Models and strategies for metallic systems:
bulk and surfaces
Klaus Doll
University of Ulm
Institute of Electrochemistry
Albert-Einstein-Allee 47
D-89069 Ulm, Germany
ISAMS, Regensburg, July 2015
Motivation:
• explanation of experimental results
(experiments performed e.g. at a synchrotron)
• importance of topics such as catalysis, corrosion
• technical: test of local basis set for metallic systems
Outline:
• computational parameters
• structure optimisation with gradients
• bulk metals
• surfaces
• adsorption
1. Computational Parameters
• Method: usually density functional theory;
functionals:
PWGGA, PBE: most popular
LDA: overbinds
RHF, B3LYP: underbind
see e.g. M. Sgroi, C. Pisani, M. Busso, Thin solid films 400, 64(2001)
in general: Fock exchange gives vanishing density of states at Fermi energy
see Ashcroft & Mermin, Solid State Physics, chapter 17
• basis set: diffuse functions are necessary:
enlarge basis, reoptimize exponents
• ~k-points: typically (16×16×16) for bulk;
(16×16) for surface studies
• finite temperature scheme used:
keyword SMEAR, typical value 0.01 Eh or lower;
very low values for magnetic materials required; e.g. Ni: Curie temperature is
631 K =
ˆ 0.0020 Eh
1
E(T = 0) = 2 (E(T ) + F (T ))
(E0 in output)
makes numerical integration more stable
Convergence
• PROBLEM, especially for metals
• general rule: start from a simple problem
• if you have never done a calculation with CRYSTAL:
start with an insulator, e.g. NaCl, reproduce data from literature
• metals: 1. step: bulk
2. step: thin surface
3. step: thick surface
4. step: adsorbate + surface
• convergence tools:
- always use FMIXING, often very large mixing required (> 90%)
- usually no level shifting
- speedup possible with keywords ANDERSON, BROYDEN
(avoid level shift together with these keywords!)
• verify solution!!!
check: Mulliken population, binding energy, surface energy ...,
compare schemes:
try FMIXING only (safest, but slow), try FMIXING+ANDERSON ...
2. Structure optimisation with gradients
Gradients with respect to nuclear positions:
K. Doll, V. R. Saunders and N. M. Harrison, Int. J. Quant. Chem. 82, 1 (2001)
K. Doll, Comp. Phys. Comm. 137, 74 (2001)
Gradient with respect to the cell parameter:
3 D periodic systems: K. Doll, R. Dovesi, R. Orlando, Theo. Chem. Acc. 112, 394 (2004)
1 D, 2D periodic systems: K. Doll, R. Dovesi, R. Orlando, Theor. Chem. Acc. 115, 354 (2006)
Input for a full optimisation
minimum input:
OPTGEOM
ENDOPT
default: full geometry optimisation (atom positions, unit cell)
for 3 D periodic systems, the stress tensor is printed in output file e.g. input.out (first
geometry) and SCFOUT.LOG (following geometries)
σlm
3 ∂E
X
1 ∂E
=
aim
=
V ∂lm i=1 ∂ail
in the case of hydrostatic pressure, with a pressure p:

σ=




−p 0 0
0 −p 0
0 0 −p





⇒ pressure p available as an analytical derivative, and also the enthalpy H = E + pV
K. Doll, Mol. Phys. 108, 223-227 (2010)
optimisation with external hydrostatic pressure: keyword EXTPRESS
alternatively CVOLOPT to constrain the volume
(1)
Gradient for metals
Question: is there an extra term for metals, due to the shape of the Fermi
surface, compared to the case of insulators ?
