Minimum conditions for accurate modeling of urea production via co-electrolysis

ARTICLE
Minimum condi ions o accu a e modeling o u ea
p oduc ion ia co-elec olysis
Rica do U ego-O iz 1,2, San iago Builes3, F ancesc Illas 1, S e an T. B omley1,4,
Ma a Cos a Figuei edo 5& Fede ico Calle-Vallejo 2,6✉
Co-elec olysis o ca bon oxides and ni ogen oxides p omise o simul aneously help es o e
he balance o he C and N cycles while p oducing aluable chemicals such as u ea. Howe e ,
co-elec olysis p ocesses a e s ill la gely ine ficien and nume ous knowledge oids pe sis .
He e, we p o ide a solid he modynamic basis o modelling u ea p oduc ion ia co-
elec olysis. Fi s , we de e mine he ene ge ics o aqueous u ea p oduced unde elec o-
chemical condi ions based on expe imen al da a, which enables an accu a e assessmen o
equilib ium po en ials and o e po en ials. Nex , we use densi y unc ional heo y (DFT)
calcula ions o model a ious co-elec olysis eac ions p oducing u ea. The calcula ed eac-
ion ee ene gies de ia e significan ly om expe imen al alues o well-known GGA, me a-
GGA and hyb id unc ionals. These de ia ions s em om e o s in he DFT-calcula ed
ene gies o molecula eac an s and p oduc s. In pa icula , he e o o u ea is app oxima ely
-0.25 ± 0.10 eV. Finally, we show ha all hese e o s in oduce la ge inconsis encies in he
calcula ed ee-ene gy diag ams o u ea p oduc ion ia co-elec olysis, such ha gas-phase
co ec ions a e s ongly ad ised.
h ps://doi.o g/10.1038/s42004-023-00990-7 OPEN
1Depa amen de Ciència de Ma e ials i Química Física & Ins i u de Química Teò ica i Compu acional (IQTCUB), Uni e si a de Ba celona, C/ Ma í i
F anquès 1, 08028 Ba celona, Spain. 2Nano-Bio Spec oscopy G oup and Eu opean Theo e ical Spec oscopy Facili y (ETSF), Depa men o Polyme s and
Ad anced Ma e ials: Physics, Chemis y and Technology, Uni e si y o he Basque Coun y UPV/EHU, A . Tolosa 72, 20018 San Sebas ián, Spain. 3Escuela
de Ciencias Aplicadas e Ingenie ía, Uni e sidad EAFIT, Ca e a 49 # 7 su 50, 050022 Medellín, Colombia. 4Ins i ució Ca alana de Rece ca i Es udis
A ança s (ICREA), Passeig Lluís Companys 23, 08010 Ba celona, Spain. 5Eindho en Ins i u e o Renewable Ene gy Sys ems (EIRES), Eindho en Uni e si y o
Technology, PO Box 513 Eindho en 5600 MB, The Ne he lands. 6IKERBASQUE, Basque Founda ion o Science, Plaza de Euskadi 5, 48009 Bilbao, Spain.
✉email: [email p o ec ed]
COMMUNICATIONS CHEMISTRY | (2023) 6:196 | h ps://doi.o g/10.1038/s42004-023-00990-7 | www.na u e.com/commschem 1
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The elec ochemical co- educ ion o species con aining
ni ogen and ca bon o p oduce chemical commodi ies can
be ca ied ou using enewable elec ici y1–4, simul a-
neously aiding o es o e he se e ely imbalanced cycles o
ni ogen and ca bon5–7. Among he po en ial p oduc s, u ea
(CO(NH
2
)
2
) is an appealing C-N compound gi en i s eno mous
ele ance in mode n ag icul u e8–10, and he la ge ene gy
demands o i s indus ial p oduc ion2,9,11,12. Al hough elec o-
ca aly ic u ea p oduc ion om N- and C-oxides has been s udied
a he labo a o y scale o mo e han wo decades13–18, c i ical
challenges ega ding he elec ochemis y o he C-N coupling a e
ye o be sol ed be o e indus ial applica ions a e a hand19,20.
Some o hese challenges a e he la ge associa ed o e po en ials,
elusi e eac ion mechanisms, and low selec i i y caused by he
concu en o ma ion o H
2
, CO, o mic acid (HCOOH),
ammonia (NH
3
), and o he single-ca bon and/o single-ni ogen
species16,21–23.
Ei he in andem wi h expe imen s o in s andalone com-
pu a ional s udies, densi y unc ional heo y (DFT) me hods
ha e been ex ensi ely used o in es iga e he elec osyn hesis o
u ea om N- and C-con aining eeds ocks and design enhanced
ca alys s2,24–28. These s udies equen ly use exchange-
co ela ion (xc) unc ionals ollowing he gene alized g adien
app oxima ion (GGA), as hey p o ide a easonable adeo
be ween compu a ional cos and accu acy o he p ope ies o
molecules and su aces29–32. A ecen example is he wo k o
Wane al.,inwhichDFT-based he modynamicandkine ic
models we e p oposed o explain he selec i e C-N bond o -
ma ion on Cu elec odes and a ionalize he expe imen al
obse a ions o Shiba a e al.14,16,33 using he BEEF- dW
unc ional34. No wi hs anding, he limi a ions o GGA unc-
ionals a e well known o desc ibing gaseous molecules con-
aining mul iple bonds, such as O
2
30,35,36,N
2
and NO
x
37–39,
and ca bon-con aining species40–43. These limi a ions can cause
la ge disc epancies be ween calcula ed and expe imen al equi-
lib ium po en ials and impai he p edic i e capabili ies o
GGA-based he e ogenous (elec o)ca aly ic models, whe e
molecules and su aces a e simul aneously in ol ed39,44,45.
