MM/MD Hybrid Calculations MM/MD Hybrid Calculations ffor Predicting or Predicting The Selective The Selective Extraction ofExtraction of Metallic IonMetallic Ion

Kazuharu YoshizukaKazuharu YoshizukaDepartment of Chemical Processes and Environments,Department of Chemical Processes and Environments,

The University of KitakyushuThe University of Kitakyushu11--1 Hibikino, Kitakyushu 8081 Hibikino, Kitakyushu 808--0135, Japan0135, Japan

EE--mail: yoshizuka@env.kitakyumail: yoshizuka@env.kitakyu--u.ac.jpu.ac.jp

Notice of MM CalculationsNotice of MM Calculations1. 1. TransferabilityTransferability of force field parameters between different of force field parameters between different

potential functions potential functions e.g. MM F.F.e.g. MM F.F.≠≠MOMEC F.F.MOMEC F.F.≠≠AMBER F.F.AMBER F.F.

2. 2. Different force field parameters for same atoms withDifferent force field parameters for same atoms withdifferent bondsdifferent bondse.g. C bonded with H e.g. C bonded with H ≠≠ C bonded with CC bonded with C

3. Physicochemical means of force field parameters3. Physicochemical means of force field parameters？？e.g. Bond stretching force constants, e.g. Bond stretching force constants, Valence angle bending force constants, etc. Valence angle bending force constants, etc.

Relative comparison of potential energies of Relative comparison of potential energies of a series of metal complexes can be available. a series of metal complexes can be available.

As a fullAs a full--empirical empirical calculationscalculations

However, ...However, ...

Calculable Atoms by MM CalculationsCalculable Atoms by MM Calculations

MOMEC F.F.MOMEC F.F.

MM F.F.MM F.F.

* * Our Our newnew workwork

What is Molecular Dynamics ?What is Molecular Dynamics ?

Thermodynamic Thermodynamic equilibriumequilibriumDynamics Dynamics

Large number of atoms Large number of atoms and moleculesand molecules

Molecular Molecular Dynamics (MD)Dynamics (MD)

Thermodynamic Thermodynamic equilibriumequilibrium

Large number of atoms Large number of atoms and moleculesand moleculesMonte Carlo (MC)Monte Carlo (MC)

Optimized geometryOptimized geometryOne moleculeOne moleculeMolecular Molecular Mechanics Mechanics ((MM)MM)

Main resultsMain resultsTarget material Target material Calculation Calculation methodmethod

Successive configurations of system are generated by integratingSuccessive configurations of system are generated by integratingNewtonNewton’’s laws of motion, and result is a trajectory (positions and s laws of motion, and result is a trajectory (positions and velocities) of particles (atoms or molecules) in the system withvelocities) of particles (atoms or molecules) in the system with time. time. TimeTime--dependent phenomena (dynamics)dependent phenomena (dynamics)MMacroscopic information of the systemacroscopic information of the systemSimulation of various materials, such as organics, inorganics, mSimulation of various materials, such as organics, inorganics, metals,etals,semiconductors, and liquid crystals in different phases (gassemiconductors, and liquid crystals in different phases (gas--, liquid, liquid--, and , and solidsolid--phase)phase)

MMolecular dynamics generates a series of timeolecular dynamics generates a series of time--dependent properties dependent properties (positions and velocities) of all atoms and molecules in the sys(positions and velocities) of all atoms and molecules in the system by solving tem by solving NewtonNewton’’s equations of motion.s equations of motion.

Molecular Dynamics Fundamentals Molecular Dynamics Fundamentals

““Input InformationInput Information””＝＝““Initial StateInitial State””＋＋““Potential Energy FunctionsPotential Energy Functions””

““Initial StateInitial State””＝＝““IInitial Configurationsnitial Configurations””＋＋““VVelocities of all particleselocities of all particles””““IInitial Configurationsnitial Configurations””IIn case of random structure materials, such as amorphous solids, n case of random structure materials, such as amorphous solids, liquid crystals, liquid crystals, and liquids, initial configurations greatly affect the success oand liquids, initial configurations greatly affect the success or failure of a r failure of a simulation!simulation!