Answer: • at zero temperature, there is no extra term
• at finite temperature (keyword SMEAR), the gradient is
consistent with the free energy
M. Weinert and J. W. Davenport, Phys. Rev. B 45, 13709 (1992)
R. M. Wentzcovitch, J. L. Martins, and P. B. Allen, Phys. Rev. B 45, 11372 (1992)
Test: compare numerical and analytical gradients
Example 1: Cu bulk, LDA (at a = 3.4 Å)
smearing
− ∂E
∂a
temperature (Eh ) (numerical,
0.001
0.0315
0.01
0.0310
0.03
0.0212
0.05
0.0098
− ∂F
∂a
Eh
)
(numerical,
a0
0.0315
0.0319
0.0390
0.0540
− ∂F
∂a
Eh
)
(analytical,
a0
0.0317
0.0320
0.0393
0.0542
Example 2: Cl/Cu(111)
smearing temperature:
0.001 Eh
K. Doll, Chem. Phys. Lett. 535, 187 (2012)
Eh
a0 )
2. Bulk metals
Basis set reoptimization is recommended:
• start from an existing basis set
e.g. Cu: M. D. Towler, R. Dovesi and V.R. Saunders Phys. Rev. B 52, 10150 (1995)
• reoptimize diffuse exponents
(e.g. exponents with value smaller than 1)
keep inner exponents fixed
• reoptimization means: determination of exponent with lowest energy of
reference system (here: copper bulk)
Reoptimization: How does it work?
e.g. copper outermost exponents were:
sp : 0.559 and d : 0.430
good for Cu2+, e.g. KCuF3
1)
2)
3)
4)
add one sp
reoptimize
reoptimize
reoptimize
shell, start with e.g. sp 0.6, 0.2 and d : 0.430 (guess)
tight sp, keep others fixed
diffuse sp, keep others fixed
d, keep others fixed
is energy converged? - if not return to step 2
typically: 2-3 iterations of this type necessary
Result: sp 0.596, 0.150 d 0.392 (PWGGA level)
metals: outermost diffuse sp exponent usually in the range 0.1 ... 0.2
Copper bulk: input file
Copper Metal
CRYSTAL
000
225
3.63
1
29 0. 0. 0.
END
29 8
0 0 8 2.0 1.0
398000.0
56670.0
12010.0
3139.0
947.2
327.68
128.39
53.63
0 1 6 8.0 1.0
1022.0
← space group
← lattice constant
← copper
← basis set .....
0.000227
0.001929
0.01114
0.05013
0.17031
0.3693
0.4030
0.1437
-0.00487 0.00850
238.9 -0.0674 0.06063
80.00 -0.1242 0.2118
31.86 0.2466 0.3907
13.33
0.672 0.3964
4.442
0.289
0.261
0 1 4 8.0 1.0
54.7 0.0119 -0.0288
23.26 -0.146 -0.0741
9.92 -0.750
0.182
4.013
1.031
1.280
0 1 1 1.0 1.0
1.582
1.0
1.0
0 1 1 0.0 1.0
0.596
1.0
1.0
0 1 1 0.0 1.0
0.150
1.0
1.0
0 3 4 10.0 1.0
48.54
0.031
13.55
0.162
4.52
0.378
1.47
0.459
0 3 1 0.0 1.0
0.392
1.0
99 0
END
← reoptimized exponent
← reoptimized/new exponent
← reoptimized exponent
← ..... end of basis set input
DFT
EXCHANGE
PWGGA
CORRELAT
PWGGA
END
SHRINK
16 32
MAXCYCLE
60
FMIXING
70
NOSHIFT
SMEAR
0.01
PPAN
END
← PW-functional
← ~k-point sampling
← enable more SCF cycles
← convergence tool
← no level shifting (0.6 hartree level shift default in CRYSTAL14)
← finite temperature scheme
← Mulliken population
use keyword FIXINDEX when comparing calculations at various lattice constants (smooth
potential curve)
Band structure calculation (properties-part)
BAND
Copper band structure
5 8 500 10 15 1 0
0 0 0 4 0 4 G-X
4 0 4 4 2 6 X-W
4 2 6 4 4 4 W-L
4 4 4 0 0 0 L-G
0 0 0 4 8 4 G-K-X’
END
visualise with: xmgrace -nxy BAND.DAT
5:
8:
500:
10 15:
1 0:
5 lines in Brillouin zone
ˆ ( 48 0 48 )
divisor, e.g. X is ( 12 0 21 ) but is expressed as (4 0 4 ) =
number of points computed along path
first, last band to be plotted:
Cu, 1s, 2s, 2p, 3s, 3p: 9 bands, flat, core-like
Cu 4s, 3d : 6 bands, the interesting ones
output options
note the different paths G-X and G-K-X’ ; X = ( 84 0 84 ) and X’=( 48
lattice vector: ( 48 88 48 ) = (0 1 0) + ( 48 0 48 )
8 4
8 8)
differ by a reciprocal
Brillouin zones: see e.g. :
C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry
in Solids (Clarendon Press, Oxford, 1972)
W. Setyawan, S. Curtarolo, Comp. Mat. Sci. 49, 299 (2010)
incorrect Brillouin zone is a frequent source of error!
