Firefly/PC GAMESS DOCUMENTATION - NEW MP2 GRADIENT CODE

Firefly and PC GAMESS v. 7.1 (AND ABOVE) NEW MP2 GRADIENT MODULE DOCUMENTATION

New semidirect MP2 properties/gradient code was developed to speed up MP2 gradient and related jobs, to seriously reduce memory demands and to allow efficient parallel execution. It is based on FASTINTS code and runs in parallel using P2P interface. It has very modest memory demands, namely, asymptotically they are proportional to N_occ ∙( N_occ + N_core) ∙N_vir, where N_occ is the number of active (not counting frozen core) occupied orbitals, N_core is the number of frozen core occupied orbitals, and N_vir is the number of virtual orbitals. Intrinsically, it is very fast and has very good parallel scalability, with most of the memory demands reducing linearly with the number of used computing nodes. At present, it is limited to RMP2 case only, but will be extended for ZAPT2 in the future.

New MP2 gradient code uses disk I/O and (large) temporary files to store half-transformed 2-electron integrals (file DASORT) and non-separable part of MP2 2-particle density matrix (DM2, stored in file DAFL30 by gradient runs only) and thus can be disk I/O intensive. When running in parallel, the contents of these files is evenly distributed across all nodes. If one is running this code in parallel on SMP or multicore system, it is recommended to assign a separate physical disk to each of the parallel PC GAMESS/Firefly processes.

Note, the exact amount of disk space required to store files DASORT and DAFL30 cannot be predicted exactly because of two reasons. First, the PC GAMESS/Firefly uses sparsity of half-transformed integrals and DM2 to save disk space by storing only non-zero values. Second, half-transformed integrals, DM2 elements as well as their labels are further packed, and it is impossible to predict the exact packing ratio. However, it is possible to provide upper bounds on the overall maximum sizes of DASORT and DAFL30. Note, these bounds usually seriously overestimate the real size of these files!

Namely, the overall size of all DASORT files is less or equal than:

6N_occN_virtN_ao(N_ao+1) bytes

Similarly, the overall size of all DAFL30 files is less or equal than:

8N_occN_virtN_ao(N_ao+1) bytes

Here, N_occ is the number of active occupied orbitals (i.e., excluding frozen core orbitals), N_virt is the number of virtual orbitals, and N_ao is the number of Cartesian atomic orbitals.

The new code is controlled by two keywords of the $MP2 group and by several additional keywords of $MP2GRD group. New code is triggered on by the presence of METHOD=1 keyword in $MP2 group and its behavior is further controlled by either $MP2 GRDMET=1 $END or $MP2 GRDMET=2 $END (the default) switch. GRDMET=2 uses less memory and is usually faster, but for some combinations of computer systems and particular tasks GRDMET=1 can be the preferred option.

The fine tuning of the new properties/gradient module is possible via the following keywords of the $MP2GRD group:

CACHE (logical, default value depends on the particular task). If turned on, reduces disk reads during second MP2 gradient 2-electron integral half-transformation by using some extra memory.
ASYNC (logical, default is true). If turned on, activates asynchronous disk I/O during 2-e gradient computation by using some extra memory
ASYSNC (logical, default is false). When turned on, activates asynchronous "sync" (e.g., "disk flush") calls.
FUSED (logical, default is true). Changes the ordering of loops so that the disk I/O becomes less irregular.
DBLBF (logical, default is true). Enables double buffering and asynchronous I/O for disk writes during second MP2 gradient 2-electron integral half-transformation. Causes minor memory overhead. See also the discussion of ioflgs(30)=1 option below.
GLBLSN (logical, default is false). Enables global synchronization of disk I/O during second MP2 gradient 2-electron integral half-transformation when running in parallel.
MXI (integer, default is min(N_occ,256)). The maximum number of occupied orbitals to be processed in one slice during first and second integral half-transformation. Seriously affects amount of memory required by both first and second half-transformation. Cannot be larger than 256 by design.
MXPQ (integer, default is 225). The maximum number of AO orbital pairs to be processed in one slice during second 2-e integral half-transformation and 2-e gradient computation. Seriously affects amount of memory required by both second half-transformation and gradient code itself
RSIZE1 (integer, default value is 32768). Record size (in elements) used to store half-transformed 2-e integrals. Seriously affects amount of memory required by the first half-transformation, as well as disk I/O performance.
RSIZE2 (integer, default value is 32768). Record size (in elements) used to store half-transformed DM2 elements. Seriously affects amount of memory required by the second half-transformation, as well as disk I/O performance.
NBUFS (integer, default value is calculated to be close to the optimum). Number of buffers used for double buffered asynchronous I/O (see DBLBF option).
TOL1 (double precision, default value is 10^-9). Threshold to store half-transformed 2-e integrals.
TOL2 (double precision, default value is 10^-9). Threshold to store half-transformed DM2 elements.
RANDOM (double precision, default value is 1/3). The random seed to initialize random number generator used while distributing AO shell pairs over nodes.

