http://www.ugc-inno-nehu.com/events-2017.html#E09

CLARIFICATION ON PRE-CONCEIVED NOTIONS:

AS in the diagram above, When energy levels are indicated

one above the other it does not imply, that there is such a

distance measurable in units of length between the particles

having the higher enrgy. The energy level diagram is y-axis

scaled in energy units and not cm/km units. It is quite possible

that two particles are much closer (adjacent) to each other but

the energy of the two particles can be much different. Thus

energy level diagrams for our convenience of sketching on

paper drawn a few cms away from each other, in reality no

such line can be darwn for any given energy. The lines drawn

for representing energy by levels is all imaginary. Energy

level differences correspond to actual distances only

depending upon the nature of interactions how much they

depend on distances. Gravitational forces and potential energy

of body at a height is different from the potential energy of

object at lesser height from ground. The objects from a height

fall to the ground, hence the energy differences really

correspond to height from ground. Electrostatic interactions

depend on distance of separation between charges. But this

level may not be referred as high or low from ground level, in

which ever direction it may be it depends only on the distance

of separation; horizontal or vertical.

In view of the clarifications in the previous para, the diagram

below can be less confusing and more realistic.

Thus the situation of why, H2O + hole+ =H2O+ (unstable and

decomposes to products as radicals) occurs more readily, but

not H2O+e-=H2O- is not only to be answered redox potential

wise but also the source or dissipation of energy associated

with oxidation reduction has to be considered and what really

are the energy diffenernces of the positive water ion and

negative water ion has to be known.

To get a preliminary trends a semi empirical QM calculations

are carried out and the results are given numerically in Table,

and graphically as plots which should be aiding in the context

of such queries more convincingly and restore confidence in

students asserting the reasons.

The QM Calculation software ARGUS LAB can be

downloaded and installed from:

http://www.ugc-inno-nehu.com/arguslab/

Another convenient access is to http://www.webmo.net which

calculates at remote server and bring results to to display in

the browser window of the PC.

All QM Calculations are

by PM3 - UHF Method

PM3 is a semi empirical method. In this method as it is semi

empirical, certain integral values (as occurring in secular determinant

elements) are obtained not by evaluating mathematically performing

the integration, but by recognizing the integral as evaluating a

quantity which can be obtained experimentally. Then where ever

such integrals occur, the value obtained experimentally (and tested

well for the transferability of experimental values from one molecule

to another) is substituted for the integral value. In a ab initio

method, all integrals are explicitly evaluated at every stage. For the

details of the PM3 method, in the software ARGUSLAB, used for the

calculation, descriptions that is adequate.

These are all-valence electron calculations, by which it means that

the in each atom only the electron outer most orbit of quantum

number “n” (the primary quantum number) are included and in the

bonding sense, these are the electrons which participate in bonding

to form molecules. Other electrons in the inner orbits are called core

electrons, which has standard parameterized value for each atom.

Thus for C- atom, 1s2 is designated as the core of the atom and

2s2and 2p2 together constitute the valence electrons.

For Oxygen atom, electronic configuration is 1s2, 2s2, 2p4. The 6

electrons of outer most orbits with primary quantum number 2 are

the valence electrons. The core electrons are supposed to remain

unaffected.

There are options to be chosen, depending on the number of valence electrons

in the molecular system is even or odd. Atomic and molecular orbital hold

maximum of a pair of electrons and these electrons obey Hund’s rule and

remain paired in a given Eigen energy value. (If there are possibilities of

degenerate Eigen sates, then since the electrons can occupy one electron each

or together in one state which would be energetically equivalent. And hence

Hund’s rule would not be applicable as a criterion of electron occupancy). It is

this spin pairing designated by α and β states. The spin angular momentum

vectors are oriented opposite to each other and such a paired electron states

to prevail would require an even number of electrons and non degenerate

energy levels. When there is even number of electrons in the system, then all

the electrons all get paired and in remain paired is possible depending on

prevailing degeneracy of eigen states. If there is only odd number of electrons

in the system, then there must be at least one unpaired electron in the system.

