Seminario IV: Fuerzas intermolecularesdepa.fquim.unam.mx/jesusht/sfi_sapt.pdf · A1 1 2m 52 1 r B2 (7) H 0 no es sim etrico a las permutaciones de los electrones El Hamiltoniano total,

MotivacionDistancias intermedias y cortas

EjemplosBibliografıa

Fuerzas intermoleculares: alcance medio

Fernando Jose Holguın Gallego

Seminario IV:Fuerzas intermoleculares

Instituto de QuımicaUniversidad Nacional Autonoma de Mexico

Septiembre 8 de 2014

Fernando Jose Holguın Gallego Alcance medio 1 / 31



Contenido

1 Motivacion

2 Distancias intermedias y cortas

3 Ejemplos

4 Bibliografıa




Dimero de 1,3,5-Triamino-2,4,6-Trinitrobenceno

Distancias intermedias: 2−8A. Los efectos de intercambio son apreciables

Taylor, D.E.,J. Phys. Chem. A 117, 3507-3520 p, 2013




Contenido

1 Motivacion


3 Ejemplos

4 Bibliografıa




Teorıa de perturbacion con intercambio

Cuando las interacciones entre las moleculas no es tan grande sepuede considerar una pequena perturbacion y el Hamiltoniano delas dos moleculas es:

H = H0 + V H0 = HA +HB (1)

con funciones propias

Φ(0)nm = ΨAn Ψ

Bm (2)

H0Φ(0)nm =

(EAn + EBm

)ΨAn Ψ

Bm (3)






H = H0 + V H0 = HA +HB (1)


Φ(0)nm = ΨAn Ψ

Bm (2)

H0Φ(0)nm =

(EAn + EBm

)ΨAn Ψ

Bm (3)






H = H0 + V H0 = HA +HB (1)


Φ(0)nm = ΨAn Ψ

Bm (2)

H0Φ(0)nm =

(EAn + EBm

)ΨAn Ψ

Bm (3)




Φ(0)nm = ΨAn Ψ

Bm (4)

No provee contribucion a la energıa de intercambio, conduciendoa soluciones no fısicas.

La funcion de onda de muchos electrones debe satisfacer elprincipio de exclusion de Pauli.

⇒ La funcion de onda (Φ(0)nm) debe ser ANTISIMETRICA.

Φ(0)nm 6= ΨAn Ψ

Bm (5)

Ψ(0)nm(antisimetrica) = AΦ(0)

nm = AΨ (0)n Ψ (0)

m (6)

A es el operador de antisimetrıa.




Φ(0)nm = ΨAn Ψ

Bm (4)




Φ(0)nm 6= ΨAn Ψ

Bm (5)


nm = AΨ (0)n Ψ (0)

m (6)





Φ(0)nm = ΨAn Ψ

Bm (4)




Φ(0)nm 6= ΨAn Ψ

Bm (5)


nm = AΨ (0)n Ψ (0)

m (6)





Φ(0)nm = ΨAn Ψ

Bm (4)




Φ(0)nm 6= ΨAn Ψ

Bm (5)


nm = AΨ (0)n Ψ (0)

m (6)





Φ(0)nm = ΨAn Ψ

Bm (4)




Φ(0)nm 6= ΨAn Ψ

Bm (5)


nm = AΨ (0)n Ψ (0)

m (6)

A es el operador de antisimetrıa.Fernando Jose Holguın Gallego Alcance medio 6 / 31



Ψ(0)nm(antisimetrica) no es funcion propia de H0

Para el caso de dos atomos de hidrogeno:

H0 = HA +HB = − 1

2m52 − 1

rA1− 1

2m52 − 1

rB2(7)

H0 no es simetrico a las permutaciones de los electrones

El Hamiltoniano total, (H) es simetrico al incluir el operadorde interaccion, (V ) a H0

V = − 1

rA2− 1

rB1+

1

RAB+

1

r12(8)

La funcion de onda

Ψ(0)nm =

1√N !det|ψ1αψ2β| (9)






H0 = HA +HB = − 1

2m52 − 1

rA1− 1

2m52 − 1

rB2(7)



