Q-Chem 4.0:
Expanding the Frontiers
Jing Kong
Q-Chem Inc.
Pittsburgh, PA
Q-Chem: Profile
• Q-Chem is a high performance quantum chemistry
program;
• Contributed by best quantum chemists from 40 universities
worldwide, including Berkeley, MIT, USC, Tubigen, ANU;
• Led by Board: Head-Gordon, Gill, Schaefer, Krylov, Pople,
Kong.
Q-Chem: Notables
• 1997: First version Q-Chem 1.0: first linear-scaling DFT
with continuous fast multiple method;
• 1999: Prof. John Pople joined Q-Chem after winning
Nobel Prize;
• 2002: New Spartan with Q-Chem as the back end
engine;
• Last release: Q-Chem 3.2;
• Happening Now: Q-Chem 4.0.
• Eight releases in the last 11 years;
Q-Chem 3.0 Paper
Advances in methods and algorithms in a modern
quantum chemistry program package
Physical Chemistry Chemical Physics
Vol 8, 3172 (2006)
66 authors worldwide
37 institutes
Quantum Chemistry Methods
Hierarchy of Methods
• HF: low accuracy, clear phys. Picture;
• MP2: accurate for equalibrium structures, weak
interactions;
• Coupled clusters: very accurate, high cost;
• Multireference methods: even more expensive;
• DFT: accurate, low cost, picture less clear, a bit
empirical.
Quantum Chemistry Methods
Challenges for Method Developers
• Computational cost: speed, memory;
• Nondynamic correlation: transition state, bond stretching,
multiple-bonds, transition metals, radicals;
• Weak interactions: dispersion, H-bonding;
• Real (read ‘Large’) systems;
• Fundamentally, how to make predictions accurate enough
with what we have;
Density Functional Theory
• The accuracy of DFT is determined by the exchange-
correlational functional used;
• Q-Chem has almost all the conventional functionals: B3LYP,
BMK, M06-2X;
Deficiencies of Conventional Functionals
• No dispersion;
• Self-interaction error;
• Fail on static correlation.
DFT: Dispersion
Solutions in Q-Chem for Dispersion
• MM-like empirical formulism: Grimme’s DFT-D, DFT-D3,
Q-Chem’s wB97X-D;
• Electronic: DF-vdW, XDM;
• Add MP2 to DFT.
DFT: Dispersion
• Proposed by Becke and Johnson
• Electronic model with few parameters
• We made efficient implementation in SCF
ccpVTZ
Basis
Eeq-Eax
(kcal/mol)
B3LYP 0.63 (-0.12)
CCSD(T) 1.47 (0.49)
B3LYP+XDM 1.07 (0.32)
Experiment (0.47 ± 0.3)
CH3
O
O
CH3
O
O
Exchange Dipole Moment (XDM)
DFT: Dispersion
Mix DFT with MP2
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
3.00 3.50 4.00 4.50 5.00 5.50 6.00
Enegy (
kcal/m
ol)
|
B3LYP
MP2
XYG3
XYGJ-λOS
CCSD(T)
• Parameterization similar to mixing DFT with HF;
• An example: XJGS-OS;
• Improve both the long-range and short-range.
0.00
3.00
6.00
9.00
12.00
15.00
18.00
21.00
-2.00 -1.00 0.00 1.00 2.00
Reaction coordinateE
nerg
y (
kcal/m
ol)
||
B3LYP
MP2
XYG3
XYGJ-λOS
CCSD(T)
H + CH4 H2 + CH3
CH4-C6H6 CH4-C6H6
DFT: Speed
Q-Chem Has Some of the Best DFT Algorithms
• Continuous fast multipole, the first linear-scaling Coulomb
in quantum chemistry;
• J-engine makes Coulomb fast for even small molecules;
• More recently Fourier transform Coulomb;
• LinK the linear-scaling HF exchange;
• All without error!
New DFT Algorithms in 4.0
• XC is a major part of DFT calculation
• Compact density on atom-centered grid
• Smooth density on even-spaced grid
• Super fast with no errors
Basis set # of basis
functions
Errors
10-6
a.u./atom
Speed-up Speed-up
with FTCa
6-31G(df,pd) 1925 0.03 3.9 5.0
cc-pvTZ 2574 0.1 5.8 9.6
Example: taxol with BLYP (113 atoms)
Multiresolution Exchange-Correlation (mrXC)
New DFT Algorithms in 4.0
• Do SCF with the small basis
• Do one projection step to the large basis
• 10 times faster
• DFT, HF, MP2 energy and gradient
Large Basis Calculation at the Cost of Small Basis
G2 database thermochemistry with B3LYP in kcal/mol.
Small basis single basis dual basis
6-311G MAD = 24.3 MAD = 4.0
6-311G* MAD = 7.0 MAD = 2.2
6-311++G(3df,3pd) MAD = 2.2 MAD = 2.2
NMR Chemical Shifts
O(N) NMR Chemical Shifts
• Build on LinK and O(N) Coulomb
• Using sparse-matrix techniques
• Can treat much larger system than before
NMR Chemical Shifts
DFT Speed: Accelarate with GPU
XC on GPU (Graphic Processing Unit)
• Take advantage of BLAS
• Achieve very good performance:
• 60% of peak performance
• Example:
• Tesla: 960 [email protected], Peak 312 Gflops
• CPU: Quad core Xeon @ 2.8GHz, Peak 44.8Gflops
Hybrid Computing
DFT: More…
Other DFT Features
• Parallel frequency calculation with shared memory;
• TDDFT energy, gradient, and Hessian.