Then the identity of which electron in which orbital should be the unpaired

electron? Most possibly it could be the Highest Occupied Molecular Orbital –

the HOMO level. When there is even number of electron, one may choose to

have different multiplicities to result. The final pair of electrons may be left for

unpaired occupation then there would be two unpaired electrons – this would

require system to be in Triplet state. Completely paired system would be

Singlet. Odd number electron systems would have invariably doublet state.

Even number of electrons can have a Singlet or Triplet states. Thus when spin

multiplicity is singlet, The Restricted Hartree Fock (RHF) method is set for

calculations. For such even number electron systems in singlet state,

Unrestricted Hartree Fock (UHF) method is chosen, the spin pairing may not be

conditionally binding, but one may find that energetic of the system during

calculation, results the same RHF type of result for UHF method also. If for odd

number of electrons in the system software would permit only UHF

calculation, and return an error message if RHF option, even by default, is set

for the calculation. Thus one may find for RHF calculation, there would be one

orbital Eigen state for each of the energy and spin paired occupation is

ensured. The paired electrons would occupy one and the same energy Eigen

state. For UHF calculation, corresponding to each one of the RHF Eigen state,

there would be two states one for the α-spin orientation, and another for β-

spin orientation. Thus the energy levels themselves would occur in pairs for the

two spin states. If UHF is set when RHF is a definite possibility, then also the

program would report pair of energy levels corresponding to RHF results, with

the pair of orbital each member having same energy as the other.

Hydrogen Molecule; neutral in charge; 2 electron system.

RHF result:

LUMO

HOMO <α|β>

-----------------------------------------------------------------------------------------

UHF result

α β

LUMO There is one Unoccupied orbital “U”.

HOMO There is one Occupied orbital “O”.

------------------------------------------------------------------

Case of H2 Molecule (UHF)

α β HOMO LUMO

Hydrogen Molecule; neutral in charge; 2 electron system.

αβ

LUMO There is one Unoccupied orbital “U”.

HOMO There is one Occupied orbital “O”.

------------------------------------------------------------------

Hydrogen Molecule negatively charged ion; H2- ; 3 electron system

αβ

LUMO There is only β spin Unoccupied orbital “U”.

HOMO There is one Occupied orbital “O”.

--------------------------------------------------------------------

Hydrogen Molecule positively charged ion; H2+ ; 1 electron system

αβ

LUMO There is one Unoccupied orbital “U”.

HOMO There is only α spin Occupied orbital

------------------------------“-O--”-.---------------------------------------

H2O neutral molecule: 8-electron system

UHF results RHF results

αβ αβ

H2O- negative ion: 9-electron system

αβ

H2O+ positive ion: 7-electron system

αβ

************************************************

**

* ArgusLab (tm) *

**

* Version 4.0 *

**

* Copyright (c) 1996-2003 *

**

* Planaria Software LLC *

* ALL RIGHTS RESERVED *

**

* [email protected] *

* http://www.planaria-software.com *

**

************************************************

*******************************************************************

****

WARNING -- ArgusLab may not be used in any manner that competes

with

the business of Planaria Software LLC or will provide assistance to

any competitor of Planaria Software LLC. The licensee of this

program

is prohibited from giving any competitor of Planaria Software LLC.

access to this program. By using this program, the user

acknowledges

that Planaria Software LLC. is engaged in the business of creating

and

licensing software in the field of computational chemistry and

represents and warrants to Planaria Software LLC that it is not a

competitor of Planaria Software LLC. and that it will not use this

program in any manner prohibited above.

*******************************************************************

****

********* Validated Experiment & Chemical System Settings **********

Calculation started: Tue Jan 16 17:27:47 2018

Title:

D:\h2o-pos-neg-chrg\h2o-go-sp.gouhf-sprhf

System Type Quantum Mechanical

Hamiltonian PM3 (NDDO)

SCF Type RHF

Run Type SCF

Atoms 3

Electrons 8

Water Model SPCE

Coordinates angstroms

Basis set Minimal Valence Basis as STO 6G

Max. SCF cycles 800

SCF convergence 1.5936e-013 au. for energy

PM3 param file C:\Program Files\ArgusLab\params\pm3.prm

SCF saved every 1000 cycles

Two-electron integrals 1000

buffer size random list in core

storage

one center

Property integrals length operator

Dipole integrals

Input Atomic Information

************************

1 O -0.020530 -0.006928 0.000000

2 H -0.020530 -0.569806 0.768970

3 H -0.020530 -0.569806 -0.768970

Cite ArgusLab as:

*****************

ArgusLab 4.0

Mark A. Thompson

Planaria Software LLC, Seattle, WA.

http://www.arguslab.com

Journal Citations for this Calculation

**************************************

Thompson, M. A., Zerner M. C.