App oaches o o e come some o he sho comings o GGA
unc ionals, such as me a-GGA46 and hyb id unc ionals47, end
o pe o m be e o he p edic ion o gas-phase he mo-
chemis y. Unlike GGA unc ionals, me a-GGA unc ionals
include an app oxima e dependence on he kine ic ene gy
densi y48, while hyb id unc ionals inco po a e a p opo ion o
exac nonlocal Fock exchange49–52. In e es ingly, p e ious wo ks
ha e shown ha when GGA, me a-GGA, and/o hyb id unc-
ionals a e used o model a ious amilies o C- 40,43 and
N-con aining compounds38,39,53,H
2
O
2(g)
and O
2(g)
36,44,45, sizable
gas-phase e o s a e s ill ound. Such e o s a e sys ema ic and
can be mi iga ed by means o inexpensi e semiempi ical
co ec ions38,40,41,43,53. This s ongly sugges s ha a cau ious and
ea ly assessmen o gas-phase e o s is needed o gua an ee he
accu acy o (elec o)ca aly ic models based upon DFT
calcula ions.
He ein, we s udy he co-elec olysis o di e en ni ogen (N
2(g)
,
NO
(g)
,NO
3aq
ðÞ
) and ca bon oxides (CO
(g)
,CO
2(g)
) as eeds ocks
o p oduce aqueous u ea (CO(NH
2
)
2(aq)
) using se e al exchange-
co ela ion unc ionals: ou GGA unc ionals, wo me a-GGA
unc ionals, and wo hyb id unc ionals. Fo mos gas-phase
compounds unde s udy a hese h ee le els o DFT, we pinpoin
and co ec la ge gas-phase e o s in he calcula ed ene gies. Ou
esul s s ess he impo ance o gas-phase e o assessmen in
compu a ional elec oca alysis and p o ide an accu a e s a ing
poin o modeling u ea p oduc ion on eal ca alys s by co-
elec olysis o CO
x
and NO
x
eeds ocks.
Me hodology
Compu a ional me hods. The Vienna ab ini io simula ion
package (VASP)54 was used o pe o m he DFT calcula ions o
H
2(g)
,N
2(g)
,O
2(g)
,H
2
O
(g)
,NH
3(g)
, CO(NH
2
)
2(g)
,CO
(g)
,CO
2(g)
,
NO
(g)
, HNO
3(g)
, and C
(s)
. All compounds we e modeled in hei
gas-phase in boxes o 15 × 15 × 15 A3(in some cases, we changed
he size o he ec o s by ±0.1 Å o see i mo e nega i e ene gies
we e ound, which was he case only o NO). C
(s)
was ep e-
sen ed he e by g aphene as a easonable DFT model o g aphi e.
The la e app oxima ion is enabled by he ac ha he in e laye
cohesi e ene gy o g aphi e is small (0.031–0.064 eV)55–59. The
calcula ions we e ca ied ou o a ange o DFT unc ionals
ascending he so-called “Jacob’s ladde ”60: namely GGAs (PBE61,
PW9162, RPBE63, BEEF- dW64), me a-GGAs (TPSS48, SCAN65),
and hyb ids (PBE066, B3LYP67). The C-C dis ances o g aphene
ob ained in all cases we e close o he expe imen al alue o 1.42
A(PBE: 1.43 A, PW91: 1.43 A, RPBE: 1.43 A, BEEF- dW: 1.43 A,
TPSS: 1.42 A, SCAN: 1.42 A, B3LYP: 1.42 A, PBE0: 1.42 A)68.
The p ojec o augmen ed-wa e (PAW) me hod was used o
ep esen he in e ac ions be ween co e elec on densi y and
alence elec ons69. A plane-wa e cu o o 450 eV was used in all
calcula ions, assu ing con e ged ΔZPE and eac ion ene gies o
he gaseous u ea p oduc ion om N
2(g)
and CO
2(g)
using PBE
(N2g
ðÞþCO2g
ðÞþ3H2g
ðÞ!CO NH2

2g
ðÞþH2Og
ðÞ
). In ac ,
he di e ence be ween he eac ion ene gy and ΔZPE ob ained
wi h his cu o di e ed only by ~0.01 eV om hose ob ained
wi h a igh e cu o o 1000 eV (see Supplemen a y Fig. 1 and
Supplemen a y Table 1 in Supplemen a y No e 1). The geome y
o each molecule was elaxed using he conjuga e g adien algo-
i hm un il he final o ces be ween he a oms we e lowe han
0.01 eV A
−1. Gaussian smea ing wi h an elec onic empe a u e
o 10−3eV was used o ease he con e gence o he sel -consis en
field p ocedu e and, upon con e gence, all ene gies we e ex a-
pola ed o 0 K. Since he code used is in insically pe iodic, he
calcula ions o molecules we e ca ied ou a he Γ-poin . Con-
e sely, o g aphene a Monkho s -Pack g id70 o 8 × 8 × 1 special
k-poin s was used. Spin-un es ic ed calcula ions we e pe o med
o O
2(g)
( iple ) and NO
(g)
(double ). Fu he de ails o he inpu
files used o pe o m he calcula ions a e p o ided in Supple-
men a y No e 7 and he coo dina es o he con e ged geome ies
a e gi en in Supplemen a y No e 8.
The he modynamic analyses in his s udy a e based upon ee
ene gies. The ee ene gy o compound i(GDFT
i) is app oxima ed by
means o i s DFT ene gy (EDFT
i), he calcula ed ze o-poin ene gy
(ZPEi) using ha monic equencies, he di e ence be ween he
o ma ion en halpies a 298.15 and 0 K (Δ Hi@298:15KΔ Hi@0K),
and he en opic con ibu ions (TSi) aken om he modynamic
ables a T=298.15 K, as shown in Eq. 171–75. Supplemen a y
Table 2 compiles he DFT-calcula ed ene gies, ZPEs, expe imen al
TS, and he di e ences be ween he expe imen al o ma ion
en halpies be ween 0 and 298.15 K o he compounds unde
s udy (see also Supplemen a y Table 5). We p o ide mo e de ails o
he he mal con ibu ions in Supplemen a y No e 4.