V = − 1

rA2− 1

rB1+

1

RAB+

1

r12(8)

La funcion de onda

Ψ(0)nm =







H0 = HA +HB = − 1

2m52 − 1

rA1− 1

2m52 − 1

rB2(7)



V = − 1

rA2− 1

rB1+

1

RAB+

1

r12(8)

La funcion de onda

Ψ(0)nm =







H0 = HA +HB = − 1

2m52 − 1

rA1− 1

2m52 − 1

rB2(7)



V = − 1

rA2− 1

rB1+

1

RAB+

1

r12(8)

La funcion de onda

Ψ(0)nm =





El Hamiltoniano total, H, conmuta con el antisimetrizador, A:

[H, A] = 0 (10)

∃ un conjunto de funciones propias en comun para H y A

y el Hamiltoniano de orden cero, H0 y el operador perturbacion, Vno conmutan con A

[H0, A] 6= 0 [V, A] 6= 0 (11)

Por lo tanto las funciones de onda antisimetrizadas, Ψ(0)nm no per-

miten el uso de las teorias de perturbacion como la de Rayleigh-Schrodinger.





[H, A] = 0 (10)



[H0, A] 6= 0 [V, A] 6= 0 (11)







[H, A] = 0 (10)



[H0, A] 6= 0 [V, A] 6= 0 (11)






Adicionalmente las funciones AΦ(0)nm no son ortogonales unas a otras

y no pueden ser funciones propias de cualquier operador Hermıtico.

Estos inconvenientes conducen a diferentes versiones de la teorıade perturbacion usando AΦ

(0)nm, por la eleccion de los coefi-

cientes de la funcion de onda bajo diferentes condiciones.

Hay dos principales grupos dependiendo del Hamiltoniano deorden cero usado (H0):

1 empleando un Hamiltoniano no simetrico de orden cero,H0:Teorıas de perturbacion adaptadas a la simetrıa (SAPT).

2 empleando un especial Hamiltoniano de orden cero,H0 para elcual funciones antisimetricas son funciones propias.
















































Simetrıa adaptada a la teorıa de perturbaciones

Las frecuentes aproximaciones SAPT usadas son denotadas por abre-viaciones:

EL-HAV metodo Eisenschitz-London (1930)

MS-MA metodos de Murrell-Shaw y Musher-Amos (1967)

AM metodo de Amos-Musher (1969)

HS metodo de Hirschfelder-Siley (1966)

CBH aproximacion Chipman-Bowman-Hirschfelder (1973)

JK aproximacion Jeziorski-Kolos (1977)




La correcta funcion de onda solucion del Hamiltoniano total, H,puede ser representado como:

νΨ =νAΦν (12)

donde νA es el operador simetrizador, Φν es la funcion no simetrica

La ecuacion de Schrodinger para la funcion de onda simetrica:

H(νAΦν) =νE(νAΦν) (13)





νΨ =νAΦν (12)








νΨ =νAΦν (12)







¿Cual es la mejor aproximacion?

Muchos criterios para elegir al funcion de onda son sugeridos,algunos de ellos estan basados en la mas pequena desviacionde la funcion propia, φν , del Hamiltoniano no perturbado, H0

Jeziorski y Kolos (1977) propusieron una aproximacion basadaen un procedimiento iterativo para la solucion de la ecuacionde Schrodinger.

se obtienen expresiones generales que conectan la energıa y lasfunciones de onda en cada paso iterativo

























εn = En − E0 =⟨

Φ0|V |GΨn−1

⟩(14)

Ψn = Φ0 + R0(εn − V )FΨn−1 (15)

donde Φ0 es la funcion propia y R0 es el resolvente reducido delHamiltoniano de orden cero, H0:

R0 =∑k 6=0

|Φk 〉〈 Φk|E

(0)0 − E

(0)k

(16)

E0k es la energıa de un estado exitado de H0, F y G son los opera-

dores de forzado de simetrıa

Diferentes elecciones de estos operadores de simetrıaconducen a diferentes aproximaciones SAPT




εn = En − E0 =⟨

Φ0|V |GΨn−1

⟩(14)