J. Am. Chem. Soc., 113, 8210, (1991)

Mark A. Thompson, Eric D. Glendening,

and David Feller J. Phys. Chem. 98,

10465-10476, (1994)

Mark A. Thompson, and Gregory K. Schenter

J. Phys. Chem. 99, 6374-6386, (1995)

Mark A. Thompson, J. Phys. Chem. 100,

14492-14507, (1996)

PM3 references:

***************

James J. P. Stewart, J. Comp. Chem., 10,

209-220 (1989)

James J. P. Stewart, J. Comp. Chem., 10,

221-264, (1989)

*************************************************************

Constructing Chemical System(s)

Basis Set

***********

basis functions : 6

shells :4

primitives : 24

AtNum Atom Type Nzeta STO coeff STO exp. Contraction

------------------------------------------------------------------------

-----------------------------

1HS 1 1.0000 0.9678

7.150641 C(1) = 0.009164 Exp(1) = 21.639463 Norm(1) =

2.003566 C(2) = 0.049361 Exp(2) = 3.967572 Norm(2) =

0.770722 C(3) = 0.168538 Exp(3) = 1.109984 Norm(3) =

0.345834 C(4) = 0.370563 Exp(4) = 0.381309 Norm(4) =

0.170125 C(5) = 0.416492 Exp(5) = 0.148074 Norm(5) =

0.087463 C(6) = 0.130334 Exp(6) = 0.060985 Norm(6) =

8O S 1 1.0000 3.7965

C(1) = -0.004151 Exp(1) = 399.044026 Norm(1) =

63.632019 C(2) = -0.020670 Exp(2) = 73.180617 Norm(2) =

17.832291 C(3) = -0.051503 Exp(3) = 20.565332 Norm(3) =

6.882748 C(4) = 0.334627 Exp(4) = 2.940888 Norm(4) =

1.600549 C(5) = 0.562106 Exp(5) = 1.334756 Norm(5) =

0.885037 C(6) = 0.171299 Exp(6) = 0.636538 Norm(6) =

0.507900

8OP 1 1.0000 2.3894

114.895290 C(1) = 0.007924 Exp(1) = 33.503464 Norm(1) =

21.411366 C(2) = 0.051441 Exp(2) = 8.737022 Norm(2) =

5.925285 C(3) = 0.189840 Exp(3) = 3.126190 Norm(3) =

1.991611 C(4) = 0.404986 Exp(4) = 1.306807 Norm(4) =

0.748890 C(5) = 0.401236 Exp(5) = 0.597561 Norm(5) =

0.293579 C(6) = 0.105186 Exp(6) = 0.282506 Norm(6) =

Memory for Main Chemical System

Max. number 2-ele. ints. = 39

Memory Requirements (bytes)

*****************************

Core 32928

Scratch 1344

Contents Of Parameter Database For Relevant Atoms

*************************************************

energy in EV. others in AU.

** WARNING ** PrintParams: under construction for this HamType

System charge 0.000000

***** Integrals *****

PM3 two-center two-electron integrals

MNDO-type Two-electron integrals: elapsed time 0 sec.

elapsed time 0 sec.

Coulomb integrals for semi-empirical

elapsed time 0 sec.

One-center exchange integrals for semi-empirical

elapsed time 0 sec.

Total number of 2-ele integrals 33

Dipole length integrals

elapsed time 0 sec.

Overlap integrals

elapsed time 0 sec.

Transformation Matrix

elapsed time 0 sec.

Integrals elapsed time 0 sec.