““VVelocities of all particleselocities of all particles””Sum of kinetic energy values of individual atoms is related toSum of kinetic energy values of individual atoms is related to temperature of temperature of thermodynamic equilibrium system!thermodynamic equilibrium system!

““Potential Energy FunctionPotential Energy Function””＝＝““Function FormsFunction Forms””＋＋““Parameter ValuesParameter Values””Validity of potential energy functions is the most important fValidity of potential energy functions is the most important factor for successful actor for successful simulation, because MD simulation tracks the motion of particlessimulation, because MD simulation tracks the motion of particles interacting interacting each other!each other!

Potential Energy FunctionsPotential Energy Functions

Bond stretching energyBond stretching energy

EEbb = k= kbb/2 (r /2 (r -- rr00))22

Bond angle deformation energyBond angle deformation energy

EEqq = k= kqq/2 (q /2 (q -- q q 00))22

Torsion angle deformation energyTorsion angle deformation energy

EEff = k= kff/2 (1 + /2 (1 + coscos((m(f + fm(f + f00))))))

Van der Waals nonVan der Waals non--bonding interaction bonding interaction energyenergy

EEVdWVdW = a= a··exp(exp(--bdbdijij)) -- cc··ddijij--66

EEee = q= qiiqqjj/(e/(e··ddijij))

NonNon--Bonded Interaction Point Charge Coulomb InteractionBonded Interaction Point Charge Coulomb Interaction

Pote

ntia

lPo

tent

ial

V(r)

V(r)

Atomic distanceAtomic distance rr

Buckingham potentialBuckingham potentialEEVdWVdW = a= a··exp(exp(--brbrijij)) -- cc··rrijij--66

Morse potentialMorse potentialEEVdWVdW = D[1 = D[1 -- exp(exp(--a(ra(rijij -- rr00)])]22 -- DD

rr

TwoTwo--body interactionbody interactionOnly distance between 2 atomsOnly distance between 2 atoms

ThreeThree--body interactionbody interactionIncorporating the effects of the Incorporating the effects of the angles between 3 atomsangles between 3 atoms

MultiMulti--body interactionbody interactionIncorporating the effects of manyIncorporating the effects of manysurrounding atomssurrounding atoms

Only twoOnly two--body interactionbody interaction

Construction of Force Field Parameters of Construction of Force Field Parameters of Metal Complexes using QM CalculationsMetal Complexes using QM Calculations

AbAb initio initio programprogram

Input QM Input QM datadata

Assign FF Assign FF attributesattributes

Fit charge Fit charge parametersparameters

Fit valence Fit valence parametersparameters

Validate on Validate on isolated isolated

molecules molecules

Optimize Optimize vdWvdW

parameters parameters using liquid using liquid simulationssimulations

Overall Overall validationvalidation

FF parametersFF parameters

Empirical Empirical liquid liquid datadata

Necessary QM Parameters for Necessary QM Parameters for Construction of FF Parameter setConstruction of FF Parameter set

1.1. Optimized structure and its energyOptimized structure and its energyex. 6ex. 6--31G*(RHF), DFT31G*(RHF), DFT

2.2. Conformer structures and their energiesConformer structures and their energies

3.3. Hessian matrix (Basic vibration analysis) Hessian matrix (Basic vibration analysis)

4.4. Energy slope Energy slope

5.5. Mulliken charge or electrostatic chargeMulliken charge or electrostatic chargeconvert using charge equilibrium methodconvert using charge equilibrium method

Molecular MechanicsMolecular Mechanics

Application Application to Extractive separation of to Extractive separation of lanthanides and actinideslanthanides and actinides

Solvent Extraction, Solvent Extraction, already you know...already you know...