Ψn = Φ0 + R0(εn − V )FΨn−1 (15)


R0 =∑k 6=0

|Φk 〉〈 Φk|E

(0)0 − E

(0)k

(16)







εn = En − E0 =⟨

Φ0|V |GΨn−1

⟩(14)

Ψn = Φ0 + R0(εn − V )FΨn−1 (15)


R0 =∑k 6=0

|Φk 〉〈 Φk|E

(0)0 − E

(0)k

(16)







εn = En − E0 =⟨

Φ0|V |GΨn−1

⟩(14)

Ψn = Φ0 + R0(εn − V )FΨn−1 (15)


R0 =∑k 6=0

|Φk 〉〈 Φk|E

(0)0 − E

(0)k

(16)







εn = En − E0 =⟨

Φ0|V |GΨn−1

⟩(14)

Ψn = Φ0 + R0(εn − V )FΨn−1 (15)


R0 =∑k 6=0

|Φk 〉〈 Φk|E

(0)0 − E

(0)k

(16)







Si se elige G = 1 y F = A, con la funcion inicial Ψ0 =⟨

Φ0|AΦ0

⟩−1AΦ0

se obtiene:

El esquema JK (Jeziorski y Kolor, 1977) da buenos resultados parainteracciones fuertes

En algunos casos se elige G =⟨

Φ0|AΦ0

⟩−1A y F = 1, con la

funcion inicial Ψ0 = Φ0 que es opuesto al esquema JK

No hay un criterio teorico para la seleccion del mejor metodoSAPT; solo los calculos numericos proveen un criterio paraidentificar cual aproximacion es mejor.





Φ0|AΦ0

⟩−1AΦ0

se obtiene:El esquema JK (Jeziorski y Kolor, 1977) da buenos resultados parainteracciones fuertes


Φ0|AΦ0








Φ0|AΦ0

⟩−1AΦ0



Φ0|AΦ0








Φ0|AΦ0

⟩−1AΦ0



Φ0|AΦ0







Metodos que permiten la aplicacion de la teorıa deperturbacion Rayleigh-Schrodinger

El problema de que las funciones de onda no son funciones propiasdel Hamiltoniano de orden cero, se puede solucionar construyendoun Hamiltoniano simetrizado H0.

H = H0 + V (17)

H0AΦ0 ≡ (T + U0)AΦ0 = E0AΦ0 (18)

U0 = AU0Φ0/AΦ0 potencial − Sternheimer (19)

Similar al potencial de Sternheimer se obtiene

V = AV Φ0/AΦ0 (20)






H = H0 + V (17)

H0AΦ0 ≡ (T + U0)AΦ0 = E0AΦ0 (18)



V = AV Φ0/AΦ0 (20)






H = H0 + V (17)

H0AΦ0 ≡ (T + U0)AΦ0 = E0AΦ0 (18)



V = AV Φ0/AΦ0 (20)




La aplicacion del formalismo de Sternheimer no es aplicable asistemas de muchos electrones.

Existen diferentes modificaciones al Hamiltoniano Sternheimerpara obtener resultados exitosos.

La teorıa de perturbacion Moller-Plesset (MPPT) basada enla teorıa de perturbacion RS toma encuenta el intercambio,esta ha sido ampliamente difundida despues que el codigo fueraintroducido en las suites de programas como Gaussian.
















H0 =

N∑i=1

hHFi (21)

Ψ(0) =1√N !det|ψ1αψ2βψ3α . . . ψNβ| (22)

Φ(0) es funcion propia del Hamiltoniano, H0 y es antisimetrica.

La perturbacion es:

V = H −N∑i=1

hHFi (23)




H0 =

N∑i=1

hHFi (21)

Ψ(0) =1√N !det|ψ1αψ2βψ3α . . . ψNβ| (22)


La perturbacion es:

V = H −N∑i=1

hHFi (23)




H0 =

N∑i=1

hHFi (21)

Ψ(0) =1√N !det|ψ1αψ2βψ3α . . . ψNβ| (22)


La perturbacion es:

V = H −N∑i=1

hHFi (23)




La energıa de interaccion es la diferencia total de la “supermolecula“y las energıas de las moleculas cosntituyentes. Para un sistema dedos moleculas (dos atomos):

Eint = E(AB)− [E(A) + E(B)] (24)

Cada termino es calculado con MPPT usando la formulacion estandarde Rayleigh-Schrodinger. Produce buenos resultados a distancias in-termedias pero no en distancias muy cortas.