***** SCF *****

Core repulsion 5.48205 au

Calculating one electron matrix

Diagonalizing starting one-ele. matrix

Performing SCF

Cycle Energy (au) Difference

**********************************************

1 -11.804580 -0.0158553

2 -11.820435218 -0.0975803

3 -11.918015512

4 -11.935564538 -0.017549

5 -11.938926856 -0.00336232

6 -11.939562475 -0.000635619

7 -11.939683675

8 -11.939707228 -0.0001212

9 -11.939711915 -2.35527e-005

10 -11.939712872 -4.68749e-006

11 -11.939713073 -9.57012e-007

12 -11.939713115 -2.00312e-007

13 -11.939713125 -4.28914e-008

14 -11.939713127 -9.36675e-009

15 -11.939713127 -2.07924e-009

16 -11.939713128

17 -11.939713128 -4.6764e-010

-1.06251e-010

-2.4329e-011

18 -11.939713128 -5.60618e-012

19 -11.939713128 -1.29319e-012

20 -11.939713128 -3.01981e-013

21 -11.939713128 -6.75016e-014

SCF converged

Writing final SCF to disk

Final SCF Energy = -11.9397131275 au

Final SCF Energy = -7492.2899 kcal/mol

Saving the final SCF to the restart file D:\h2o-pos-neg-chrg\h2o-

go-sp.gouhf-sprhf.restartscf

SCF elapsed time 0 sec.

***** Properties *****

Ground state properties

*****************************

***** Heat of Formation *****

-53.3387 kcal/mol

ZDO Atomic Charges

*******************

1 O -0.3583

2 H 0.1792

3 H 0.1792

Wiberg Atom-Atom Bond Orders

*****************************

1 2 3

0.000000

1 0.000000 0.000000

2 0.967905 0.000001

3 0.967905

Ground State Dipole (debye) length

1.74037840

XYZ

-0.00000000 -1.74037840 -0.00000000

Mulliken Atomic Charges

************************

1 O -0.3742

2 H 0.1871

3 H 0.1871

SCF eigenvalues (au) eigenvectors

**********************************

MO number -> 1234 5

Eigenvalues -> -1.351840 -0.645407 -0.533857 -0.452589

0.148595

1 O 2S 0.878297 0.000000 -0.333034 0.000000 -

0.343048 0.000000 0.000000 0.000000 1.000000 -

-0.104822 0.000000 -0.834172 0.000000

1 O 2Px 0.000000 -0.768115 0.000000 0.000000

0.000000 0.329853 -0.452769 0.310842 0.000000

0.329853 0.452769 0.310842 -0.000000

1 O 2Py

0.541451

1 O 2Pz

0.000000

2 H 1S

0.542747

3 H 1S

0.542747

MO number -> 6

Eigenvalues -> 0.195282

1 O 2S 0.000000

1 O 2Px -0.000000

1 O 2Py -0.000000

1 O 2Pz -0.640312

2 H 1S

3 H 1S 0.543139

-0.543139

Properties elapsed time 0 sec.

Total Elapsed Time 0 sec.

************************************************

**

* ArgusLab (tm) *

**

* Version 4.0 *

**

* Copyright (c) 1996-2003 *

**

* Planaria Software LLC *

* ALL RIGHTS RESERVED *

**

* [email protected] *

* http://www.planaria-software.com *

**

************************************************

*******************************************************************

****

WARNING -- ArgusLab may not be used in any manner that competes

with

the business of Planaria Software LLC or will provide assistance to

any competitor of Planaria Software LLC. The licensee of this

program

is prohibited from giving any competitor of Planaria Software LLC.

access to this program. By using this program, the user

acknowledges

that Planaria Software LLC. is engaged in the business of creating

and

licensing software in the field of computational chemistry and

represents and warrants to Planaria Software LLC that it is not a

competitor of Planaria Software LLC. and that it will not use this

program in any manner prohibited above.

*******************************************************************

****

********* Validated Experiment & Chemical System Settings **********

Calculation started: Tue Jan 16 19:21:39 2018

Title:

D:\h2o-pos-neg-chrg\h2o-go-sp.gouhf-spuhf

System Type Quantum Mechanical

Hamiltonian PM3 (NDDO)

SCF Type UHF

Run Type SCF

Atoms 3

Electrons 8

4

Alpha 4

Beta

1

Multiplicity SPCE

Water Model angstroms

Coordinates Minimal Valence Basis as STO 6G

Basis set 800

Max. SCF cycles 1.5936e-015 au. for energy

SCF convergence

C:\Program Files\ArgusLab\params\pm3.prm

PM3 param file 1000 cycles

SCF saved every

1000

Two-electron integrals random list in core

buffer size

storage one center

length operator

Property integrals

Dipole integrals

Input Atomic Information

************************

1 O -0.020530 -0.006928 0.000000

2 H -0.020530 -0.569806 0.768970

3 H -0.020530 -0.569806 -0.768970

Cite ArgusLab as:

*****************

ArgusLab 4.0

Mark A. Thompson

Planaria Software LLC, Seattle, WA.

http://www.arguslab.com

Journal Citations for this Calculation

**************************************

Thompson, M. A., Zerner M. C.