Contact of aqueous solution containing Contact of aqueous solution containing various metal ions with organic solutionvarious metal ions with organic solutioncontaining extractantcontaining extractant

Vigorous Stirring of aqueous and organic Vigorous Stirring of aqueous and organic solutionssolutions

Transfer of objective metal ion from Transfer of objective metal ion from aqueous to organic solutions to achieve aqueous to organic solutions to achieve separationseparation

MM+QSPRMM+QSPR

MD+QSPRMD+QSPR

Modeling of Solvent Extraction MechanismModeling of Solvent Extraction Mechanism

KKMM

MMn+n+ + n(HR)+ n(HR)oo ((MRMRnn))oo + + nHnH++

Org. Ph. n(HR)Org. Ph. n(HR)oo ((MRMRnn))oo

InterfaceInterface KKD,HRD,HR KKD,HRD,HR

AqAq. Ph.. Ph. ((MRMRnn))ww

KKaan(HR)n(HR)ww nHnH++ + + nRnR--

+ + MMn+n+

Solvent Extraction of LanthanidesSolvent Extraction of LanthanidesHydrogen Phosphate ExtractantsHydrogen Phosphate Extractants

BisBis(4(4--ethylcyclohexylethylcyclohexyl) hydrogen phosphate ) hydrogen phosphate ((D4ECHPA)D4ECHPA)

BisBis(4(4--cyclohexylcyclohexylcyclohexylcyclohexyl) ) hydrogen phosphate (D4DCHPA)hydrogen phosphate (D4DCHPA)

BisBis(2(2--ethylhexylethylhexyl) ) hydrogen phosphate hydrogen phosphate ((D2EHPA)D2EHPA)

CH 2 O

OCH 2

PO

OH

CHC2H5

CHC2H5

CH 2CH 2CH 2CH 3

CH 2CH 2CH 2CH 3

O

OP

O

OH

H H

H H

C2H5 O

OC2H5

PO

OH

H

H

Extraction Constants of Lanthanides with Extraction Constants of Lanthanides with Hydrogen Phosphate ExtractantsHydrogen Phosphate Extractants

Yoshizuka et al., Yoshizuka et al., Bull. Chem. Soc. Bull. Chem. Soc. JpnJpn.., 69, 589, 69, 589--596 (1996)596 (1996)

Order of lanthanideOrder of lanthanide

Extr

actio

n co

nsta

nt,

Extr

actio

n co

nsta

nt, KK

ex,L

nex

,Ln

LaLa CeCe PrPr NdNd PmPmSmSmEuEu GdGd TbTb DyDy HoHoYYErEr TmTm YbYb LuLu1010--33

1010 --22

1010 --11

1010 00

1010 11

1010 22

1010 33

1010 44

D4DCHPAD4DCHPAD4ECHPAD4ECHPA

D2EHPAD2EHPA

OO

OOPP

OOHH

OOCCHH22

CCHH22

CCHH

CCHH

CC22HH55

CC22HH55

CC44HH99

CC44HH99

D2EHPAD2EHPA

CC22HH55 OO

CC22HH55 OOPP

OOHH

OOHH

HH

D4ECHPAD4ECHPA

OO

OOPP

OOHH

OOHH HH

HHHH

D4DCHPAD4DCHPA

Concept of MM Calculations of Concept of MM Calculations of Lanthanide ComplexesLanthanide Complexes

1. 1. Calculations of extractantsCalculations of extractants::Parameterization of all atoms including extractantsParameterization of all atoms including extractants

2. Calculations of metal center:2. Calculations of metal center:(1) Valence and torsion angles(1) Valence and torsion angles