Cohesive properties:
a [Å] Ecoh[Eh] B[GPa]
HF
3.95 0.018
69
LDA
3.53 0.182
195
PWGGA 3.63 0.143
155
exp.
3.604 0.129
142
K. Doll, N. M. Harrison, Chem. Phys. Lett. 317, 282 (2000)
3. Surfaces
model: finite number of layers
not repeated in the third dimension ⇒ no vacuum layers
difference in geometry input:
SLABCUT
111
13
← cut slab
← (111) surface
← 3 layers
use e.g. keyword ANDERSON to achieve convergence
nice exercise: try as many layers as possible
Compute surface energy:
Two ways of calculating surface energies:
[1] Esurf ace =
[2] Esurf ace =
1
2 (Eslab (n) − nEbulk )
1
2 Eslab (n) − [Eslab (n)
Cu(111): computed 2.01 J/m2 (PW);
exp.: 1.83 J/m2
− Eslab(n −
n
m)] m
4. Adsorption on metallic surfaces
Cl/Cu(111):
Coverage: one third of a monolayer
exp.: structure is
√
3×
√
3 R30◦ (LEED):
P. J. Goddard and R. M. Lambert,
Surf. Science 67, 180 (1977)
fcc hollow as adsorption site (SEXAFS):
M. D. Crapper, C. E. Riley, P. J. J. Sweeney,
C. F. McConville, and D. P. Woodruff,
Europhys. Lett. 2, 857 (1986)
Input
Chlorine on copper
CRYSTAL
000
225
← space group
3.63
← lattice constant
1
29 0. 0. 0.
← copper
SLAB
← 3 layers, (111) surface
111
13
SUPERCEL
← supercell
21
12
ATOMINSE
← add chlorine adsorbate, hcp site
1
17 0.0 0.0 3.99
ATOMDISP
3
1 0.0 0.0 -0.04
← relaxation of top Cu layer
2 0.0 0.0 -0.04
← relaxation of top Cu layer
3 0.0 0.0 -0.04
← relaxation of top Cu layer
END
17 6
0 0 8 2. 1.
135320.
19440.
4130.
1074.
323.4
111.1
43.4
18.18
0 1 6 8. 1.
324.8
73.00
23.71
9.138
3.930
1.329
0 1 3 7. 1.
4.755
1.756
0.785
0 1 1 0. 1.
0.294
0 1 1 0. 1.
0.090
0 3 1 0. 1.
0.50
0.000225
0.00191
0.01110
0.04989
0.1703
0.3683
0.4036
0.1459
← Cl basis set: on the web, modified:
enlarged (d-exponent)
slightly different diffuse exponents
-0.00763 0.00820
-0.0829
0.0605
-0.1046
0.2115
0.2540
0.3765
0.695
0.3967
0.399
0.186
-0.3740
-0.4754
1.3400
-0.0340
0.1617
0.9250
1.
1.
1.