J. Am. Chem. Soc., 113, 8210, (1991)

Mark A. Thompson, Eric D. Glendening,

and David Feller J. Phys. Chem. 98,

10465-10476, (1994)

Mark A. Thompson, and Gregory K. Schenter

J. Phys. Chem. 99, 6374-6386, (1995)

Mark A. Thompson, J. Phys. Chem. 100,

14492-14507, (1996)

PM3 references:

***************

James J. P. Stewart, J. Comp. Chem., 10,

209-220 (1989)

James J. P. Stewart, J. Comp. Chem., 10,

221-264, (1989)

*************************************************************

Constructing Chemical System(s)

Basis Set

***********

basis functions : 6

shells :4

primitives : 24

AtNum Atom Type Nzeta STO coeff STO exp. Contraction

------------------------------------------------------------------------

-----------------------------

1HS 1 1.0000 0.9678

7.150641 C(1) = 0.009164 Exp(1) = 21.639463 Norm(1) =

2.003566 C(2) = 0.049361 Exp(2) = 3.967572 Norm(2) =

0.770722 C(3) = 0.168538 Exp(3) = 1.109984 Norm(3) =

0.345834 C(4) = 0.370563 Exp(4) = 0.381309 Norm(4) =

0.170125 C(5) = 0.416492 Exp(5) = 0.148074 Norm(5) =

0.087463 C(6) = 0.130334 Exp(6) = 0.060985 Norm(6) =

8O S 1 1.0000 3.7965

C(1) = -0.004151 Exp(1) = 399.044026 Norm(1) =

63.632019 C(2) = -0.020670 Exp(2) = 73.180617 Norm(2) =

17.832291 C(3) = -0.051503 Exp(3) = 20.565332 Norm(3) =

6.882748 C(4) = 0.334627 Exp(4) = 2.940888 Norm(4) =

1.600549 C(5) = 0.562106 Exp(5) = 1.334756 Norm(5) =

0.885037

C(6) = 0.171299 Exp(6) = 0.636538 Norm(6) =

0.507900

8OP 1 1.0000 2.3894

114.895290 C(1) = 0.007924 Exp(1) = 33.503464 Norm(1) =

21.411366 C(2) = 0.051441 Exp(2) = 8.737022 Norm(2) =

5.925285 C(3) = 0.189840 Exp(3) = 3.126190 Norm(3) =

1.991611 C(4) = 0.404986 Exp(4) = 1.306807 Norm(4) =

0.748890 C(5) = 0.401236 Exp(5) = 0.597561 Norm(5) =

0.293579 C(6) = 0.105186 Exp(6) = 0.282506 Norm(6) =

Memory for Main Chemical System

Max. number 2-ele. ints. = 39

Memory Requirements (bytes)

*****************************

Core 33672

Scratch 1344

Contents Of Parameter Database For Relevant Atoms

*************************************************

energy in EV. others in AU.

** WARNING ** PrintParams: under construction for this HamType

System charge 0.000000

***** Integrals *****

PM3 two-center two-electron integrals

MNDO-type Two-electron integrals: elapsed time 0 sec.

elapsed time 0 sec.

Coulomb integrals for semi-empirical

elapsed time 0 sec.

One-center exchange integrals for semi-empirical

elapsed time 0 sec.

Total number of 2-ele integrals 33

Dipole length integrals

elapsed time 0 sec.

Overlap integrals

elapsed time 0 sec.

Transformation Matrix

elapsed time 0 sec.

Integrals elapsed time 0 sec.