-- Flexibility of coordination structures (Flexibility of coordination structures (e.g., tetrahedral (109.5e.g., tetrahedral (109.5ºº), square ), square planar (90planar (90ºº, 180, 180ºº), octahedral (90), octahedral (90ºº, 180, 180ºº))) ) --Distance of metalDistance of metal--ligandligand、、ligand structureligand structure Interaction energies Interaction energies ((van der van der Waals, electrostatics)Waals, electrostatics)

(2) Non(2) Non--bonded (bonded (Van der Waals) interactionsVan der Waals) interactions-- Electrostatic effects (Electrostatic effects (e.g., square planer vs. e.g., square planer vs. tetrahedral)tetrahedral)--1,31,3--UreyUrey--Bradly type nonBradly type non--bonded interactionsbonded interactions((e.g., e.g., ４４--coordinate structure tetrahedralcoordinate structure tetrahedral66--coordinate structure octahedral)coordinate structure octahedral)

Potential energy function for MM calculationsPotential energy function for MM calculationsUU = = ΣΣ ( ( EEbb + + EEθθ + + EEφφ + + EEnbnb ))

1

2

3

13

Comparison of Extractant Structures Comparison of Extractant Structures calculated by MOMEC and MOPAC(PM3)calculated by MOMEC and MOPAC(PM3)

RMS = 0.27 Å

RMS = 0.22 Å

RMS = 0.21 Å

D4DCHPAD4DCHPA

D2EHPAD2EHPA

D4ECHPAD4ECHPA

QSPR between Extraction Constant and Steric QSPR between Extraction Constant and Steric Energy Difference with Extraction ProcessEnergy Difference with Extraction Process(1) (1) Change of steric energies with complex formationChange of steric energies with complex formation::

Ln(HLn(H22O)O)993+3+ + 6HR + 6HR LnRLnR33··33HR + 3HHR + 3H33OO++UULnLn 66UUHRHR UULnXLnX 33UUH3OH3O

Difference in steric energiesDifference in steric energies::ΔΔUULnLn = = UULnXLnX + 3+ 3UUH3OH3O -- UULnLn -- 66UUHRHR

For relative comparison of steric energy difference of differentFor relative comparison of steric energy difference of differentextractantsextractants::

ΔΔUULnLn -- ΔΔUULaLa = (= (UULnXLnX -- UULaXLaX) ) -- ((UULnLn -- UULaLa))

(2) Linear free energy relationship of extraction constant(2) Linear free energy relationship of extraction constant::ΔΔGGLnLn = = --RTRT lnln KKex,Lnex,Ln

ΔΔUULnLn -- ΔΔUULaLa = = αα ·· log (log (KKex,Lnex,Ln// KKex,Laex,La))αα : apparent QSPR constant: apparent QSPR constant

QSPR between Steric Energy Differences QSPR between Steric Energy Differences and Extraction Constantsand Extraction Constants

ΔΔUULnLn -- ΔΔUULaLa = = αα ·· log (log (KKex,Lnex,Ln// KKex,Laex,La))αα : apparent QSPR constant: apparent QSPR constant

log(log(KKex,Lnex,Ln//KKex,Laex,La))00 11 22 33 44 55 66

00

22

44

66

88

D4DCHPAD4DCHPAD4ECHPAD4ECHPA

D2EHPAD2EHPA

ΔΔUU

MM-- ΔΔ

UULALA

[kJ

[kJ ··

mol

mol

-- 11]]

SlopeSlope ((αα)) = 1.26= 1.26

OO

OOPP

OOHH

OOCCHH22

CCHH22

CCHH

CCHH

CC22HH55

CC22HH55

CC44HH99

CC44HH99

D2EHPAD2EHPA

CC22HH55 OO

CC22HH55 OOPP

OOHH

OOHH

HH

D4ECHPAD4ECHPA

OO

OOPP

OOHH

OOHH HH

HHHH

D4DCHPAD4DCHPA

Extraction Equilibrium Constants of UranylExtraction Equilibrium Constants of Uranyl