1.
1.
29 8
0 0 8 2.0 1.0
398000.0 0.000227
56670.0 0.001929
12010.0
0.01114
3139.0
0.05013
947.2
0.17031
327.68
0.3693
128.39
0.4030
53.63
0.1437
0 1 6 8.0 1.0
1022.0 -0.00487 0.00850
238.9
-0.0674 0.06063
80.00
-0.1242
0.2118
31.86
0.2466
0.3907
13.33
0.672
0.3964
4.442
0.289
0.261
0 1 4 8.0 1.0
54.7
0.0119 -0.0288
23.26
-0.146 -0.0741
9.92
-0.750
0.182
4.013
1.031
1.280
0 1 1 1.0 1.0
1.582
1.0
1.0
0 1 1 0.0 1.0
0.596
1.0
1.0
0 1 1 0.0 1.0
0.150
1.0
1.0
0 3 4 10.0 1.0
48.54
0.031
13.55
0.162
4.52
0.378
1.47
0.459
0 3 1 0.0 1.0
0.392
1.0
99 0
END
←
Cu basis set, on the web ....
DFT
EXCHANGE
PWGGA
CORRELAT
PWGGA
END
SHRINK
16 32
SCFDIR
MAXCYCLE
100
FMIXING
90
ANDERSON
NOSHIFT
SMEAR
0.01
PPAN
END
← PW91 functional
← convergence tools
Results of the optimization:
Site
dCl−Cu
Eadsorption
Cl coordination
number
fcc
2.40 Å
3.696 eV
hcp
2.41 Å
3.691 eV
bridge
2.33 Å
3.609 eV
top
2.17 Å
3.235 eV
exp.: fcc 2.39 ± 0.02 Å
∼ 2.6 eV
(SEXAFS) (therm. desorption)
Rules:
• higher coordination number ⇒ higher binding energy
• lower coordination number ⇒ shorter bond length
(only one “bond“ which is strong)
K. Doll, N. M. Harrison, Chem. Phys. Lett. 317, 282 (2000).
3
3
2
1
Cl/Ag(111)
Site
dCl−Ag
Eadsorption
fcc
2.62 Å
hcp
2.62 Å
bridge
2.54 Å
top
2.38 Å
exp.a,b: fcc 2.48 Å; 2.70 Å
3.039
3.027
2.959
2.573
∼ 2.4
eV
eV
eV
eV
eV
CRYSTAL: K. Doll, N. M. Harrison, Phys. Rev. B 63, 165410 (2001)
a
A. G. Shard and V. R. Dhanak, J. Phys. Chem. B 104, 2743 (2000)
b
G. M. Lamble, R. S. Brooks, S. Ferrer, D. A. King and D. Norman, Phys. Rev. B 34, 2975
(1986)
CRYSTAL results confirmed by VASP-calculation:
fcc
hcp
bridge
top
2.64
2.64
2.56
2.39
Å
Å
Å
Å
3.124
3.117
3.044
2.684
eV
eV
eV
eV
VASP: L. Jia, Y. Wang, and K. Fan, J. Phys. Chem. B 107, 3813 (2003)
Compute effective chlorine radius:
subtract radius of metal : rM e
√
= a/ 8
substrate
Cu
Ag
Ni
a
rCl
3.63 Å 1.12 Å
4.10 Å 1.17 Å
3.53 Å 1.09 Å
compare with data from Kittel’s book:
radius of Cl: 0.99 Å
radius of Cl−: 1.81 Å
consistent with Mulliken charge:
Cl carries always only small negative charge (∼ -0.1 ... -0.2 |e|)
Charge of chlorine
consider: Cl on Ag(111)
site
fcc
hcp
bridge
top
charge 3s level, relative to EF
-0.198
-0.563
-0.204
-0.562
-0.218
-0.555
-0.252
-0.532
note: Mulliken charge increases
⇒ 3s level gets destabilized
(nuclear charge less well screened because more electronic charge on chlorine)
Potassium as adsorbate
Cu(111)(2×2)-K: top site occupied!