***** SCF *****

Core repulsion 5.48205 au

Calculating one electron matrix

Diagonalizing starting one-ele. matrix

Performing SCF

Cycle Energy (au) Difference

**********************************************

1 -11.804580 -0.107359

2 -11.911938843 -0.022431

3 -11.934369829 -0.00432905

4 -11.938698883 -0.000820006

5 -11.939518889 -0.000156319

6 -11.939675208 -3.03375e-005

7 -11.939705546 -6.027e-006

8 -11.939711573 -1.22811e-006

9 -11.939712801 -2.56574e-007

10 -11.939713057 -5.48458e-008

11 -11.939713112 -1.19602e-008

12 -11.939713124 -2.6518e-009

13 -11.939713127

14 -11.939713127 -5.95858e-010

15 -11.939713127 -1.35284e-010

16 -11.939713128

17 -11.939713128 -3.0969e-011

18 -11.939713128 -7.1374e-012

19 -11.939713128 -1.6378e-012

20 -11.939713128 -3.83693e-013

21 -11.939713128 -8.88178e-014

22 -11.939713128 -1.77636e-014

23 -11.939713128 -7.10543e-015

24 -11.939713128 -3.55271e-015

SCF converged 0

Writing final SCF to disk

Final SCF Energy = -11.9397131275 au

Final SCF Energy = -7492.2899 kcal/mol

Saving the final SCF to the restart file D:\h2o-pos-neg-chrg\h2o-

go-sp.gouhf-spuhf.restartscf

SCF elapsed time 0 sec.

***** Properties *****

Ground state properties

*****************************

***** Heat of Formation *****

-53.3387 kcal/mol

ZDO Atomic Charges

*******************

1 O -0.3583

2 H 0.1792

3 H 0.1792

Wiberg Atom-Atom Bond Orders

*****************************

123

1 0.000000 0.000000 0.000000

2 0.967905 0.000001

3 0.967905

Atomic spin densities

**********************

1 O 0.0000

2 H 0.0000

3 H 0.0000

S2 operator 0.000000

*********** 0.000000

exact

calculated

Ground State Dipole (debye) length

1.74037824

XYZ

-0.00000000 -1.74037824 -0.00000000

Mulliken Atomic Charges

************************

1 O -0.3742

2 H 0.1871

3 H 0.1871

SCF alpha eigenvalues (au) & eigenvectors

*****************************************

MO number -> 1234 5

Eigenvalues -> -1.351840 -0.645407 -0.533857 -0.452589

0.148595

1 O 2S 0.878297 -0.000000 -0.333034 0.000000

0.343048 0.000000 -0.000000 0.000000 1.000000 -

-0.104822 -0.000000 -0.834172 -0.000000 -

1 O 2Px

0.000000

1 O 2Py

0.541451

1 O 2Pz 0.000000 0.768115 -0.000000 0.000000

0.000000

0.329853 0.452769 0.310842 -0.000000 -

2 H 1S

0.542747 0.329853 -0.452769 0.310842 0.000000 -

3 H 1S 6

0.542747

0.195282

MO number ->

0.000000

Eigenvalues -> 0.000000

-0.000000

1 O 2S -0.640312

1 O 2Px 0.543139

1 O 2Py -0.543139

1 O 2Pz

2 H 1S

3 H 1S

SCF beta eigenvalues (au) & eigenvectors

****************************************

MO number -> 1234 5

Eigenvalues -> -1.351840 -0.645407 -0.533857 -0.452589

0.148595

1 O 2S 0.878297 -0.000000 -0.333034 0.000000

0.343048 0.000000 -0.000000 0.000000 1.000000 -

-0.104822 -0.000000 -0.834172 -0.000000 -

1 O 2Px 0.000000 0.768115 -0.000000 0.000000

0.000000 0.329853 0.452769 0.310842 -0.000000 -

0.329853 -0.452769 0.310842 0.000000 -

1 O 2Py

0.541451

1 O 2Pz

0.000000

2 H 1S

0.542747

3 H 1S

0.542747

MO number -> 6

Eigenvalues -> 0.195282

1 O 2S 0.000000

1 O 2Px 0.000000

1 O 2Py -0.000000

1 O 2Pz -0.640312

2 H 1S 0.543139

3 H 1S -0.543139

Properties elapsed time 0 sec.

Total Elapsed Time 0 sec.

http://www.ugc-inno-nehu.com/events-2017.html#E07