Introduction to Computational Quantum Chemistry Lesson 8: Population analysis Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 Pictures of orbitals are informative, however numerical values are much easier to quantified and compared. For example a vs tt bonding in organic molecules. What does a population analysis deliver? • Determination of the distribution of electrons in a molecule • Creating orbital shape • Derivation of atomic charges and dipole ( multiple ) moments Methods of calculation • Based on the wave function ( Mulliken, NBO) • Based on the electron density (Atoms in Molecules) • Fitted to the electrostatic potential (CHELPG, MK) Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 2/30 Mulliken Population Analysis Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 3/30 Mulliken Population Analysis Advantages • Most popular method • Standard in program packages like Gaussian • Fast and simple method for determination of electron distribution and atomic charged Disadvantage • Strong dependance of the results from the level of theory (basis set or kind of calculation) Example: Li-charge in LiF Population basis set q(Li,RHF) q(l_i,B3l_YP) Mulliken STO-3G 6-31G 6-311G(d) +0.227 +0.743 +0.691 +0.078 +0.593 +0.558 Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 4/30 Natural Bond Orbital Analysis Martin Novák & Pankaj Lochan Bora Population Analysis Natural Bond Orbital Analysis Based on the theory of Natural Orbitals by Lowdin. Two parts of the methods • NPA Natural population analysis to identify the population numbers • NBO -> Analysis of the bond order based on the electron population obtained by NPA Advantages • Smaller dependence on the basis set • better reproducibility for different molecules • Orientates itself at the formalism for Lewis formulas Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 Practical task • Draw HF molecule, optimize the geometry and generate G09 input. • Use pop=(nbo,savenbo) for NBO or Pop=Full for Mulliken • After Pop command, add a space and type "FormCheck" • Run the calculation Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 I hfMO.out - Notepad 0 File £rjit Format View Help Population analysis using the scf density. orbital symmetries: Occupied (5G) (5G) (sg) (pi) (pi) virtual (sg) (sg) (sg) (pi) (pi) (sg) (pi) (pi) (dlta) (DLTa) (sg) (sg) The electronic state is 1-sg. Alpha occ, eigenvalues — -26.27930 -1. Alpha virt. eigenvalues — 0.21047 1, Alpha virt. eigenvalues -- 1.7S292 2. Alpha virt. eigenvalues — 2.93583 4, 57238 -0,73584 -0.62619 -0.62619 07341 1.33089 1.49191 1.49191 09228 2.09228 2.15811 2.15811 06424 1 2 3 4 5 0 0 a 0 0 ^1 Eigenvalues — -26.27930 -1,57238 -0.73584 -0.62619 -0, 62619 • Create Surface • Select "Molecular Orbital" as surface type • Choose the MO you want to visualize and calculate Martin Novák & Pankaj Lochan Bora Population Analysis □ ► 4 13 You should be able to see something like these that shows the HOMO and LUMO of HF molecules Population Analysis October 13, 2015 10/30 Lesson 8: Solvation models Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 11/30 Solvent effects • The solvent environment influences structure, energies, spectra • Short-range effects • Typically concentrated in the first solvation sphere • Examples: h-bonds, preferential orientation near an ion • Long-range effects o Polarization etc Population Analysis October 13, 2015 12/30 Imlicit vs. Explicit solvation • Implicit solvation • Dielectric continuum • No water molecules perse • Wavefunction of solute affected by dielectric constant of solvent • At 20 °C: Water - e = 78.4; benzene: e = 2.3 ... • Explicit solvation • Solvent molecules included (i.e. with electronic & nuclear structure) • Used mainly in MM approaches • Microsolvation: only few solvent molecules placed around solute o Charge transfer with solvent can occur Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 13/30 mplicit Models Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 14/30 Basic assumptions • Solute characterized by QM wavefunction • Born-Oppenheimer approximation • Only interactions of electrostatic origin • Isotropic solvent at equilibrium • Static model Martin Novák & Pankaj Lochan Bora Population Analysis • Solute is placed in a void of surrounding solvent called "cavity" • Size of the cavity: • Computed using vdW radii of atoms (from UFF, for example) • Taken from the electronic isodensity level (typically ~0.001 a.u.) • The walls of cavity determine the interaction interface (Solvent Excluded Surface, SES) • Size of the solvent molecule determines the Solvent Accessible Surface (SAS) Solvent □ Population Analysis October 13, 2015 16/30 Visualizing cavity • Geomview software (in the modules) • SCRF=(read) in the route section of the job • Use G03Defaults in SCRF command • "geomview" in the SCRF specification • Visualize the "tesserae.off" file Martin Novák & Pankaj Lochan Bora Population Analysis □ Electrostatic Interactions • Self-consistent solution of solute-solvent mutual polarizations • Solute induces polarization at the interface of cavity • This polarization acts back on the solute changing its wavefunction • Various solvation models use different schemes for evaluation of solvation effects • Problems arise when electrostatics do not dominate solvent-solute interactions Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 18/30 Polarizable Continuum Model (PCM) • Treats the solvent as polarizable dielectric continuum • Induced surface charged represent solvent polarization • Implemented in Gaussian, GAMESS Martin Novák & Pankaj Lochan Bora Population Analysis October Solvation Model "Density" (SMD) Full solute density is used instead of partial charges Lower unsigned errors against experimental data than other models Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 COnductor-like Screening MOdel (COSMO) • Solute in virtual conductor environment • Charge q on molecular surface is lower by a factor /(e): Q = f(e)v* • where /(e) = (e - l)/(e + x)\ x being usually set to 0.5 or 0 • Implemented in Turbomole, ADF Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 Beyond basic models Anisotropic liquids Concentrated solutions Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 22/30 Explicit Models Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 23/30 Two models • Microsolvation • Few solvent molecules (1 to 3) put at chemically reasonable place • Water close to exchangeable protons (OH, NH2...) • Macrosolvation • First (sometimes second) solvent layer around the whole molecule • Usually snapshots from MD Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 24/30 Pros & Cons • +++ Modelling of real interactions with solvent (this can be crucial for exchangeable protons in protic solvents) • - Microsolvation lacks sampling • - Computationally more demanding • - For macrosolvation only single point calculations - the geometry is as good as forcefield Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 25/30 Practical task Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 26/30 • Model the CI" + CH3Br -> CH3CI + Br" • Find the energy barrier for the reaction • Select any solvent from Gaussian library (be not concerned about solubility of species or chemical relevance) • Assume Sni and Sn2 reaction pathways • Use "SCRF=(solvent=XY)" in the route section of the calculation Population Analysis October 13, 2015 27/30 • Use B3LYP 6-31++g(d,p) method • Usage of difuse functions when dealing with anions is crucial! • Use ultrafine integration grid • Use Frequency calculations to be sure where on PES you are • For the scan use the distance between C and CI as RC • Negative value of step defines two atoms approaching Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 28/30 • Extraction of values from gaussian runs: • extract-gopt-ene logfile • extract-gopt-xyz logfile • extract-gdrv-ene logfile • extract-gdrv-xyz logfile • extract-xyz-str xyzfile framenumber o extract-xyz-numstr xyzfile • Values ready for plotting in your favorite software Martin Novák & Pankaj Lochan Bora Population Analysis October 13, 2015 29/30 furbomole • Prepare job using define module (see presentation 6 for help) • Setup COSMO using cosmoprep module • Set epsilon to 78.4 and rsolv to 1.93 • Leave all other values at their default • Define radii of atoms using "r all o" for optimized values • Optimize all geometries Martin Novák & Pankaj Lochan Bora Population Analysis □