S. Å. Lindgren, L. Walldén, J. Rundgren, P. Westrin and J. Neve, Phys. Rev. B 28, 6707
(1983).
Simulations prove:
Cu atom under potassium adsorbate is pushed into substrate
atoms 1,2,3 upwards, relative to clean surface
Substate rumpling crucial:
Site
dK−Cu nn
Eadsorption per Cl atom
with rumpling
(without rumpling)
fcc
3.11 Å
1.265 eV
(1.249)
hcp
3.11 Å
1.263 eV
(1.243)
bridge
3.04 Å
1.265 eV
(1.243)
top
2.83 Å
1.287 eV
(1.227)
exp.a: top (SEXAFS) 3.05 ± 0.02 Å
a
D. L. Adler, I. R. Collins, X. Liang, S. J. Murray, G. S. Leatherman, K.-D. Tsuei, E. E.
Chaban, S. Chandravarkar, R. McGrath, R. D. Diehl and P. H. Citrin, Phys. Rev. B 48,
17445 (1993)
energy gain by substrate rumpling:
∼ 0.02 eV for fcc, hcp, bridge, but 0.06 eV for top site!
K. Doll, Eur. Phys. J. B 22, 389 (2001).
K/Ag(111):
two coverages considered:
coverage
Mulliken charge on K
bond length [Å]
exp.a [Å]
h
i
h
binding energy K Eatom
K 3s, 3p levels (relative to EF )
3s
3p
(2 × 2)
0.25
√
√
( 3 × 3)R30◦
0.3333
0.24
3.20
3.27 ± 0.03
0.041
0.16
3.27
3.29± 0.02
0.042
-1.194
-0.600
-1.184
-0.590
a
K-K distance recuced
⇒ stronger repulsion
⇒ depolarisation
⇒ larger radius and bond length
⇒ core levels destabilized
G. S. Leatherman, R. D. Diehl, P. Kaukasoina and M. Lindroos, Phys. Rev. B 53, 10254
(1996)
K. Doll, Phys. Rev. B 66, 155421 (2002)
CO/Pt(111)
Photograph: Wikimedia Commons
Standard functionals give wrong site: fcc (PW91) versus top (experiment)
”The CO/Pt(111) puzzle”
P.J. Feibelman, B. Hammer, J. K. Nørskov, F. Wagner, M. Scheffler, R. Watwe, R. Dumesic,
J. Phys. Chem. 105, 4018 (2001)
Possible solution
when adsorbed:
1) C gives charge to Pt
2) Pt back donates charge:
more in the case of the hollow site, less in the case of the top site
Standard functionals favor charge transfer too strong (gaps too small), prefer
hollow site
Suggestions:
• B3LYP, Cluster+extrapolation
A. Gil, A. Clotet, J. M. Ricart, G. Kresse, M. Garcı́a-Hernández, N. Rösch, and Ph. Sautet,
Surf. Sci. 530, 71 (2003)
• LDA+U:
G. Kresse, A. Gil, and Ph. Sautet, Phys. Rev. B 68, 073401 (2003)
Periodic B3LYP calculation
Standard-functional (PW91) B3LYP
3 fold hollow site
bridge site
+0.06 eV
+0.02 eV
top site
+0.08 eV
-0.04 eV
CO charge:
∼ -0.05
∼ -0.35
B3LYP: describes band gaps and excitation energies better
CO/Pt(111): K. Doll, Surf. Sci. 573, 464 (2004)
CO/Cu(111): M. Neef and K. Doll, Surf. Sci. 600, 1085 (2006)
Work function
Work function: electrostatic potential at infinity, minus Fermi energy
But: Cu(111), input as early in the talk: Φ = 0.142 Eh
exp.: 0.183 Eh
strongly basis set dependent, e.g. when varying the outermost diffuse exponent!