GDFT
iEDFT
iþZPEiþðΔ Hi@298:15KΔ Hi@0KÞTSið1Þ
Co-elec olysis modeling. We conside he six eac ions shown
below in which u ea is p oduced by he simul aneous educ ion o
di e en C- and N-con aining species.
N2g
ðÞþCO g
ðÞþ4Hþþ4e!CO NH2

2aq
ðÞ ð2Þ
N2g
ðÞþCO2g
ðÞþ6Hþþ6e!CO NH2

2aq
ðÞ
þH2OlðÞ ð3Þ
ARTICLE COMMUNICATIONS CHEMISTRY | h ps://doi.o g/10.1038/s42004-023-00990-7
2COMMUNICATIONS CHEMISTRY | (2023) 6:196 | h ps://doi.o g/10.1038/s42004-023-00990-7 | www.na u e.com/commschem
2NO g
ðÞþCO g
ðÞþ8Hþþ8e!CO NH2

2aq
ðÞ
þ2H2OlðÞ
ð4Þ
2NO g
ðÞþCO2g
ðÞþ10Hþþ10e!CO NH2

2aq
ðÞ
þ3H2OlðÞ
ð5Þ
2NO
3aq
ðÞ
þCO g
ðÞþ16Hþþ14e!CO NH2

2aq
ðÞ
þ6H2OlðÞ
ð6Þ
2NO
3aq
ðÞ
þCO2g
ðÞþ18Hþþ16e!CO NH2

2aq
ðÞ
þ7H2OlðÞ
ð7Þ
These eac ions in ol e eac an s and p oduc s in di e en
physical s a es, such ha , unde he app op ia e ex e nal po en ial,
gaseous and aqueous compounds eac o p oduce hyd a ed u ea and
liquid wa e . As DFT simula ions o liquids and aqueous sys ems a e
possible bu challenging and ime-consuming and addi ional s a is-
ical analyses a e necessa y, he DFT alues o he co esponding gas-
phase e e ences, which a e apidly calcula ed, se e as he basis o
es ima e hei ene ge ics ia semiempi ical conside a ions, as
depic ed in Fig. 1. Mo eo e , as compu a ional sol a ion me hods
ha e disc epancies wi h espec o expe imen s76 ha a e la ge han
he accu acies o he expe imen al measu emen s, we do no expec
ha calcula ing he sol a ion ene gies o he species using DFT
would yield lowe e o s.
The scheme in Fig. 1shows he ene gy di e ences be ween he
s a es o a gene ic compound HX. Figu e 1along wi h he
addi ional conside a ions de ailed below we e used o calcula e
he ee ene gies o all he compounds in he co-elec olysis
eac ions. We no e ha he modynamic cycles based on
expe imen al equilib ium po en ials ha e also been used o
semiempi ically ob ain he ee ene gies o ionic species om he
DFT-calcula ed ene gies o neu al solids and gaseous
compounds37,77,78. In he Supplemen a y No e 6, we show in a
s epwise ashion how he ee ene gy o ni a e can be es ima ed
using his app oach.
(i) The ene ge ics o p o on-elec on pai s was calcula ed by
means o he compu a ional hyd ogen elec ode, which is
based on he ollowing equilib ium in solu ion:
Hþþe$1
2H2g
ðÞ
, such ha 1
2μ0
H2g
ðÞ ¼μ0
Hþþe
ðÞ
79.
(ii) Based on Fig. 1, he ee ene gy o o ma ion o aqueous u ea
ðΔ G0
CO NH2
ðÞ
2aq
ðÞ
Þwas es ima ed by adding he expe imen al
sol a ion ene gy ðΔsol Gexp
CO NH2
ðÞ
2aq
ðÞ
Þ o he DFT-calcula ed
o ma ion ene gy o gaseous u ea ðΔ GDFT
CO NH2
ðÞ
2g
ðÞ
Þ, i.e,
Δ G0
CO NH2
ðÞ
2aq
ðÞ
¼Δ GDFT
CO NH2
ðÞ
2g
ðÞ
þΔsol Gexp
CO NH2
ðÞ
2aq
ðÞ
. The
expe imen al sol a ion ene gy can be ob ained as he
di e ence be ween he expe imen al o ma ion ene gy o
aqueous u ea ðΔ Gexp
CO NH2
ðÞ
2aq
ðÞ
Þand he expe imen al
o ma ion ene gy o gaseous u ea
ðΔ Gexp
CO NH2
ðÞ
2g
ðÞ
¼1:57eVÞ71,73.Δ Gexp
CO NH2
ðÞ
2aq
ðÞ
is calcu-
la ed, in acco dance wi h Fig. 1, by combining he
expe imen al ee ene gy o solu ion
ðΔsolGexp
CO NH2
ðÞ
2
¼0:07eVÞ73 and he expe imen al o ma-
ion ene gy o solid u ea ðΔ Gexp
CO NH2
ðÞ
2sðÞ
¼2:04 eVÞ71, hus
Δ Gexp
CO NH2
ðÞ
2aq
ðÞ
¼2:11eV. Finally, Δsol Gexp
CO NH2
ðÞ
2aq
ðÞ
¼
0:54eV and Δ G0
CO NH2
ðÞ
2aq
ðÞ
¼Δ GDFT
CO NH2
ðÞ
2g
ðÞ
0:54eV.
(iii) Following Fig. 1, he ee ene gy o o ma ion o liquid
wa e (Δ G0
H2OðlÞ
) was ob ained by sub ac ing he
expe imen al wa e apo iza ion ene gy
ðΔ apGexp
H2O¼0:09eVÞ72 om he DFT-calcula ed ee
ene gy o o ma ion o wa e in he gas phase ðμDFT
H2Og
ðÞ
Þ,
i.e, Δ G0
H2OlðÞ
¼Δ GDFT
H2OðgÞ
0:09eV.