Order of atomic numberOrder of atomic numberLaLa CeCe PrPr NdNdPmPmSmSmEuEuGdGd TbTb DyDy HoHo YY ErEr TmTmYbYb LuLu UU

Extr

actio

n Eq

uilib

rium

Con

stan

t, Ex

trac

tion

Equi

libriu

m C

onst

ant,

KKexex

1010 --44

1010 --33

1010 --22

1010 --11

1010 00

1010 11

1010 22

1010 33

1010 44

1010 55

D2EHPAD4DCHPAD4ECHPA

OO

OOPP

OOHH

OOCCHH22

CCHH22

CCHH

CCHH

CC22HH55

CC22HH55

CC44HH99

CC44HH99

D2EHPAD2EHPA

CC22HH55 OO

CC22HH55 OOPP

OOHH

OOHH

HH

D4ECHPAD4ECHPA

OO

OOPP

OOHH

OOHH HH

HHHH

D4DCHPAD4DCHPA

Molecular Structure of Uranyl Molecular Structure of Uranyl Complex with D4DCHPAComplex with D4DCHPA

White: CarbonWhite: CarbonRed : OxygenRed : OxygenYellow: PhosphorusYellow: PhosphorusBlue: UraniumBlue: UraniumHydrogen are omittedHydrogen are omitted

O

U

O

OP

O

OROR

OP

O

OROR

OP

O

ORRO

OP

O

ORRO

HH

1.751.75ÅÅ

178178oo

9595oo

O = RH H

Molecular Structures of Uranyl Complexes Molecular Structures of Uranyl Complexes and Their Molecular Volumesand Their Molecular Volumes

D4DCHPA D4ECHPA D2EHPD4DCHPA D4ECHPA D2EHPAAV=4.36V=4.36ÅÅ3 3 V=3.71V=3.71ÅÅ3 3 V=3.29V=3.29ÅÅ33

White: Carbon, White: Carbon, Red: OxygenRed: Oxygen, , Yellow: PhosphorusYellow: Phosphorus, , Blue: UraniumBlue: Uranium, Hydrogen are omitted., Hydrogen are omitted.

Extractability trendExtractability trend: : D4DCHPA > D4ECHPA > D2EHPAD4DCHPA > D4ECHPA > D2EHPA

Molecular Dynamics Molecular Dynamics

Application Application to solvent extraction of to solvent extraction of metallic ionmetallic ion

Setup of Initial State of Water and Toluene Setup of Initial State of Water and Toluene with 3D Boundary Conditionwith 3D Boundary Condition

Water no.=267, Toluene no.=45Water no.=267, Toluene no.=45

Molecular no. x Molecular weightMolecular no. x Molecular weight

Cell volume(20x20x20Cell volume(20x20x20ÅÅ) x Avogadro no.) x Avogadro no.Density =Density =

Molecular weight: Water=18.02; Toluene=92.14Molecular weight: Water=18.02; Toluene=92.14

MD condition of NTVMD condition of NTV＆＆NTPNTPT = 50 KT = 50 KTime step = 0.1fsTime step = 0.1fsPotential = MOMEC Potential = MOMEC

MD Calculation (NTP) under 3D Boundary MD Calculation (NTP) under 3D Boundary ConditionCondition

Volume shrinking Volume shrinking of solution box to of solution box to real density statereal density state

Initial State of WaterInitial State of Water--Toluene Interface with Toluene Interface with 3D Boundary Condition3D Boundary Condition

MD Calculation with NPT(100ps)+NVT(100ps) EnsembleMD Calculation with NPT(100ps)+NVT(100ps) Ensemble

Density Distribution near WaterDensity Distribution near Water--Toluene InterfaceToluene Interface

00 1010 2020 3030 40400.00.0

0.50.5

1.01.0

Distance [Distance [ÅÅ]]

