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 cores@1.45GHz, 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.