(i ) Because calcula ing he ene gies o dissol ed ni a e ðNO
3aq
ðÞ
Þ
wi h DFT is p oblema ic37,he eweuse1
2H
2(g)
and HNO
3(g)
as e e ences, as shown in Eq. 8:
HNO3ðgÞ!NO
3ðaqÞþHþð8Þ
We no e ha HNO
3(g)
dissocia ion in Eq. 8is comple e, as i is
a s ong acid80. The ee ene gy o Eq. 8ðΔGexp
8Þcan be exp essed
Fig. 1 The modynamic amewo k. Scheme ela ing he ene gy di e ences be ween he s a es o a gene ic compound HX. The subindices s, l, and g
ep esen HX in he solid, liquid, and gas phases, espec i ely. The o al ene gy o HX in he gas phase (in g een) can be es ima ed om DFT, using Eq. 1.
The subindex aq e e s o hyd a ed HX, i.e, HX
(s)
su ounded by wa e . In ed, an anion is p oduced om he dissocia ion o HX
(aq)
.ΔsolGis he ee ene gy
o solu ion ( he ene gy associa ed o he dissolu ion o one mole o HX
(s)
in an infini e amoun o wa e ); Δ usGis he usion ee ene gy; Δ apGis he
apo iza ion ene gy; Δsol Gis he sol a ion ee ene gy, defined as he ene gy equi ed o b ing a mole o HX
(g)
om acuum o a wa e ese oi ; ΔdissGis
he dissocia ion ee ene gy in solu ion. The dashed ed lines indica e ha dissocia ion occu s only o HNO
3
in his s udy.
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COMMUNICATIONS CHEMISTRY | (2023) 6:196 | h ps://doi.o g/10.1038/s42004-023-00990-7 | www.na u e.com/commschem 3
as:
ΔGexp
8¼Δ G0
NO
3ðaqÞþ1
2Δ G0
H2ðgÞΔ G0
HNO3ðgÞð9Þ
As shown in Fig. 1,ΔGexp
8co esponds o he sum o he
sol a ion and dissocia ion ene gies o HNO
3
ðΔsol þdissGexp
HNO3Þ,
which can be calcula ed as he di e ence be ween he expe i-
men al o ma ion ene gy o NO
3aq
ðÞ(−1.15 eV) and ha o
HNO
3(g)
(−0.76 eV)72. Hence, in his s udy ΔGexp
8¼
Δsol þdissGexp
HNO3¼0:39eV. Based on Eq. 9, he ee ene gy o
o ma ion o NO
3aq
ðÞ
can be assessed om DFT and expe imen al
da a as:
Δ GDFT
NO
3aq
ðÞ
¼Δ GDFT
HNO3g
ðÞ
μDFT
Hþ0:39 eV ð10Þ
whe e he ene ge ics o p o ons (μDFT
Hþ) is ob ained by in oking
he compu a ional hyd ogen elec ode79. Wi h hese conside a-
ions, DFT and expe imen al alues can be combined o
semiempi ically calcula e he ee ene gies o each compound in
Eqs. 2 o 7, and he associa ed ee ene gies o eac ion.
Gas-phase e o assessmen . An impo an conside a ion in he
modeling o he e ogenous (elec o)ca aly ic eac ions is he
de ec ion and co ec ion o he e o s in he DFT-calcu-
la ed ene gies o gas-phase compounds. The e o s o O
2(g)
,N
2(g)
,
NO
(g)
, HNO
3(g)
,CO
(g)
, and CO
2(g)
, ha e p e iously been calcu-
la ed using se e al unc ionals and la ge alues ha e been
epo ed in a ious cases36,38–40,45,53. These significan e o s
p e en accu a e es ima ions o impo an quan i ies in ca alysis
o he h ee easons de ailed below.
Fi s , an accu a e equilib ium po en ial o a gi en eac ion
may only be a ionally ob ained by co ec ing he gas-phase
e o s o all eac an s and p oduc s. This is because he
equilib ium po en ial (U
eq
) is a unc ion o he eac ion ee
ene gy (Δ G) and he numbe o elec ons ans e ed (n). Fo a
educ ion eac ion: Ueq ¼Δ G=n:Fo example, he eac ion in
Eq. 2has an expe imen al Δ Go -0.69 eV and in ol es 4 p o on-
elec on ans e s. Thus, i s expe imen al Ueq is 0:69 eV
4e¼0:17 V.
Now, he Δ Gusing unco ec ed PBE is -1.68 eV and Ueq is
1:68eV
4e¼0:42 V, which de ia es by 0.250 V om he expe i-
men al alue. When he e o s o N
2
and CO ( he eac an s) a e
co ec ed, he new PBE equilib ium po en ial is 0.22 V, which is
0.05 V away om he expe imen al alue. A e co ec ing he
e o in u ea, he PBE calcula ions ma ch he expe imen al alue.
Second, i he po en ial-limi ing s ep in ol es molecules,
co ec ing he gas-phase e o o no may lead o di e en
quali a i e and quan i a i e conclusions because he eac ion
ene gy expe iences a shi .
Thi d, when he o e po en ial is calcula ed, gas-phase e o s
a e always impo an because he o e po en ial is he di e ence
be ween a gi en po en ial and he one a equilib ium ( o a
educ ion eac ion: η¼Ueq U).
I has also been shown ha gas-phase e o s can a ec
adso p ion-ene gy scaling ela ions and olcano plo s36,39,44,
impai ing he p edic i e capabili y o desc ip o -based models o
cus oma y use in compu a ional elec oca alysis.
