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IV.D.1. (XII.C.1.)

Geometry Comparison

Na2 (Sodium diatomic)


distance is atom 1 (Na) to atom 2 (Na)

Experimental bond length is 3.079  Å

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Calculated bond length in Å
Methods with predefined basis sets
semi-empirical PM6 4.750
composite G2 3.189
G3 3.189
G3B3 3.038
G4 3.132
CBS-Q 3.189

Calculated bond length in Å
Methods with standard basis sets
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ
hartree fock HF 2.359 3.228 2.465 3.190 3.189 3.189 3.191 3.194 3.194 3.189 3.194 3.194 3.213 3.203   3.191 3.198 3.194 3.194 3.195 3.195
density functional LSDA 2.374 3.051 2.177 2.980 2.970 2.970 2.969 2.983 2.983 2.899 2.967 2.967 3.015 2.978 2.972 2.967 2.970 2.967 2.964 2.991 2.983
SVWN 2.374 3.051 2.177 2.980 2.970 2.970 2.969 2.983 2.983 2.899 2.967 2.967 3.015 2.978 2.971 2.967 2.970 2.967 2.964 2.991 2.983
BLYP 2.406 3.078 2.249 3.054 3.048 3.048 3.047 3.064 3.065 3.019 3.047 3.047 3.086 3.052 3.050 3.048 3.047 3.047 3.044 3.066 3.064
B1B95 2.379 3.120 2.309 3.057 3.056 3.056 3.056 3.070 3.070 3.033 3.062 3.062 3.097 3.070 3.068 3.061 3.068 3.066 3.056 3.074 3.071
B3LYP 2.388 3.072 2.269 3.043 3.038 3.038 3.038 3.052   3.014 3.039 3.039 3.073 3.044   3.040 3.041 3.038 3.037 3.053 3.051
B3LYPultrafine 2.388 3.072 2.270 3.043 3.038 3.038 3.038 3.051 3.051 3.015 3.039 3.039 3.071 3.044 3.043 3.040 3.041 3.040 3.037 3.052 3.050
B3PW91   3.163 2.323 3.099 3.098 3.098 3.097 3.108   3.071 3.099 3.099 3.131 3.108 3.105 3.099 3.107 3.103 3.094 3.112 3.109
mPW1PW91   3.152   3.100 3.097 3.097 3.097 3.108 3.109 3.075 3.101 3.101 3.132 3.109   3.100 3.107 3.104 3.096 3.112 3.109
M06-2X 2.358 3.095 2.303 2.953 2.948 2.948 2.948 2.952 2.952 2.926 2.944 2.944 2.988 2.964 2.951 2.943 2.960 2.948 2.943 2.964 2.956
PBEPBE   3.116     3.076 3.076 3.076 3.091 3.091 3.043 3.078 3.077 3.112 3.086 3.084 3.079   3.080 3.074 3.092 3.090
PBEPBEultrafine 2.400 3.115 2.275 3.078 3.075 3.075 3.074 3.089 3.089 3.044 3.076 3.076 3.112 3.084 3.081 3.078 3.080 3.078 3.074 3.090 3.089
PBE1PBE 2.381 3.128 2.315 3.086 3.084 3.084 3.084 3.096 3.096 3.062 3.087 3.087 3.116 3.093 3.090 3.088 3.092 3.089 3.085 3.097 3.095
HSEh1PBE 2.381 3.129 2.310 3.091 3.089 3.089 3.089 3.100 3.100 3.066 3.091 3.091 3.121 3.099 3.095 3.092 3.097 3.094 3.090 3.101 3.099
TPSSh         3.172   3.172               3.173            
Moller Plesset perturbation MP2   3.232 2.440 3.187 3.169 3.169 3.171 3.168 3.168 3.172 3.177 3.177 3.226 3.205   3.173 3.200 3.177 3.177 3.189 3.178
MP2=FULL 2.360 3.231 3.185 3.184 3.153 3.152 3.152 3.119   2.996 3.054 3.054 3.204 3.209 3.081 2.965 3.188 3.064 2.237 3.151 3.083
MP3 15.787 3.227 3.183 3.178 3.159 3.159 3.161 3.159 3.159 3.163 3.174 3.174 3.226 3.198 3.171 3.172 3.195 3.172 3.172 3.182 3.172
MP3=FULL         3.170   3.170                            
MP4   3.226 3.182 3.176 3.159 3.159 3.160 3.160 3.159 3.165 3.177 3.177 3.226 3.199 3.175 3.175 3.197 3.175 3.175 3.182 3.175
MP4=FULL 6.007 3.225 3.170 3.174 3.142 3.142 3.143 3.109 3.109 2.970 3.053 3.053 3.208 3.204 3.071 2.958 3.186 3.053 1.954 3.152 3.088
B2PLYP         3.080                                
Configuration interaction CID 2.379 3.225 3.181 3.176 3.158 3.159 3.160 3.159 3.158 3.167 3.180 3.180 3.226 3.201 3.177 3.177 3.200 3.177 3.177 3.184 3.178
CISD 2.381   3.190 3.189 3.164   3.166 3.165 3.165 3.168 3.181 3.181 3.242 3.205 3.178 3.177 3.203 3.178 3.177 3.189 3.178
Quadratic configuration interaction QCISD 2.381 3.238 3.190 3.189 3.164   3.166 3.165 3.164 3.168 3.181 3.181 3.242 3.205 3.178 3.177 3.203 3.178 3.177 3.189 3.178
QCISD(T) 2.381 3.239 3.190 3.189 3.164 3.164 3.166 3.165 3.165 3.168 3.181 3.181 3.242 3.205 3.178 3.177 3.203 3.178 3.177 3.187 3.178
Coupled Cluster CCD 2.379 3.225 3.181 3.176 3.158 3.159 3.160 3.159 3.158 3.167 3.179 3.179 3.226 3.201 3.177 3.177 3.200 3.177 3.177 3.184 3.178
CCSD 2.381 3.239 3.190 3.189 3.164 3.164 3.166 3.164 3.165 3.168 3.181 3.181 3.242 3.205 3.178 3.177 3.203 3.178 3.177 3.189 3.178
CCSD=FULL 2.366 3.238 3.181 3.188 3.149 3.149 3.150 3.123 3.123 2.981 3.070 3.070 3.229 3.211 3.078 2.965 3.193 3.060 2.234 3.162  
CCSD(T) 2.381 3.239 3.190 3.189 3.164 3.164 3.166 3.164 3.164 3.168 3.181 3.181 3.242 3.205 3.178 3.177 3.203 3.180 3.177 3.187 3.178
CCSD(T)=FULL 2.367 3.238 3.181 3.188 3.149 3.150 3.150 3.119 3.119 2.975 3.066 3.066 3.230 3.211 3.075 2.960 3.193 3.056 1.954 3.161 3.099