Den

sity

[kg

Den

sity

[kg ･･

dmdm-- 33

]]total densitytotal density

water water toluenetoluene

Water no.=267, Toluene no.=45Water no.=267, Toluene no.=45

Molecular no. x Molecular weightMolecular no. x Molecular weight

Cell volume(20x20x20Cell volume(20x20x20ÅÅ) x Avogadro no.) x Avogadro no.Density =Density =

Molecular weight: Water=18.02; Toluene=92.14Molecular weight: Water=18.02; Toluene=92.14

Insertion of Extractant into WaterInsertion of Extractant into Water--Toluene Toluene 3D Boundary Cell3D Boundary Cell

Insertion of extractant optimized by MOMECInsertion of extractant optimized by MOMECD2EHPA monomerD2EHPA monomer

MD calculation with NVT ensembleMD calculation with NVT ensemble((100ps)100ps)

Molecular Structure of D2EHPA at WaterMolecular Structure of D2EHPA at Water--Toluene Toluene Interface between and in Toluene PhaseInterface between and in Toluene Phase

MD Calculation with NPT(100ps)+NVT(100ps) EnsembleMD Calculation with NPT(100ps)+NVT(100ps) Ensemble

In Toluene PhaseIn Toluene Phase At the InterfaceAt the Interface

AqAq. side Org. side. side Org. side

QSPR between Steric Energy and Interfacial QSPR between Steric Energy and Interfacial Adsorption Equilibrium ConstantAdsorption Equilibrium Constant

AqAq.. InterfaceInterface Org.Org.

--ΔΔUUHRHR(=(=UUinin toluenetoluene ––U U at interfaceat interface) = ) = αα RT RT lnlnKKadadRT RT = 2.52 = 2.52 kJmolkJmol--11;; αα = apparent QSPR Constant= apparent QSPR Constant

--77--66--55--44--33--22--114040

4242

4444

4646

4848

5050

5252

5454

5656

log(log(KKadad/m/m33molmol--11))ΔΔ

UUH

R

HR

[k J

/mol

][k

J/m

ol] D2EHPAD2EHPA

D4ECHPAD4ECHPA

D4DCHPAD4DCHPA

Slope (Slope (αα) =1.31) =1.31

Molecular Dynamics Molecular Dynamics

Application Application to the estimation of logto the estimation of logPPvalues of Re and values of Re and TcTc complexes as complexes as

nuclear medicinesnuclear medicines

Modern Imaging Techniques in MedicineModern Imaging Techniques in Medicine

Ultrasound Computed Ultrasound Computed Tomography (CT)Tomography (CT)Magnetic Resonance Imaging (MRI)Magnetic Resonance Imaging (MRI)

give anatomic informationgive anatomic information

Magnetic Resonance Functional ImagingMagnetic Resonance Functional ImagingMagnetic Resonance Spectroscopy (MRS)Magnetic Resonance Spectroscopy (MRS)

inform on few functional changes and metabolitesinform on few functional changes and metabolites

Emission Tomography (PET and SPECT)Emission Tomography (PET and SPECT)informs on physiological functions and metabolites informs on physiological functions and metabolites

PETPET--CameraCamera

DMSADMSA--Me Complexes for ExoMe Complexes for Exo-- and and EndoEndo--radionuclide radionuclide Therapy of Tumor CellTherapy of Tumor Cell

Dimercapto succinicnate derivatives Dimercapto succinicnate derivatives (DMSA)(DMSA)

S

Me

SHOOC

HOOC S

S COOH

COOH

O

S

Me

S(C2H5- or) H3C-OOC

(C2H5- or) H3C-OOC S

S COO-CH3 (or -C2H5)

COOH

O

S

Me

S(C2H5- or) H3C-OOC

(C2H5- or) H3C-OOC S

S COO-CH3 (or -C2H5)

COO-CH3 (or -C2H5)

O

Me =99mTc, 186Re, 188Re

Tetraacid typeTetraacid type

Triester Triester Monoacid typeMonoacid type

Tetraester typeTetraester type

Requirements for The Construction of Requirements for The Construction of Nuclear Medicines Capable To Serve AsNuclear Medicines Capable To Serve As

Imaging / Therapeutic AgentsImaging / Therapeutic Agents

The The ligand ligand should form an inclusion compound witshould form an inclusion compound with h the the oxoanionoxoanion in isotonic NaCl solution. in isotonic NaCl solution.