To ob ain a gene al exp ession o assess he gas-phase e o s,
we fi s conside he o ma ion eac ion o a hypo he ical
compound HαCβNγOδ:
α
2H2g
ðÞþβCsðÞþγ
2N2g
ðÞþδ
2O2g
ðÞ!HαCβNγOδð11Þ
whe e α;β;γ;and δa e in ege s, he molecules a e in hei
s anda d s a es, and CsðÞ is modeled as g aphene. The o al e o
in he DFT-calcula ed ee ene gy o o ma ion o HαCβNγOδ,
deno ed εT, is de e mined as he di e ence be ween he DFT
p edic ion (Δ GDFT
HαCβNγOδ) and he expe imen al alue
ðΔ Gexp
HαCβNγOδÞas shown in Eq. 12:36,38–40,44,45,53
εT¼Δ GDFT
HαCβNγOδΔ Gexp
HαCβNγOδð12Þ
In addi ion, he o al e o is he di e ence be ween he
indi idual e o s o he p oduc s and eac an s o
Eq. 11:36,38–40,44,45,53
εT¼εHαCβNγOδα
2εH2g
ðÞ
βεCsðÞ γ
2εN2g
ðÞ
δ
2εO2g
ðÞ
ð13Þ
The DFT e o o N
2(g)
is calcula ed om he ammonia
syn hesis eac ion (1
2N2g
ðÞþ3
2H2g
ðÞ!NH3g
ðÞ
)38 and εO2g
ðÞ om
he wa e o ma ion eac ion (H2g
ðÞþ1
2O2g
ðÞ!H2Og
ðÞ
)35,79.
Assuming ha DFT p o ides an accu a e desc ip ion o he
ene ge ics o H
2(g)
and C
(s)
(i.e, εH2g
ðÞ εCsðÞ 0)30, combining
Eqs. 12 and 13, and eo ganizing, we find an exp ession o he
assessmen o he gas-phase e o o HαCβNγOδ, see Eq. 14.
εHαCβNγOδg
ðÞ ¼Δ GDFT
HαCβNγOδg
ðÞþγ
2εN2þδ
2εO2

Δ Gexp
HαCβNγOδ
ð14Þ
A de ailed example o he use o hese equa ions o u ea is
p esen ed in Supplemen a y No e 2. We no e ha he expe i-
men al s anda d ee ene gies o o ma ion and hea s o
o ma ion o he molecules unde s udy a e epo ed wi hin
chemical accu acy (4.18 kJ mol−1o 0.04 eV). In ac , he e o s
epo ed on he NIST websi e o he hea s o o ma ion o CO
2
,
CO, wa e , and u ea a e 0.13, 0.17, 0.040, and 1.2 kJ mol−1
( e s. 71,81), espec i ely, and he e o s a e smalle in he ATcT
da abase82. In addi ion, he F eeSol da abase commonly epo s
2.51 kJ mol−1as he unce ain y o he expe imen al hyd a ion
ee ene gies76. Hence, he expe imen al alues o in e es a e
known o a g ea e p ecision compa ed o he DFT esul s, which
usually in ol e e o s abo e 0.1 eV (~10 kJ mol−1).
We ema k ha e o s may also exis in he adso bed s a e.
Howe e , as GGA unc ionals accu a ely desc ibe he a omic
s uc u e, cohesi e ene gy, and bulk moduli o ansi ion me als
and hei low Mille -index su aces29,31, we expec hese e o s o
be smalle han hose o he gas phase. The e o assessmen
de ailed in his sec ion may be ex ended o adso ba es i accu a e
expe imen al adso p ion ene gies a e a ailable, bu hese a e
sca ce in he li e a u e83. We a e awa e o wo app oaches o
es ima e e o s in he adso bed s a e. Based on unce ain y
conside a ions, he fi s me hod links gas-phase e o s o hose o
he co esponding adso ba es and p o ides specific co ec ions
o a gi en species on a subs a e (e.g, *COOH on Cu(111))43.
Wi hou compa ing o expe imen s, he second me hod iden ifies
sys ema ic e o s o a gi en adso ba e on a subs a e by
compa ing he adso p ion ene gies using a a ie y o DFT se ups,
(i.e, *O on RuO
2
(110))84.
To close his sec ion, we ema k ha including o neglec ing
he he mal con ibu ions in Eq. 1may shi he alues o he gas-
phase e o s. These e ec s a e de ailed in Supplemen a y No e 4.
Supplemen a y Table 6 shows he di e ence o he e o s wi h
and wi hou he mal en halpic con ibu ions om 0 o 298.15 K.
Resul s
E o s in co-elec olysis eac ions. The expe imen al and DFT-
calcula ed ene gies o he s udied eac ions a e shown in Sup-
plemen a y Table 4 and Fig. 2. These alues we e ob ained using
he unco ec ed DFT ene gies in Supplemen a y Table 3 as
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explained in Supplemen a y No e 3. Fo each unc ional used, he
mean absolu e e o s (xc-MAEs) and maximum absolu e e o s
(xc-MAXs) wi h espec o expe imen s a e shown in Supple-
men a y Table 4. In addi ion, Supplemen a y Table 4 con ains he
mean and maximum absolu e e o s o each eac ion ( -MAE
and -MAX, espec i ely).
The -MAEs and -MAXs in Supplemen a y Table 4 indica e
ha , o he six co-elec olysis eac ions s udied he e, pu e GGA-
based DFT calcula ions yield significan de ia ions wi h espec o
expe imen s, wi h -MAEs spanning om 0.47 o 1.47 eV, and
-MAX alues in he ange o 1.00 o 2.64 eV. No e in passing ha
he eac ion ene gies, -MAE and -MAX end o inc ease as he
eac an s a e mo e oxidized, as shown in Supplemen a y Fig. 2.
Mo eo e , he la ge mean and maximum absolu e e o s o each
unc ional in Supplemen a y Table 4 (xc-MAE and xc-MAX),
indica e ha none o he s udied unc ionals co ec ly desc ibes
all he co-elec olysis eac ions, ega dless o he unc ional ung
on Jacob’s ladde . In ac , o GGA unc ionals he a e age xc-
MAE and xc-MAX a e 0.97 and 2.02 eV; o me a-GGA
unc ionals hey a e 0.88 and 1.80 eV; and o he hyb id
unc ionals hey a e 0.49 and 0.84 eV, espec i ely. Hence, he e is
an e o dec ease upon climbing Jacob’s ladde , bu e en hyb id
unc ionals display conside able de ia ions.