La energıa de interaccion es la diferencia total de la “supermolecula“y las energıas de las moleculas cosntituyentes. Para un sistema dedos moleculas (dos atomos):

Eint = E(AB)− [E(A) + E(B)] (24)

Cada termino es calculado con MPPT usando la formulacion estandarde Rayleigh-Schrodinger. Produce buenos resultados a distancias in-termedias pero no en distancias muy cortas.




Error de superposicion del conjunto de base

En la aproximacion supermolecular la inconsistencia de las basesproduce aumentos en la energıa de interaccion intermolecular

Eint(R) = EAB({AB} , R)−[EA({A} ,∞) + EB({B} ,∞)

](25)

tamano de la base {AB} > {A} y {B} causando una estabilizacionartificial

ECPint (R) = EAB({AB} , R)−[EA({AB} , R) + EB({AB} , R)

](26)

CP-contrapeso







](25)



](26)

CP-contrapeso







](25)



](26)

CP-contrapeso




SAPT-DFT

La teorıa de perturbacion de 3 orden y de cumulos acoplados usadaen SAPT hace muy difıcil su implementacion y demanda muchosrecursos computacionales

La teorıa del funcional de la densidad (DFT) ofrece una alter-nativa atractiva ya que los efectos de correlacion son incluidosdesde el inicio y solamente hay una perturbacion simple.

Puede se aplicada a sistemas con muchos electrones

Como en HF es una aproximacion de 1 electron para la ec.Schrodinger de muchos electrones con un potencial especial deintercambio-correlacion




SAPT-DFT








SAPT-DFT








SAPT-DFT








Contenido

1 Motivacion


3 Ejemplos

4 Bibliografıa





Dimer C is equivalent to the π-stacked structure discussed inthe work by Zhang14 and, as discussed below, corresponds tothe SAPT(DFT) minimum energy configuration among all of

the geometries analyzed in this study. The center of massseparation, 3.34 Å, compares with Zhang’s value of ∼3.4 Å, andin this configuration, the amine nitrogens of the upper

Figure 3. Minima on PES. Left and right columns are different perspectives of the same configuration.

Table 2. Interaction Energies (kcal/mol) Using ab Initio SAPT(DFT) and Fitted Forcefielda

dimer R (Å) electrostatic exchange induction dispersion ETotal forcefield error

A 9.04 −5.395 7.290 −2.385 −4.893 −5.384 −4.834 0.550B 4.73 −4.892 16.616 −5.301 −16.468 −10.046 −9.798 0.248C 3.34 −5.428 24.117 −7.876 −22.465 −11.652 −11.521 0.131D 7.36 −3.867 6.348 −2.161 −5.117 −4.798 −4.885 −0.087E 5.89 0.439 7.161 −2.681 −8.523 −3.603 −4.090 −0.487F 6.52 −4.634 9.361 −3.083 −7.569 −5.926 −5.135 0.791G 9.07 −4.065 5.508 −1.84 −4.059 −4.465 −4.113 0.352H 5.89 −4.467 11.302 −3.711 −9.215 −6.091 −5.893 0.198

aExchange value is sum of first order exchange, and second order exchange-induction/exchange-dispersion energies. Induction energy includes δEintHF

contribution.

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp4005289 | J. Phys. Chem. A 2013, 117, 3507−35203512

Se utilizo SAPT(DFT) del programa SAPT2008, que permitecalcular energıas de interacion intermolecular para dimeros ytrimeros.