other properties are much less basis set dependent!
solution: use basis functions in the vacuum (keyword GHOSTS)
1-2 ghost layers are sufficient:
without ghosts:
1 ghost layer on each side:
2 ghost layers on each side:
experiment:
0.142
0.189
0.190
0.183
Eh
Eh
Eh
Eh
K. Doll, Surf. Sci. 600, L321 (2006)
see also: P. J. Feibelman, Phys. Rev. B 51, 17867 (1995)
5. Summary
• geometry and energetics are in very good agreement with experiment and
plane-wave results
• typical properties:
total energy, geometry, Mulliken population (surprisingly reliable!),
core levels, charge+spin density maps, overlayer density of states
• basis sets must be carefully chosen, possibly readjusted
work function: use ghosts in the vacuum region above the surface
• B3LYP versus standard functional shows: HOMO and LUMO position
important for CO adsorption
• Gaussian type orbitals suitable for all types of structures, also metals,
all-electron calculations are possible
review: K. Doll, Ab initio calculations with a Gaussian basis set for metallic surfaces and the adsorption
thereon, in ”Quantum Chemical Calculations of Surfaces and Interfaces of Materials”, edited
by Vladimir Basiuk and Piero Ugliengo, American Scientific Publishers, 2009, p. 41-53
Basis sets
In the following, some of the basis sets used are given.
Note that they are calibrated for systems where the
atom is neutral. For systems where the atom is positively charged, it may be necessary to remove the
outermost diffuse exponents, or shift them to higher
values, possibly reoptimise.
Lithium
33
0 0 6 2. 1.
840.0 0.00264
217.5 0.00850
72.3 0.0335
19.66 0.1824
5.044 0.6379
1.5
1.0
0 1 1 1. 1.
0.50
1.0 1.0
0 1 1 0. 1.
0.10
1.0 1.0
K. Doll, N. M. Harrison, V. R. Saunders, J. Phys.: Condens. Matter 11, 5007-5019 (1999)
note: calibrated for Li metal - for a system where Li is positively charged, it may be
necessary to remove the outermost diffuse exponent, or shift it to a higher value, possibly
reoptimise.
Copper
29 8
0 0 8 2.0 1.0
398000.0
56670.0
12010.0
3139.0
947.2
327.68
128.39
53.63
0 1 6 8.0 1.0
1022.0
238.9
80.00
31.86
13.33
4.442
0 1 4 8.0 1.0
54.7
23.26
9.92
4.013
0 1 1 1.0 1.0
1.582
0 1 1 0.0 1.0
0.596
0 1 1 0.0 1.0
0.150
0 3 4 10.0 1.0
48.54
13.55
4.52
1.47
0 3 1 0.0 1.0
0.392
0.000227
0.001929
0.01114
0.05013
0.17031
0.3693
0.4030
0.1437
-0.00487
-0.0674
-0.1242
0.2466
0.672
0.289
0.00850
0.06063
0.2118
0.3907
0.3964
0.261
0.0119
-0.146
-0.750
1.031
-0.0288
-0.0741
0.182
1.280
1.0
1.0
1.0
1.0
1.0
1.0
0.031
0.162
0.378
0.459
1.0
K. Doll, N. M. Harrison, Chem. Phys. Lett. 317, 282 (2000)
note: calibrated for Cu metal - for a system where Cu is positively charged, it may be necessary to remove the outermost diffuse sp
exponent, or shift it to a higher value, possibly reoptimise.