The panels in Fig. 2aid in isualizing he la ge disc epancies
be ween heo y and expe imen s. In all he eac ions, mos o he
ba s lie a om he expe imen al alue (dashed line in Fig. 2).
Consis en wi h p e ious wo ks, PBE and PW91 display
compa able e o s o all eac ions85,86. In e es ingly, BEEF-
dW, RPBE, and TPSS display simila eac ion ene gies in all
panels o Fig. 2. In con as , SCAN and TPSS p esen
la ge di e ences al hough bo h a e me a-GGA unc ionals. Some
simila i ies a e obse ed in panels e and o he hyb ids, whe e
PBE0 pe o ms be e han B3LYP, bu significan di e ences
a e obse ed as he N-con aining eac an becomes less oxidized
Fig. 2 E o s in co-elec olysis eac ions. F ee ene gies (Δ G) o six co-elec olysis eac ions calcula ed wi h se e al exchange-co ela ion unc ionals: u ea
p oduc ion om he co-elec olysis o (a)N2g
ðÞand CO g
ðÞ
,(b)N2g
ðÞand CO2g
ðÞ
,(c)NO g
ðÞand CO g
ðÞ
,(d)NO g
ðÞand CO2g
ðÞ
,(e)NO
3ðaqÞand +CO g
ðÞ
,( )NO
3ðaqÞ
and CO2gðÞ
. In all panels, he espec i e expe imen al ene gy is shown as a dashed black line. The DFT ene gies o he molecules do no include any gas-
phase co ec ions, see he alues o hese co ec ions in Table 1.
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(panels a–d) and he PBE0 accu acy wo sens wi h espec o
B3LYP. As expec ed, he wo hyb id unc ionals p o ide mo e
accu a e alues han GGA and me a-GGA unc ionals. O e all,
calcula ions using B3LYP lead o esul s wi h he smalles e o s,
p esumably as a consequence o i s pa ame e iza ion based on
he mochemical da a such as a omiza ion ene gies and ioniza ion
po en ials. Howe e , o some eac ions, he e o s o he hyb id
unc ionals su pass he accu acy necessa y o allow o accu a e
p edic ions (<0:1eV): B3LYP yields e o s o −0.45, −0.31, and
0.36 eV o eac ions a, b, and , and PBE0 yields e o s o −1.23,
−1.00, −1.04, −0.81, and −0.28 eV o he eac ions in Fig. 2a–e.
E o s in he molecules. Table 1summa izes he gas-phase e o s
o he species in ol ed in he co-elec olysis eac ions o all he
unc ionals unde analysis using Eq. 14. No e ha NO
3aq
ðÞ
and
CO(NH
2
)
2(aq)
display he same e o s as hei espec i e gaseous
e e ences, HNO
3(g)
and CO(NH
2
)
2(g)
. This is because he ene -
gies o hese species we e calcula ed semiempi ically om DFT
ene gies o he gases and expe imen al alues (see sec ion 2.2).
AsshowninTable1, he DFT e o s o mos species unde s udy
a e significan ega dless o he unc ional ung on Jacob’sladde ,
and each in some cases alues mo e nega i e han −1 eV. This is he
case o HNO
3(g)
using RPBE (−1.04 eV), BEEF- dW (−1.26 eV),
and TPSS (−1.19 eV). The hyb id unc ionals B3LYP and PBE0
yield he lowes gas-phase e o s (MAEs o 0.17 and 0.24 eV in
Table 1) bu s ill exhibi la ge MAX figu es (0.28 and 0.71 eV). In
ac , PBE0 displays he la ges e o o N
2(g)
(0.71 eV), which pa ly
explains he subs an ial de ia ions o his unc ional in Fig. 2a, b.
The alues in Table 1can be employed o apidly es ima e he
e o cancella ion o a unc ional when modeling a chemical
eac ion. E o cancella ion may lead o accu a e p edic ions o
eac ion ene gies. Fo ins ance, in Fig. 2 we obse e o PBE0 an
almos comple e e o cancella ion because he e o s o eac an s
and p oduc s di e only by 0.05 eV: εu ea 2εNO
3aq
ðÞ
εCO2¼
0:11eV 20:12eVðÞ0:18eVðÞ0:05eV. Fu he mo e,
he e o s in N
2(g)
and O
2(g)
a e la ge o all unc ionals, spanning
om -0.16 o 0.71 eV o N
2(g),
and om -0.80 o -0.17 eV o
O
2(g)
. Fo u ea, significan e o s a e ound o all sc u inized
unc ionals wi h PBE0 p esen ing he lowes alue (-0.11 eV) and,
su p isingly, BEEF- dW displaying he la ges (-0.40 eV). I is
wo h no ing ha his ange o e o s o u ea is na ow
compa ed o he o he molecules in Table 1and ha all alues a e
nega i e. Hence, a en a i e es ima e o he DFT-based e o o
he o ma ion ene gy o u ea is -0.25 ± 0.10 eV, which co e-
sponds o he a e age and s anda d de ia ion o he co espond-
ing alues in Table 1.
Figu e 3p o ides a g aphical ep esen a ion o he alues in
Table 1. The anges o he e o s a e la ge han 0.20 eV in all
cases. Fo mos molecules, we obse e ha RPBE, BEEF- dW,
and TPSS exhibi he la ges nega i e e o s. In con as , PBE0
always yields he la ges posi i e de ia ions o N
2(g)
and CO
(g)
bu also he lowes e o s o O
2(g)
, u ea and HNO
3(g)
/NO-
3(aq)
.
Finally, while ex en o he e o fluc ua ion o PBE, PW91, and
SCAN o e he whole se o molecules is a he simila , B3LYP
shows he smalles and ela i ely s able se o e o s, all ela i ely
close o ze o. Howe e , as men ioned be o e, ou gene al
conclusion is ha none o he unc ionals in Table 1yields
sa is ac o y ene gies o he co-elec olysis eac ions unde
analysis.