Tales energıas son separadas en componentes fısicos (electrostatico,induccion, dispersion e intercambio)

La geometrıa del monomero es tomada de datos experimentales










A 9.04 −5.395 7.290 −2.385 −4.893 −5.384 −4.834 0.550B 4.73 −4.892 16.616 −5.301 −16.468 −10.046 −9.798 0.248C 3.34 −5.428 24.117 −7.876 −22.465 −11.652 −11.521 0.131D 7.36 −3.867 6.348 −2.161 −5.117 −4.798 −4.885 −0.087E 5.89 0.439 7.161 −2.681 −8.523 −3.603 −4.090 −0.487F 6.52 −4.634 9.361 −3.083 −7.569 −5.926 −5.135 0.791G 9.07 −4.065 5.508 −1.84 −4.059 −4.465 −4.113 0.352H 5.89 −4.467 11.302 −3.711 −9.215 −6.091 −5.893 0.198


contribution.















A 9.04 −5.395 7.290 −2.385 −4.893 −5.384 −4.834 0.550B 4.73 −4.892 16.616 −5.301 −16.468 −10.046 −9.798 0.248C 3.34 −5.428 24.117 −7.876 −22.465 −11.652 −11.521 0.131D 7.36 −3.867 6.348 −2.161 −5.117 −4.798 −4.885 −0.087E 5.89 0.439 7.161 −2.681 −8.523 −3.603 −4.090 −0.487F 6.52 −4.634 9.361 −3.083 −7.569 −5.926 −5.135 0.791G 9.07 −4.065 5.508 −1.84 −4.059 −4.465 −4.113 0.352H 5.89 −4.467 11.302 −3.711 −9.215 −6.091 −5.893 0.198


contribution.















A 9.04 −5.395 7.290 −2.385 −4.893 −5.384 −4.834 0.550B 4.73 −4.892 16.616 −5.301 −16.468 −10.046 −9.798 0.248C 3.34 −5.428 24.117 −7.876 −22.465 −11.652 −11.521 0.131D 7.36 −3.867 6.348 −2.161 −5.117 −4.798 −4.885 −0.087E 5.89 0.439 7.161 −2.681 −8.523 −3.603 −4.090 −0.487F 6.52 −4.634 9.361 −3.083 −7.569 −5.926 −5.135 0.791G 9.07 −4.065 5.508 −1.84 −4.059 −4.465 −4.113 0.352H 5.89 −4.467 11.302 −3.711 −9.215 −6.091 −5.893 0.198


contribution.









La forma del funcional utilizado es:

Vab(r) =qaqbr−Aab exp

(− r

Bab

)− Cab6

r6(27)

a,b enumeran los atomos de los monomeros A y B.

Aab, Bab, Cab6 son parametros ajustables




La forma del funcional utilizado es:

Vab(r) =qaqbr−Aab exp

(− r

Bab

)− Cab6

r6(27)

a,b enumeran los atomos de los monomeros A y B.

Aab, Bab, Cab6 son parametros ajustables









A 9.04 −5.395 7.290 −2.385 −4.893 −5.384 −4.834 0.550B 4.73 −4.892 16.616 −5.301 −16.468 −10.046 −9.798 0.248C 3.34 −5.428 24.117 −7.876 −22.465 −11.652 −11.521 0.131D 7.36 −3.867 6.348 −2.161 −5.117 −4.798 −4.885 −0.087E 5.89 0.439 7.161 −2.681 −8.523 −3.603 −4.090 −0.487F 6.52 −4.634 9.361 −3.083 −7.569 −5.926 −5.135 0.791G 9.07 −4.065 5.508 −1.84 −4.059 −4.465 −4.113 0.352H 5.89 −4.467 11.302 −3.711 −9.215 −6.091 −5.893 0.198


contribution.






Dimeros de Dimetil etil urea (DMEU)-Agua

Las dos configuraciones fueron halladas a nivel MP2. Las en-ergas se hallaron con HF, B3LYP, MP2 y con correccion CPpara cada uno de ellos.

La molecula de agua en la estructura I esta en el mismo planodel anillo formando un enlace de hidrogeno con el oxıgeno delDMEU.

Bende, A.; Almas, L.Chem. Phys. 354, 202-210 p, 2008


















Diferentes curvas obtenidas para la estructura I con niveles de teorıaHF, B3LYP, MP2 y con correccion CP para cada uno de ellos.