Nickel
28 8
0 0 8 2.0 1.0
367916.0
52493.9
11175.8
2925.4
882.875
305.538
119.551
49.9247
0 1 6 8.0 1.0
924.525
223.044
74.4211
29.6211
12.4721
4.2461
0 1 4 8.0 1.0
56.6581
21.2063
8.4914
3.6152
0 1 1 2.0 1.0
1.5145
0 1 1 0.0 1.0
0.63
0 1 1 0.0 1.0
0.13
0 3 4 8.0 1.0
41.0800
11.4130
3.8561
1.3302
0 3 1 0.0 1.0
0.38
0.000227
0.001929
0.0111
0.05
0.1703
0.369
0.4035
0.1426
-0.0052
-0.0679
-0.1319
0.2576
0.6357
0.2838
0.0086
0.0609
0.2135
0.3944
0.3973
0.2586
0.0124
-0.2218
-0.8713
1.0285
-0.018
-0.08
0.2089
1.255
1.0
1.0
1.0
1.0
1.0
1.0
0.0405
0.2022
0.4338
0.4897
1.0
K. Doll, Surf. Sci. 544, 103-120 (2003)
note: calibrated for Ni metal - for a system where Ni is positively charged, it may be necessary to remove the outermost diffuse sp
exponent, or shift it to a higher value, possibly reoptimise.
Silver
247 9
INPUT
19. 0 2 2 2 2 0
13.130000
6.510000
11.740000
6.200000
10.210000
4.380000
14.220000
7.110000
0 0 3 2.0 1.0
9.08844
7.54073
2.79401
0 0 1 1.0 1.0
1.48016
0 0 1 0.0 1.0
0.63
0 0 1 0.0 1.0
0.11
0 2 2 6.0 1.0
4.45124
3.67526
0 2 2 0.0 1.0
1.29129
0.65258
0 2 1 0.0 1.0
0.23000
0 3 4 10.0 1.0
7.99473
2.78477
1.20974
0.50539
0 3 1 0.0 1.0
0.18
255.139365
36.866122
182.181869
30.357751
73.719261
12.502117
-33.689920
-5.531120
0
0
0
0
0
0
0
0
-1.964813
2.733219
0.199115
1.000000
1.000000
1.000000
-6.083378
6.416854
0.753974
0.273060
1.000000
-0.016388
0.281411
0.486326
0.386726
1.000000
K. Doll and N. M. Harrison, Phys. Rev. B 63, 165410 (2001)
based on the pseudopotential and basis set from: D. Andrae, U. Häussermann, M. Dolg, H. Stoll, and H. Preuss, Theor. Chim. Acta
77, 123 (1990)
note: calibrated for Ag metal - for a system where Ag is positively charged, it may be necessary to remove the outermost diffuse
exponents, or shift them to higher values, possibly reoptimise
Platinum
278 9
INPUT
18 1 3 3 3 0 0
3.309569
13.428651
6.714326
3.309569
10.365944
5.182972
3.309569
7.600479
3.800240
3.309569
0 0 3 2.0 1.0
16.5595630
13.8924400
5.8536080
0 0 1 0.0 1.0
1.2873200
0 0 1 0.0 1.0
0.59
0 1 1 0.0 1.0
0.11
0 2 2 6.0 1.0
7.9251750
7.3415380
0 2 2 0.0 1.0
1.9125150
1.0715450
0 2 1 0.0 1.0
0.4379170
0 3 4 10.0 1.0
3.9395310
3.5877770
1.2862310
0.5198140
0 3 1 0.0 1.0
0.167
24.314376
579.223861
29.669491
-24.314376
280.860774
26.745382
-24.314376
120.396444
15.810921
-24.314376
0
0
0
0
0
0
0
0
0
0
-0.8849447
1.5011228
-1.5529012
1.
1.
1.0
1.0
4.9530757
-5.8982100
0.3047425
0.7164894
1.0
-0.5826439
0.5922576
0.4736921
0.5765202
1.0
K. Doll, Surface Science 573, 464-473 (2004).
based on the pseudopotential and basis set from: D. Andrae, U. Häussermann, M. Dolg, H. Stoll, and H. Preuss, Theor. Chim. Acta
77, 123 (1990)
note: calibrated for Pt metal - for a system where Pt is positively charged, it may be necessary to remove the outermost diffuse
exponents, or shift them to higher values, possibly reoptimise