Impo an ly, i expe imen al esul s a e no a ailable o calcula e
he gas-phase e o s using Eq. 14, one could ely on highly accu a e
quan um chemical me hods based on wa e- unc ion heo y such as
CCSD(T) using la ge basis se s. Al e na i ely, one can use
co ec ion app oaches based on s uc u al ea u es, such as he
numbe o oxygen a oms in he molecule39, he p esence o ce ain
unc ional g oups38, o he occu ence o specific chemical
s uc u es wi hin he compound, such as CO-, OCO-, ONO-,
NNO-, o -NOH backbones41,43,53. Fo ins ance, om a unc ional
g oup pe spec i e, CO(NH
2
)
2(g)
can be conside ed an amide wi h
an amino g oup bound o i . The espec i e PBE e o s o he
amino and amide g oups a e 0.00 and −0.17 eV38, yielding a o al
e o o −0.17 eV, which ag ees well wi h ha in Table 1
(−0.20 eV). This app oxima ion is somewha sa is ac o y o he
o he GGAs s udied (PW91: −0.15 eV, RPBE: −0.16 eV, BEEF-
dW: −0.47 eV38 s −0.20, −0.22 and −0.40 eV in his s udy).
Howe e , we no e ha εCOðNH2Þ2g
ðÞ εamide g
ðÞþ1
2εamine g
ðÞyields a
mo e accu a e app oxima ion (PBE: −0.17 eV, PW91: −0.15 eV,
RPBE: −0.18 eV, BEEF- dW: −0.42 eV)38. This is because o he
double coun ing o one o he C-N bonds: he amide co ec ion was
designed o accoun o he e o in he bond be ween an sp3Cand
-CO(NH
2
), and he amine co ec ion o he bond be ween an sp3
C and -NH
2
.
Implica ions o elec oca alysis. To illus a e he e ec o gas-
phase e o s on elec oca alysis, he DFT-unco ec ed alues in
Supplemen a y Table 4 and he e o s in Table 1we e used o
build ee-ene gy diag ams o he he modynamically ideal ca a-
lys o each co-elec olysis eac ion, see Fig. 4and Supplemen a y
Figu es 3-7 in he Supplemen a y No e 5. The concep o an ideal
ca alys is commonly employed in elec oca alysis o ou line he
mos e ficien con e sion ha con o ms o he fi s and second
laws o he modynamics87–89, hus se ing as a benchma k o
eal ca alys s. In an ideal ca alys , he eac ion ene gy o all
elec ochemical s eps is he same and co esponds o he o e all
Table 1 Indi idual gas-phase e o s.
Species PBE PW91 RPBE BEEF- dW TPSS SCAN B3LYP PBE0
N
2(g)
0.49 0.52 0.11 −0.16 0.00 0.47 0.28 0.71
O
2(g)
−0.42 −0.27 −0.70 −0.78 −0.80 −0.40 −0.28 −0.17
NO
(g)
0.04 0.15 −0.29 −0.47 −0.41 0.05 0.00 0.26
CO
(g)
0.30 0.30 −0.04 −0.13 −0.05 0.30 −0.03 0.40
CO
2(g)
−0.14 −0.11 −0.42 −0.52 −0.47 −0.03 −0.18 0.18
HNO
3(g)
−0.88 −0.79 −1.04 −1.26 −1.19 −0.51 −0.19 −0.12
NO
3aqðÞ
−0.88 −0.79 −1.04 −1.26 −1.19 −0.51 −0.19 −0.12
CO(NH
2
)
2(g)
−0.20 −0.20 −0.22 −0.40 −0.36 −0.32 −0.20 −0.11
CO(NH
2
)
2(aq)
−0.20 −0.20 −0.22 −0.40 −0.36 −0.32 −0.20 −0.11
MAE 0.39 0.37 0.45 0.60 0.54 0.32 0.17 0.24
MAX 0.88 0.79 1.04 1.26 1.19 0.52 0.28 0.71
DFT e o s in he o ma ion ene gy o he species in ol ed in he co-elec olysis eac ions. The MAEs and MAXs a e epo ed o each unc ional. All alues a e in eV.
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eac ion ene gy di ided by he numbe o elec ons ans e ed
(i.e, ΔGi¼Δ G=n). Nume ically, he magni ude o he ideal
elec ochemical s eps is iden ical o he equilib ium po en ial.
Hence, he chemical iden i y o he in e media es need no be
known o build he ideal ee-ene gy diag am. In con as , eal
ca alys s usually display asymme ic ee-ene gy diag ams and
equi e knowledge o he chemical iden i y and ene ge ics o he
in e media es. Fo he co- educ ion o NO
3aq
ðÞand CO
2(g)
in
Fig. 4, p e ious wo ks p oposed he ollowing mechanism:20,90,91
*NO
3
educ ion o *NO
2
, hen coupling wi h *CO
2
o o m
*CO
2
NO
2
. Subsequen p o ona ion o *CO
2
NO
2
yields
*CO
2
NH
2
, which in u n educes o *COOHNH
2
in he
po en ial-de e mining s ep92.*COOHNH
2
educes o *CONH
2
,
which couples o *NO
2
, p oducing *CONO
2
NH
2
. Finally,
*CONO
2
NH
2
is hyd ogena ed wice o gi e u ea.
Figu e 4shows h ee ene gy diag ams o he NO
3aq
ðÞand
CO
2(g)
co-elec olysis eac ion o u ea on he ideal ca alys (Eq. 7).
Panel a was buil wi h he unco ec ed DFT alues, i.e, wi h no
gas-phase co ec ions. In panel b, he e o o CO
2(g)
( he
C-con aining eac an ) was accoun ed o , lea ing he DFT
ene gies o bo h NO
3aq
ðÞ
and CO(NH
2
)
2(aq)
unco ec ed. In panel
c, he DFT-ene gies o CO
2(g)
and NO
3aq
ðÞ
we e co ec ed, while
he ene gy o CO(NH
2
)
2(aq)
emained unco ec ed, excep o he
black line, in which DFT and expe imen s coincide.