Hamiltoniano del dımero

H = F + V +W (28)

F = FA + FB es el operador de Fock de los monomeros A y B.V operador intermolecular.W operador intramolecular.

EHFint = E

(10)elst + E

(10)exch + E

(20)ind,resp + E

(20)exch−ind,resp + δEHF

int,resp

ESAPT2int = EHF

int + E(12)elst,resp + ε

(1)exch +t E

(22)ind +t E

(22)exch,int

+E(20)disp + E

(20)exch,disp

EHFint Energıa HF supermolecular (cuando el operador intramolecular es de

orden cero).E(nj) Energıa de orden n del operador V y de orden j del operador W .ESAPT2

int Energıa de interaccion de segundo orden en SAPT.




opposite effect occurs at the correlation level, but the increasing ofSAPTcorr energy is the result of the collective contributions of thedifferent correlation energy components having repulsive orattractive interaction character. The most pronounced change oc-curs in the dispersion contribution Eð20Þ

disp for which the energy in-creases by about 60% for both structure I and structure II cases.The polarization effects could also generate significant changes inother second-order energy components, like e.g. Eð11Þ

exch. At the sametime, comparing these values for structure I and structure II, onecan see that the magnitude of several correlation (first or second-order) energy contributions are very different. This fact means thatthe given energy component strongly depends on the orientationsof the atomic orbitals. On the other hand, considering only the cor-relation effects, the dispersion contribution appears to be the mostrelevant component of the correlation energy (Eð20Þ

disp = �2.633 kcal/mol for structure I and Eð20Þ

disp = �3.180 kcal/mol for structure II,using D95** basis sets in both cases). This result confirms the state-ment formulated on the basis of the MP2 and DFT calculations thatdispersion effects are very important for the description of theseweakly bound molecular associates. In addition, the SAPT resultsprove also another previous statement. Namely, the e intermolec-ular interaction energy and R intermolecular distance for structureI obtained with counterpoise corrected MP2 and DFT levels of the-ory are much closer than the corresponding values in cases ofstructure II and the various DMEU dimers. This fact is due to themore significant contribution of the first order (HF) energy andsmaller second-order correlation energy for structure I in compar-ison with structure II geometry. This case could be considered sim-ilar to those discrepancies which were found for the planar andperpendicular arrangements of the DMEU dimers using two differ-ent (MP2 and B3LYP) methods (see Section 3.1.1).

Large dispersion effects were also found for TMU–water com-plexes [26], accompanied by a large BSSE. Those results were ob-tained applying the London formula as an addition at the HFlevel, hence the other second-order electron correlation effectswere missing, which could probably diminish the effect of the dis-persion contribution.

3.2.2. Dimethylethyleneurea dimersIn the previous subsection we have shown the importance of

polarization functions in the accurate description of intermolecularinteraction. However, using d functions for heavy atoms and pfunctions for hydrogen atoms the number of basis functions wouldincrease in such extent that the limited computer capacity wouldprevent us from performing SAPT calculation. As a realistic com-promise for DMEU dimer calculations, we kept only the d polariza-tion functions on heavy atoms, using the D95* basis set. Thephysically interesting intermolecular interaction energy compo-nents (Eqs. (2) and (3)) for the three different DMEU dimers arecollected in Table 4. The strongest intermolecular interaction is ob-tained for the parallel configuration (Eint ¼ EHF

int þ SAPTcorr =� .135 kcal/mol), while the weakest one is found for the perpendic-ular structure (Eint = �2.057 kcal/mol). For all the three dimer con-figurations the correlation contribution is higher then the firstorder part. But the most conspicuous of them is the parallel struc-ture where the second order contribution is higher by about oneorder of magnitude. The major contribution in the correlation en-ergy is given by the dispersion effects (Eð20Þ

disp = �2.067 kcal/mol forplanar structure, Eð20Þ

disp = �7.981 kcal/mol for parallel structure andEð20Þ

disp = �3.801 kcal/mol for perpendicular case). The other secondorder energy components are smaller. Summarizing them the po-sitive and negative energy components partially cancel each otherand finally result in a small positive contribution in ESAPT2

int energy.The first order corrections do not show any systematical behav-

iour. These energies are compounded from several electrostaticparts with negative signs and exchange parts having positive signs.The lack of pronounced trends is due to the different magnitudes ofelectrostatic and exchange contributions in the different dimerconfigurations. Thus, for planar case SAPTSCF = �1.320 kcal/mol,for parallel one SAPTSCF = �0.132 kcal/mol, and in case of perpen-dicular structure SAPTSCF = 0.928 kcal/mol.