Calculated bond length in Å
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 3.404 3.418 3.204      
density functional LSDA 3.395 3.402 3.192 3.192 3.295 2.980
SVWN 3.395 3.402 3.192 3.192 3.295 2.980
BLYP 3.394 3.393 3.180 3.174 3.286 3.054
B1B95 3.382 3.387 3.174 3.170 3.277 3.057
B3LYP 3.377 3.380 3.168 3.164   3.043
B3LYPultrafine 3.377 3.380 3.168 3.164 3.272 3.043
B3PW91 3.369 3.378 3.171 3.170 3.266 3.099
mPW1PW91 3.374 3.385 3.175 3.175 3.272 3.100
M06-2X 3.387 3.401 3.191 3.191 3.288 2.953
PBEPBE 3.391 3.398 3.188 3.186 3.289 3.079
PBEPBEultrafine 3.391 3.398 3.188 3.186 3.289 3.078
PBE1PBE 3.380 3.391 3.181 3.182 3.279 3.086
HSEh1PBE 3.384 3.394 3.184 3.183 3.283 3.091
Moller Plesset perturbation MP2 3.438 3.404       3.187
MP2=FULL 3.438 3.404 3.213 3.185 3.314 3.184
MP3 3.452 3.396 3.212 3.175 3.310 3.178
MP4 3.463 3.398 3.213 3.175 3.311 3.176
MP4=FULL 3.463 3.398 3.213 3.175 3.311 3.174
Configuration interaction CID 3.484 3.400 3.214 3.175 3.318 3.176
CISD 3.503 3.413 3.230 3.182 3.333 3.189
Quadratic configuration interaction QCISD 3.503 3.413 3.230 3.182 3.333 3.189
QCISD(T) 3.503 3.413 3.230 3.182 3.333 3.189
Coupled Cluster CCD 3.484 3.400 3.214 3.175 3.318 3.176
CCSD 3.503 3.413 3.230 3.182 3.333 3.189
CCSD=FULL 3.503 3.413 3.230 3.182 3.333 3.188
CCSD(T) 3.503 3.413 3.230 3.182 3.333 3.189
CCSD(T)=FULL 3.503 3.413 3.230 3.182 3.333 3.188
Values that are outliers may reflect incorrect atom numbering for different levels of theory.
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