Figu e 4a shows ha all unc ionals di e ge om he ee-
ene gy p ofile o he ideal ca alys s (calcula ed on he basis o
expe imen al alues) as mo e elec ochemical s eps a e consid-
e ed, eaching a maximum de ia ion a he las s ep o he
ca aly ic pa hway. This maximum de ia ion co esponds o he
di e ence be ween he DFT eac ion ene gy and i s expe imen al
coun e pa . The elescopic e ec in Fig. 4a also occu s in panels b
and c, bu wi h nuances in oduced by he pa ial co ec ions. We
no e he o al e o can also be ob ained by assessing he
di e ence be ween he e o s o eac an s and p oduc s. Fo
example, based on he alues in Table 1, o Eq. 7and BEEF- dW
he esul ing e o is 2 εNO
3aq
ðÞ
þεCO2ðgÞεCOðNH2Þ2aq
ðÞ
¼
21:26 0:52 þ0:40 ¼2:64eV. In Fig. 4c he depa u es
o he p edic ed alues om calcula ions using he a ious
unc ionals wi h espec o hose om expe imen s s em om he
e o in CO(NH
2
)
2(aq)
, as i is he only emaining unco ec ed
species. In o he wo ds, he di e ence be ween DFT-based and
expe imen al alues o he las eac ion s ep o Fig. 4cis
εCOðNH2Þ2aq
ðÞ
. Mo eo e , we no e ha a e co ec ing he e o o
u ea using he espec i e alues in Table 1, all he gas-phase
e o s a e accoun ed o and he “DFT +co ec ions”diag am
becomes ha o he ideal ca alys , which is shown in black in all
h ee panels o Fig. 4.
Analogous diag ams o he o he eac ions unde s udy a e
gi en in Supplemen a y Figs. 3–7. We emphasize ha he
conclusions d awn om Fig. 4also hold o hese Supplemen a y
figu es. Since εCOðNH2Þ2aq
ðÞ
< 0 o all he unc ionals assessed (see
Table 1), he DFT-calcula ed lines a e always below he
expe imen al alues in he bo om panels o Fig. 4and
Supplemen a y Figs. 3–7.
Conclusions
Simul aneous elec oca aly ic educ ion o ni ogen and ca bon
pollu an s o p oduce u ea is an appealing al e na i e o help
emedia e he colossal imbalances o he ni ogen and ca bon
cycles. He ein, we showed how expe imen al da a can be coupled
wi h DFT-calcula ed gas-phase ene gies o model six co-
educ ion eac ions o ca bon and ni ogen oxides o p oduce
hyd a ed u ea. The a e age MAE/MAX alues e sus expe imen s
a e 0.97 eV/2.02 eV o GGA unc ionals (PBE, PW91, RPBE, and
BEEF- dW), while hose o me a-GGAs (TPSS and SCAN) a e
0.88 eV/1.80 eV, and hose o he hyb ids (PBE0, B3LYP) a e
0.49 eV/0.84 eV. Hence, he use o DFT o model hese eac ions
en ails la ge e o s, e en o hyb id unc ionals, indica ing ha
accu a e p edic ions a e only a ained once he DFT e o s o all
he molecules unde s udy a e co ec ed.
Mo eo e , he DFT e o in he o ma ion ene gy o u ea spans
a ela i ely na ow ange o alues, such ha -0.25 ± 0.10 eV is a
easonable e o es ima e o DFT calcula ions, al hough he use
o specific co ec ions is always mo e ad isable han an a e age.
The e ec o hese nume ical de ia ions in ca alysis was illu-
s a ed o he ee-ene gy diag ams o he ideal elec oca alys
ex ac ed om expe imen al da a o a ious co-elec olysis eac-
ions. The depa u es o DFT p edic ions om he expe imen al
ends a e subs an ial o all unc ionals. Howe e , we showed ha
he e o s can easily be co ec ed in a semiempi ical manne .
All his hin s owa d he need o an assessmen o gas-phase
e o s a he ea ly s ages o compu a ional elec oca alysis
esea ch o a oid po en ially inaccu a e and misleading conclu-
Fig. 3 Indi idual e o s o he species. DFT e o s (εi) o he compounds in ol ed in he co-elec olysis eac ions. Ci cles (●) a e o GGA e o s, iangles
(▼) a e o me a-GGA e o s, and c osses (×) a e o hyb id e o s. The e ical ba s co espond o he anges spanned by he unc ionals. All alues a e in eV.
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sions, ega dless o he chosen ung on Jacob’s ladde o densi y
unc ional app oxima ions.
Da a a ailabili y
The au ho s decla e ha da a suppo ing he findings o his s udy a e a ailable wi hin
he pape and i s supplemen al ma e ial file. Addi ional da a a e a ailable om he
co esponding au ho upon easonable eques .
Recei ed: 27 Ma ch 2023; Accep ed: 22 Augus 2023;
Re e ences
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Fig. 4 F ee ene gy diag ams o he co-elec olysis o NO
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3aqðÞ
and CO(NH
2
)
2(aq)
, and he co ec ed ene gy o CO
2(g)
,(c) he
co ec ed ene gies o NO
3aqðÞ
and CO
2(g)
, and he unco ec ed DFT ene gy o CO(NH
2
)
2(aq)
. Ideal alues om expe imen s a e in black. The y-axis scale is
di ided in o mul iples o he expe imen al equilib ium po en ial.
ARTICLE COMMUNICATIONS CHEMISTRY | h ps://doi.o g/10.1038/s42004-023-00990-7
8COMMUNICATIONS CHEMISTRY | (2023) 6:196 | h ps://doi.o g/10.1038/s42004-023-00990-7 | www.na u e.com/commschem
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