Métodossemiempíricos

marquez@us.es

1

Métodos semiempíricosModelización Molecular

Antonio M. Márquez

MASTER OFICIAL

ESTUDIOS AVANZADOS EN QUÍMICA

Departamento de Química FísicaUniversidad de Sevilla

Curso 2019/20

marquez@us.es (Química Física) Métodos semiempíricos 1 / 26

Métodossemiempíricos

marquez@us.es

2

Contenidos del tema

1 Introduction

2 CNDO formalism

3 INDO formalism

4 NDDO formalism

5 Benefits and shortcomings

marquez@us.es (Química Física) Métodos semiempíricos 2 / 26

Métodossemiempíricos

marquez@us.es

3

Introduction

1 Introduction

2 CNDO formalism

3 INDO formalism

4 NDDO formalism

5 Benefits and shortcomings

marquez@us.es (Química Física) Métodos semiempíricos 3 / 26

Métodossemiempíricos

marquez@us.es

4

Introduction

Objectives

Reduce high computational cost of ab initio calculations whilekeeping a reasonable accuracyEstimate value of 2e-integrals without performing the actualcalculation

Sµν = 〈χµ | χν〉hµν = 〈χµ | h | χν〉

Fµν = hµν +all AO∑λσ

Dλσ [ (µν | λσ)− (µλ | νσ) ]

marquez@us.es (Química Física) Métodos semiempíricos 4 / 26

Métodossemiempíricos

marquez@us.es

5

Introduction

General approximations

Fµν = hµν +all AO∑λσ

Dλσ [ (µν | λσ)− (µλ | νσ) ]

2e-integrals tend to zero when the atoms are far apart1st approximation: assume 2e-integrals to be zeroUse only valence electronsUse Slater orbitals as basis set

marquez@us.es (Química Física) Métodos semiempíricos 5 / 26

Métodossemiempíricos

marquez@us.es

6

CNDO formalism

1 Introduction

2 CNDO formalism

3 INDO formalism

4 NDDO formalism

5 Benefits and shortcomings

marquez@us.es (Química Física) Métodos semiempíricos 6 / 26

Métodossemiempíricos

marquez@us.es

7

CNDO formalism

CNDOComplete Neglect of Differential Overlap

Sµν = δµν

(µν | λσ) = δµνδλσ(µµ | λλ) = γAB

γAA = IPA − EAA

γAB =γAA + γBB

2 + rAB(γAA + γBB)

hµµ = −IPµ −∑

k

(Zk − δZAZk

)γAk

hµν = βABSµν =(βA + βB)

2Sµν

Note: in this last expression S is the actual overlap matrix and β are semiempírical parameters

Minor modifications: CNDO/2, CNDO/3, CNDO/BW, PPP, . . .

marquez@us.es (Química Física) Métodos semiempíricos 7 / 26

Métodossemiempíricos

marquez@us.es

8

CNDO formalism

CNDOMain drawbacks

No geometry optimizations and p orbitals treated as equivalent when computing γAB

Failure to distinguish one-center cases between different orbitalsFailure to distinguish different orbitals orientations

These methods are obsolete now

marquez@us.es (Química Física) Métodos semiempíricos 8 / 26

Métodossemiempíricos

marquez@us.es

9

INDO formalism

1 Introduction

2 CNDO formalism

3 INDO formalism

4 NDDO formalism

5 Benefits and shortcomings

marquez@us.es (Química Física) Métodos semiempíricos 9 / 26

Métodossemiempíricos

marquez@us.es

10

INDO formalism

INDOIntermediate Neglect of Differential Overlap

More flexible handling of 2e-interactions on the same centerMotivated to model spectroscopic (vis-uv) transitions

(ss | ss) = Gss (ss | pp) = Gsp

(pp | pp) = Gpp (pp | p′p′) = Gpp′

(sp | sp) = Lsp

Many more parameters should be added if d orbitals are present

marquez@us.es (Química Física) Métodos semiempíricos 10 / 26

Métodossemiempíricos

marquez@us.es

11

INDO formalism

INDODrawbacks and potentialities

Predicted geometries are rather poorConsiderable potential for modeling vis-us spectroscopyINDO/S parametrization very succesful for d → d transitions inTM complexesLess useful for transitions not localized to a single center(i.e. M→L or L→M)

marquez@us.es (Química Física) Métodos semiempíricos 11 / 26

Métodossemiempíricos

marquez@us.es

12

INDO formalism

Modified INDO models

Mike J. S. Dewar goal

a parameter set as robust as possible across the widest set of systems(at the time -1970’s- organic chemistry and a few inorganic compoundsincluding 2nd and 3rd row elements)

marquez@us.es (Química Física) Métodos semiempíricos 12 / 26

Métodossemiempíricos

marquez@us.es

13

INDO formalism

MINDO/3 parametrization

Includes geometry optimizationSeparated s and p STOs on the same atomβAB are not averages of atomic parametersDifferent functional form for γAB