Metal complexes Metal complexes should have a wellshould have a well--balancedbalancedlipophilicitylipophilicity::ex. lex. logPogP > 2.52.5 for liver etcfor liver etc..

No No ion ion exchange reaction with endogenous species exchange reaction with endogenous species shouldshould happen in physiological environment.happen in physiological environment.

--1.091.09±±0.030.03

--0.770.77±±0.020.02

0.560.56±±0.020.020.750.75±±0.010.01

Measurement of logMeasurement of logPP of Tetraester of Tetraester Type with Solvent ExtractionType with Solvent Extraction

22 33 44 55 66 77 88

--1.01.0

--0.50.5

00

0.50.5

1.01.0

99m99mTcO(DMSA tetramethylester)TcO(DMSA tetramethylester)2299m99mTcO(DMSA tertaethylester)TcO(DMSA tertaethylester)22188188ReO(DMSA tetramethylester)ReO(DMSA tetramethylester)22188188Re(DMSA tetraethylester)Re(DMSA tetraethylester)22

pHpH

log

log PP

Measurement of logMeasurement of logPP of DMSAof DMSA--Re and Re and --Tc Tc Complexes with Solvent ExtractionComplexes with Solvent Extraction

pHpH22 33 44 55 66 77 88

log

log PP

--3.83.8

--3.63.6

--3.43.4

--3.23.2

--3.03.0

--2.82.8

--2.62.6

--2.42.4

--2.22.2

--2.02.099m99mTcO(DMSA)TcO(DMSA)22188188ReO(DMSA)ReO(DMSA)222.372.37±±0.030.03

2.122.12±±0.020.02

Measured logMeasured logP P of DMSAof DMSA--Me ComplexesMe Complexes

* Tc = * Tc = 99m99mTc, Re = Tc, Re = 188188ReRe

--00..005 005 ±± 0.010.01ReO(DMSA triethylester monocarboxylic acid)ReO(DMSA triethylester monocarboxylic acid)22

00..22 22 ±± 0.010.01TcO(DMSA triethylester monocarboxylic acid)TcO(DMSA triethylester monocarboxylic acid)22

--11..14 14 ±± 0.010.01ReO(DMSA trimethylester monocarboxylic acid)ReO(DMSA trimethylester monocarboxylic acid)22

--00..82 82 ±± 0.010.01TcO(DMSA trimethylester monocarboxylic acid)TcO(DMSA trimethylester monocarboxylic acid)22

00..56 56 ±± 0.020.02ReO(DMSA tetraethylester)ReO(DMSA tetraethylester)22

00..75 75 ±± 0.010.01TcO(DMSA tetraethylester)TcO(DMSA tetraethylester)22

--11..09 09 ±± 0.030.03ReO(DMSA tetramethylester)ReO(DMSA tetramethylester)22

--00..77 77 ±± 0.020.02TcO(DMSA tetramethylester)TcO(DMSA tetramethylester)22

--2.37 2.37 ±± 0.030.03ReO(DMSA)ReO(DMSA)22

--2.12 2.12 ±± 0.020.02TcO(DMSA)TcO(DMSA)22

log log PPMetal complexMetal complex

Setup of Interface between Water and Setup of Interface between Water and 11--Octanol with 3D Boundary ConditionOctanol with 3D Boundary Condition

Water no.=267, 1Water no.=267, 1--Octanol no.=25Octanol no.=25

Molecular no. x Molecular weightMolecular no. x Molecular weight

Cell volume(20x20x20Cell volume(20x20x20ÅÅ) x Avogadro no.) x Avogadro no.Density =Density =