Another important remark can be made for the dEHFint;resp term. As

it was mentioned in Section 2, it represents all the third- and high-er-order induction and exchange-induction terms together. Thisenergy component has the largest value in case of the parallelstructure, but in the other two cases its contribution is still signif-icant, and can substantially influence the magnitude of SAPTSCF

Table 3The different SAPT energy components (in kcal/mol) of two equilibrium DMEU–watercomplexes at SCF and second-order correlation level of SAPT theory, using D95 andD95�� basis sets.

Correction Structure I Structure II

D95 D95(d,p) D95 D95(d,p)

SCF

Eð10Þelst �13.808 �11.963 �10.718 �9.394

Eð10Þexch 8.734 8.601 8.502 8.397

Eð20Þind;resp �4.010 �3.834 �4.238 �4.130

Eð20Þexch�ind;resp 1.958 1.926 2.625 2.592

dEHFint;resp �1.118 �1.094 �1.091 �1.037

EHFint �8.245 �6.364 �4.920 �3.571

SAPTSCFresp �7.126 �5.270 �3.828 �2.534

Correlation

Eð12Þelst;resp 0.495 0.429 �0.742 �0.520

Eð11Þexch �0.211 �0.073 �0.138 0.007

Eð12Þexch 2.199 1.808 1.856 1.398

tEð22Þind �0.762 �0.654 �0.977 �0.763

tEð22Þexch�ind 0.372 0.328 0.605 0.479

Eð20Þdisp �1.615 �2.633 �2.005 �3.180

Eð20Þexch�disp 0.308 0.465 0.363 0.526

SAPTcorr �0.128 �1.094 �0.714 �1.784

Table 4The different SAPT energy components (in kcal/mol) of planar, parallel andperpendicular DMEU dimer structures at SCF and second-order correlation level ofSAPT theory, using D95� basis set.

Correction Planar Parallel Perpendicular

SCF

Eð10Þelst �3.911 �7.670 �2.366

Eð10Þexch 3.454 8.966 3.635

Eð20Þind;resp �1.411 �4.633 �1.345

Eð20Þexch�ind;resp 0.549 3.205 1.004

dEHFint;resp �0.319 �0.727 �0.215

EHFint �1.638 �0.858 0.713

SAPTSCFresp �1.320 �0.132 0.928

Correlation

Eð12Þelst;resp �0.007 �0.138 �0.528

Eð11Þexch �0.154 �0.296 �0.093

Eð12Þexch 0.915 2.382 0.860

tEð22Þind �0.122 �1.121 �0.328

tEð22Þexch�ind 0.048 0.775 0.245

Eð20Þdisp �2.067 �7.981 �3.801

Eð20Þexch�disp 0.237 0.963 0.347

SAPTcorr �1.821 �5.277 �2.770

A. Bende, L. Almásy / Chemical Physics 354 (2008) 202–210 207







Contenido

1 Motivacion


3 Ejemplos

4 Bibliografıa




Bibliografıa

Kaplan, I. G.Intermolecular Interactions: Physical Picture, Com-putational Methods and Model Potentials 1 Ed., John Wileyand Songs, INC, England, 2006.

Stone, A.,The Theory of the Intermolecular Forces 2 Ed., Ox-ford University Press, United Kingdom, 2010.


Documents

Seminario IV: Fuerzas intermolecularesdepa.fquim.unam.mx/jesusht/sfi_sapt.pdf · A1 1 2m 52 1 r B2 (7) H 0 no es sim etrico a las permutaciones de los electrones El Hamiltoniano total,