Below is the recommended part of the input file to be used with the new MP2 gradient code:

 $contrl inttyp=hondo $end
 $p2p p2p=.t. dlb=.t. xdlb=.t. $end
 $smp csmtx=.t. $end
 $mp2 method=1 $end

Depending on your Operating System (e.g., under some Windows systems), the use of the following addition options:

$system splitf=.t./.f. $end (large file splitting enabled/disabled)

and/or

$system ioflgs(30)=1 $end (activate file cache write through mode for unit # 30 which contains DM2 elements)

may have serious positive or negative impact on the overall performance as well.

The following set of parameters of the new MP2 gradient code seems to be optimal in the case you are running large problems in parallel on Linux-based SMP or multicore system which do not have a separate physical disks for each instance of the parallel PC GAMESS/Firefly processes (as recommended above).

 $system splitf=.f. $end
 $system ioflgs(30)=0 $end
 $mp2grd dblbf=0 fused=0 asysnc=1 $end

Firefly v. 7.1.E and above specific I/O options.

The following set of additional I/O parameters of the new MP2 gradient code seems to be optimal for large-scale jobs running under Windows Vista and Windows Server 2008 R1.

 $mp2 ioflgs(1)=65536,65536 ioflgs(3)=65536,65536 $end

Basically, these settings turn on direct unbuffered disk I/O for files DASORT and DICTNRY and disable standard buffered disk reads and writes.

The following set of additional parameters (one can use even tighter values) is a MUST in the case of the partial linear dependence of the AO basis set.

 $contrl icut=11 inttyp=hondo $end
 $scf nconv=7 $end
 $mp2grd tol1=1d-12 tol2=1d-12 $end

The following options of $MP2 group affects MP2 gradient calculations regardless on the particular algorithm selection:

CHFSLV (symbolic). Chooses the type of CPHF solver to use. CONJG selects an ordinary preconditioned conjugate gradient solver. DIIS selects a diis-like iterative solver (default).
THRDII (double precision). Threshold to turn on DIIS convergence accelerator if it was selected to solve CPHF. Default is 0.05
ICUTCP (integer). Sets the effective value of ICUT to be used by CONJG CPHF solver while solving CPHF equations in direct SCF mode. The main purpose of this keyword is to avoid numerical instability problems causing conjugate gradient solver to diverge upon reaching near-convergence. E.g., one may set ICUT to 9 or 10 while tighten ICUTCP to be 10 or 11. The default is the value of ICUF of $CONTRL group.

See also description of CPTOL and MXCPIT options in documentation on older PC GAMESS versions.

Firefly and PC GAMESS v. 7.1 (AND ABOVE) NEW MP2 GRADIENT MODULE DOCUMENTATION

6*Nocc*Nvirt*Nao*(Nao+1) bytes

8*Nocc*Nvirt*Nao*(Nao+1) bytes

The following options of $MP2 group affects MP2 gradient calculations regardless on the particular algorithm selection:

See also:

6N_occN_virtN_ao(N_ao+1) bytes

8N_occN_virtN_ao(N_ao+1) bytes