Molecular weight: Water=18.02; 1Molecular weight: Water=18.02; 1--Octanol=114.92Octanol=114.92

MD condition of NTVMD condition of NTV＆＆NTPNTPT = 50 KT = 50 KTime step = 0.1fsTime step = 0.1fsPotential = MOMEC Potential = MOMEC

Molecular Dynamic Simulation of DMSAMolecular Dynamic Simulation of DMSA--Re Re Complexes in WaterComplexes in Water--11--Octanol SystemOctanol System

MD simulation for 100 ps using Materials Explorer under NTV ensMD simulation for 100 ps using Materials Explorer under NTV ensambleamble

Number of water molecules = 267, Number of 1Number of water molecules = 267, Number of 1--cotanol molecules = 25, Number of cotanol molecules = 25, Number of DMSADMSA--Re complex molecule = 1, Size of cell = 1.61Re complex molecule = 1, Size of cell = 1.61××1.611.61××6.05 nm, 6.05 nm, ρρ = 0.914 g/cm= 0.914 g/cm33, , Temp. = 298 K, DMSATemp. = 298 K, DMSA--Re complex = tetra acid Re complex = tetra acid typetypeCalculation time: time step = 0.1 Calculation time: time step = 0.1 fsfs, length of run = 1000001 step (= 100 ps), length of run = 1000001 step (= 100 ps)

DMSADMSA--ReRe

Time Course of Internal Energy of DMSATime Course of Internal Energy of DMSA--Re Re Complexes in WaterComplexes in Water--11--Octanol SystemOctanol System

Estimation Concept of logEstimation Concept of logPP of DMSAof DMSA--Me Me Complexes in WaterComplexes in Water--11--Octanol SystemOctanol System

Water phase 1-Octanol phase––

Water phase 1-Octanol phase= = ΔΔUUaa

Water phase 1-Octanol phase––

Water phase 1-Octanol phase= = ΔΔUUoo

QSPR concept between internal energy QSPR concept between internal energy differnce of each binary system and logdiffernce of each binary system and logPP

ΔΔΔΔUU (= (= ΔΔUUoo –– ΔΔUUaa) =) = ααloglogPPαα: apparent QSPR constant: apparent QSPR constant

QSPR between QSPR between ΔΔΔΔU U and logand logPP

Slope (Slope (αα)) = = --11.211.2

loglogPP--3.03.0 --2.52.5 --2.02.0 --1.51.5 --1.01.0 --0.50.5 00 0.50.5 1.01.0

ΔΔΔΔ U

U [k

J/m

ol]

[kJ/

mol

]

--5050

--4040

--3030

--2020

--1010

0 0

1010

ΔΔΔΔU U = = --11.2 log11.2 logPP --29.429.4

ΔΔΔΔUU (= (= ΔΔUUoo –– ΔΔUUaa) =) = ααloglogPPαα: apparent QSPR constant: apparent QSPR constant

ConclusionConclusion1.1. Nowadays, force field parameters can be easily created by the Nowadays, force field parameters can be easily created by the

QM calculation dataQM calculation data2.2. Force field parameters can be transfer to potential functions foForce field parameters can be transfer to potential functions for r

MD simulation with some modification MD simulation with some modification 3.3. Combining MM and MD calculations as well as QSPR theory, the Combining MM and MD calculations as well as QSPR theory, the

solvent extraction behavior of metallic ions can be predictedsolvent extraction behavior of metallic ions can be predicted4.4. QQSPR theory combined with MM/MD calculations is a useful tool SPR theory combined with MM/MD calculations is a useful tool

for predicting the separation behavior of metallic ionsfor predicting the separation behavior of metallic ions

ee--ChemChem Ltd.Ltd.

Computational Chemistry SystemComputational Chemistry System

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