order function Empirical study of the polarizability α and its anisotropy Δα/α for diatomic bonds and molecules • The above terms depend on: • - the number of non bonding and total valence electrons of Atom 1 • || || Atom 2 • polarizability value of Atom 1 and Atom 2 • - distance r and equilibrium distance re Δα/αdefined in a similar way The method provides correct values for several homonuclear and heteronuclear bonds

48. R  r N2 – N interaction potential from polarizabilities atom-bond model atom-atom model

49. Diatom-diatom interaction potentials from polarizabilities

50. v(t+t/2)  v(t-t/2) + t F(t)/m r(t+t)  r(t) + t v(t+t/2) v(t)=0.5*(v(t+t/2) + v(t-t/2)) • The benzene molecule is considered as a rigid body. • Dynamical simulations have been performed in the context of the microcanonical ensemble. • A time step of 1 fs has been adopted to integrate the equa-tions of the motion. Dynamical simulations