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

Geometry Comparison

Si2 (Silicon diatomic)


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

Experimental bond length is 2.246  Å

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Calculated bond length in Å
Methods with predefined basis sets
semi-empirical AM1 1.663
PM3 1.607
PM6 1.893
composite G2 2.052
G3 2.052
G3B3 2.068
G4 2.060
CBS-Q 2.052

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) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
hartree fock HF 2.114 2.123 2.041 2.136 2.052 2.052 2.052 2.051 2.051 2.057 2.138 2.080 2.071 2.059 2.053 2.074 2.060 2.053 2.219
ROHF 2.105 2.208 2.220 2.314 2.140 2.141 2.228 2.231 2.139 2.140 2.221   2.235 2.143   2.157 2.144    
density functional LSDA 2.183 2.036 2.036 2.102 2.051 2.051 2.051 2.043 2.043 2.044     2.063 2.045   2.063 2.045    
SVWN   2.097         2.074                        
BLYP 2.208 2.119 2.069 2.143 2.088 2.088 2.088 2.082 2.082 2.081 2.300   2.099 2.082   2.204      
B1B95 2.167 2.038 2.038 2.108 2.049 2.049 2.049 2.045 2.045 2.051     2.065 2.052 2.046 2.066 2.052 2.046  
B3LYP 2.179 2.107 2.052 2.128 2.068 2.068 2.068 2.063 2.063 2.063 2.159 2.091 2.081 2.065 2.059 2.081 2.065 2.059 2.268
B3LYPultrafine         2.068           2.267           2.061    
B3PW91 2.174 2.099 2.046 2.115 2.057 2.057 2.057 2.052 2.052 2.055 2.260   2.071 2.056   2.171      
mPW1PW91 2.167 2.097 2.042 2.112 2.052 2.052 2.052 2.049 2.049 2.051 2.253   2.067 2.052   2.166      
M06-2X         2.076                            
PBEPBE 2.197 2.105 2.058 2.124 2.071 2.071 2.071 2.066 2.066 2.067 2.287   2.083 2.069 2.064 2.084 2.069 2.064 2.286
PBEPBEultrafine         2.305                            
PBE1PBE         2.053                            
HSEh1PBE         2.257                            
TPSSh         2.056   2.056             2.056          
Moller Plesset perturbation MP2 2.208 2.134 2.057 2.152 2.073 2.073 2.073 2.066 2.066 2.076 2.163 2.097 2.097 2.076 2.066 2.102 2.078 2.250 2.253
MP2=FULL 2.207 2.134 2.052 2.151 2.068 2.068 2.068 2.064 2.064 2.058 2.157   2.093 2.066 2.055 2.097 2.062   2.240
MP3         2.059   2.057           2.286            
MP3=FULL         2.055   2.055                        
MP4   2.143 2.258 2.406 2.088   2.183 2.176 2.081   2.177     2.270   2.297      
B2PLYP         2.094                 2.066          
Configuration interaction CID   2.125 2.043 2.144 2.058   2.250 2.052     2.238   2.270 2.155          
CISD   2.125 2.047 2.143 2.062 2.161 2.253 2.056     2.240   2.273 2.158          
Quadratic configuration interaction QCISD   2.142 2.066 2.162 2.083 2.083 2.083 2.077 2.077 2.086 2.164   2.114 2.084   2.282     2.249
QCISD(T)         2.096   2.271 2.272     2.261   2.131 2.100   2.134 2.102    
Coupled Cluster CCD   2.140 2.057 2.160 2.073 2.073 2.073 2.068 2.068 2.079 2.157   2.108 2.077   2.111 2.079    
CCSD         2.079   2.260 2.258     2.247   2.282 2.168   2.199      
CCSD(T)   2.415     2.094 2.180 2.271 2.270 2.270   2.261   2.130 2.099 2.086 2.133 2.102   2.262
CCSD(T)=FULL         2.089                   2.075        

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 2.150 2.083 2.352 2.070 2.311 2.132
density functional B1B95 2.388 2.297        
B3LYP 2.418 2.099 2.414 2.091 2.373 2.118
Moller Plesset perturbation MP2 2.467 2.113 2.460 2.095 2.416 2.142
Values that are outliers may reflect incorrect atom numbering for different levels of theory.
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