Empirical modifications to the nuclear repulsion energy

Every parameter was treated as a free variable suibject only to chemicalrestraints (they should be physically realistic)

marquez@us.es (Química Física) Métodos semiempíricos 13 / 26

Métodossemiempíricos

marquez@us.es

14

INDO formalism

MINDO/3 Performance

Reports energies and heat of formation

Magnitude Mean absolute error

Heat of formation 11 kcal/molIonization potential 0.7 eVBond lengths 0.022 ÅDipole moments 0.45 D

marquez@us.es (Química Física) Métodos semiempíricos 14 / 26

Métodossemiempíricos

marquez@us.es

15

NDDO formalism

1 Introduction

2 CNDO formalism

3 INDO formalism

4 NDDO formalism

5 Benefits and shortcomings

marquez@us.es (Química Física) Métodos semiempíricos 15 / 26

Métodossemiempíricos

marquez@us.es

16

NDDO formalism

NDDO basicsNeglect of diatomic differential overlap

Relax constraints on 2-center 2e-integralsAll (µAνA | λBσB) integrals are retainedNumber of distinct integrals increase to 2025 (including d orbitals)Still much less effort than evaluate all possible integralsMost modern semiempirical models are NDDO

marquez@us.es (Química Física) Métodos semiempíricos 16 / 26

Métodossemiempíricos

marquez@us.es

17

NDDO formalism

MNDOModified Neglect of Diatomic Overlap

Dewar and Thiel (1977)Atomic parametrization (up to 12 parameters per atom)H, B-F, Al-Cl, Zn, Ge, Br, Sn, I, Hg y Pb only s-p orbitalsMNDO/d adds d-orbitals - hypervalent sulphur and transitionmetalsInability to describe hydrogen bonds; poor reliability in predictingheats of formation; highly substituted steroisomers are predictedtoo unstable compared to linear isomers due to overestimation ofsteric repulsions.

marquez@us.es (Química Física) Métodos semiempíricos 17 / 26

Métodossemiempíricos

marquez@us.es

18

NDDO formalism

AM1Austin Model 1

Dewar et al. (1985)H, B-F, Al-Cl, Zn, Ge, Br, I y HgUses a modified expression for core-core repulsion and newparametrizationAllows for some description of the hydrogen bond and improvesheats of formation

marquez@us.es (Química Física) Métodos semiempíricos 18 / 26

Métodossemiempíricos

marquez@us.es

19

NDDO formalism

MNDO-PM3, PM3Parametric Method Number 3

James P. Stewart (1989)H, Li, C-F, Mg-Cl, Zn-Br, Cd-I, Hg-AtParametrized to reproduce large number of molecular propertiesBetter description of hydrogen bond but unphysicalhydrogen-hydrogen attraction in other casesProblems when analyzing molecular interactionsBetter Thermochemistry than AM1

marquez@us.es (Química Física) Métodos semiempíricos 19 / 26

Métodossemiempíricos

marquez@us.es

20

NDDO formalism

PM6Parametric Method Number 6

Careful examination of experimental data to ensure quality andconsistencyUse of ab initio/DFT results when there are no experimental dataCorrection of the core-core repulsion functionNew methods for computing 1- and 2-center integrals for TMs

marquez@us.es (Química Física) Métodos semiempíricos 20 / 26

Métodossemiempíricos

marquez@us.es

21

Benefits and shortcomings

1 Introduction

2 CNDO formalism

3 INDO formalism

4 NDDO formalism

5 Benefits and shortcomings

marquez@us.es (Química Física) Métodos semiempíricos 21 / 26

Métodossemiempíricos

marquez@us.es

22

Benefits and shortcomings

Benefits and shortcomings

Effort grows as O(N3) - Fock matrix diagonalizationPresent limit ∼ 10000 atoms ∼ 100000 basis functionsReasonable results for systems related to those used in theparametrization; results unpredictable in other casesUse to understand and rationalize experimental results

marquez@us.es (Química Física) Métodos semiempíricos 22 / 26

Métodossemiempíricos

marquez@us.es

23

Benefits and shortcomings

Usage limits (I)

The following limitations should always be kept in mindErrors are, in general, more systematic in ab initio or DFT levels.Errors in semiempirical methods are less uniform and thus harderto correct.The observed accuracy may be different for different classes ofcompounds, and there are elements that are more ”difficult” thanothers.Semiempirical methods can only be applied to moleculescontaining elements that have been parametrized.

marquez@us.es (Química Física) Métodos semiempíricos 23 / 26

Métodossemiempíricos

marquez@us.es

24

Benefits and shortcomings

Usage limits (II)

The following limitations should always be kept in mindParametrization require reliable experimental or theoreticalreference data.Different parametrizations of a given semiempirical model may berequired for different properties.There is no systematic way for improving results.There is no implicit procedure to judge the quality of results.

marquez@us.es (Química Física) Métodos semiempíricos 24 / 26

Métodossemiempíricos

marquez@us.es

25

Benefits and shortcomings

Accuracy

Average Unsigned Error in Semiempirical Predictions

Quantity PM6 PM3 AM1 Units

∆Hf 8.01 18.20 22.86 kcal/molr 0.091 0.104 0.130 Åα 7.86 8.50 8.77 degreesµ 0.85 0.72 0.67 DebyeI.P.s 0.50 0.68 0.63 eVConformer Energies 2.2-2.3 1.9-2.8 kcal/molVib. freq. 14%

marquez@us.es (Química Física) Métodos semiempíricos 25 / 26

Métodossemiempíricos

marquez@us.es

26

Benefits and shortcomings

Additional reading

Cramer - Ch. 5Jensen - Ch. 3 (p. 81 onwards)

marquez@us.es (Química Física) Métodos semiempíricos 26 / 26