BackgroundPractical tests
Summary and recommendations
VMC sampling efficiency
Pablo Lopez Rıos
TCM group. Cavendish Laboratory. University of Cambridge.
July 25, 2010
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
The VMC algorithm
In VMC we sample configurations {R1, . . . ,RM} distributedaccording to |Ψ(R)|2
We evaluate the variational energy as EVMC = 1M ∑
Mm=1 EL(Rm)
This energy has an uncertainty given by ∆ = σ√M/ncorr
σ2 is the variance of the sample of local energies, whichdepends on Ψncorr is the (integrated) correlation length of the sample oflocal energies, which depends on how we sample configurations
A VMC calculation is more efficient the less time it takes toachieve a target errorbar: E =
(∆2MTiter
)−1=
(σ2ncorrTiter
)−1
It is inefficient to attempt to maximize this directly withrespect to any parameter due to the multiple evaluations ofncorr that this would require
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
The VMC algorithm
In VMC we sample configurations {R1, . . . ,RM} distributedaccording to |Ψ(R)|2
We evaluate the variational energy as EVMC = 1M ∑
Mm=1 EL(Rm)
This energy has an uncertainty given by ∆ = σ√M/ncorr
σ2 is the variance of the sample of local energies, whichdepends on Ψncorr is the (integrated) correlation length of the sample oflocal energies, which depends on how we sample configurations
A VMC calculation is more efficient the less time it takes toachieve a target errorbar: E =
(∆2MTiter
)−1=(σ2ncorrTiter
)−1
It is inefficient to attempt to maximize this directly withrespect to any parameter due to the multiple evaluations ofncorr that this would require
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
The VMC algorithm
In VMC we sample configurations {R1, . . . ,RM} distributedaccording to |Ψ(R)|2
We evaluate the variational energy as EVMC = 1M ∑
Mm=1 EL(Rm)
This energy has an uncertainty given by ∆ = σ√M/ncorr
σ2 is the variance of the sample of local energies, whichdepends on Ψncorr is the (integrated) correlation length of the sample oflocal energies, which depends on how we sample configurations
A VMC calculation is more efficient the less time it takes toachieve a target errorbar: E =
(∆2MTiter
)−1=(σ2ncorrTiter
)−1
It is inefficient to attempt to maximize this directly withrespect to any parameter due to the multiple evaluations ofncorr that this would require
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
The VMC algorithm
In VMC we sample configurations {R1, . . . ,RM} distributedaccording to |Ψ(R)|2
We evaluate the variational energy as EVMC = 1M ∑
Mm=1 EL(Rm)
This energy has an uncertainty given by ∆ = σ√M/ncorr
σ2 is the variance of the sample of local energies, whichdepends on Ψncorr is the (integrated) correlation length of the sample oflocal energies, which depends on how we sample configurations
A VMC calculation is more efficient the less time it takes toachieve a target errorbar: E =
(∆2MTiter
)−1=(σ2ncorrTiter
)−1
It is inefficient to attempt to maximize this directly withrespect to any parameter due to the multiple evaluations ofncorr that this would require
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
The VMC algorithm
In VMC we sample configurations {R1, . . . ,RM} distributedaccording to |Ψ(R)|2
We evaluate the variational energy as EVMC = 1M ∑
Mm=1 EL(Rm)
This energy has an uncertainty given by ∆ = σ√M/ncorr
σ2 is the variance of the sample of local energies, whichdepends on Ψncorr is the (integrated) correlation length of the sample oflocal energies, which depends on how we sample configurations
A VMC calculation is more efficient the less time it takes toachieve a target errorbar: E =
(∆2MTiter
)−1=(σ2ncorrTiter
)−1
It is inefficient to attempt to maximize this directly withrespect to any parameter due to the multiple evaluations ofncorr that this would require
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
VMC sampling
{Rm}m=1,...,M are generated using the Metropolis algorithm:
Propose move from Rm to R′m with probability T(R′m← Rm)
Compute A(R′m← Rm) = min(
1, T(Rm←R′m)T(R′m←Rm)
|Ψ(R′m)|2|Ψ(Rm)|2
)Draw random number 0 < ζ < 1 from a uniform distribution,and
If ζ < A(R′m← Rm), make Rm+1 = R′m (accept move)Otherwise, set Rm+1 = Rm (reject move)
To achieve reasonable acceptance ratios, proposedconfigurations are the original plus a normally-distributedrandom displacement of variance τ
This causes serial correlation (ncorr > 1)
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
VMC sampling
{Rm}m=1,...,M are generated using the Metropolis algorithm:
Propose move from Rm to R′m with probability T(R′m← Rm)
Compute A(R′m← Rm) = min(
1, T(Rm←R′m)T(R′m←Rm)
|Ψ(R′m)|2|Ψ(Rm)|2
)Draw random number 0 < ζ < 1 from a uniform distribution,and
If ζ < A(R′m← Rm), make Rm+1 = R′m (accept move)Otherwise, set Rm+1 = Rm (reject move)
To achieve reasonable acceptance ratios, proposedconfigurations are the original plus a normally-distributedrandom displacement of variance τ
This causes serial correlation (ncorr > 1)
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
VMC sampling
{Rm}m=1,...,M are generated using the Metropolis algorithm:
Propose move from Rm to R′m with probability T(R′m← Rm)
Compute A(R′m← Rm) = min(
1, T(Rm←R′m)T(R′m←Rm)
|Ψ(R′m)|2|Ψ(Rm)|2
)Draw random number 0 < ζ < 1 from a uniform distribution,and
If ζ < A(R′m← Rm), make Rm+1 = R′m (accept move)Otherwise, set Rm+1 = Rm (reject move)
To achieve reasonable acceptance ratios, proposedconfigurations are the original plus a normally-distributedrandom displacement of variance τ
This causes serial correlation (ncorr > 1)
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
VMC sampling
{Rm}m=1,...,M are generated using the Metropolis algorithm:
Propose move from Rm to R′m with probability T(R′m← Rm)
Compute A(R′m← Rm) = min(
1, T(Rm←R′m)T(R′m←Rm)
|Ψ(R′m)|2|Ψ(Rm)|2
)Draw random number 0 < ζ < 1 from a uniform distribution,and
If ζ < A(R′m← Rm), make Rm+1 = R′m (accept move)Otherwise, set Rm+1 = Rm (reject move)
To achieve reasonable acceptance ratios, proposedconfigurations are the original plus a normally-distributedrandom displacement of variance τ
This causes serial correlation (ncorr > 1)
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
VMC sampling
{Rm}m=1,...,M are generated using the Metropolis algorithm:
Propose move from Rm to R′m with probability T(R′m← Rm)
Compute A(R′m← Rm) = min(
1, T(Rm←R′m)T(R′m←Rm)
|Ψ(R′m)|2|Ψ(Rm)|2
)Draw random number 0 < ζ < 1 from a uniform distribution,and
If ζ < A(R′m← Rm), make Rm+1 = R′m (accept move)Otherwise, set Rm+1 = Rm (reject move)
To achieve reasonable acceptance ratios, proposedconfigurations are the original plus a normally-distributedrandom displacement of variance τ
This causes serial correlation (ncorr > 1)
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
VMC sampling
{Rm}m=1,...,M are generated using the Metropolis algorithm:
Propose move from Rm to R′m with probability T(R′m← Rm)
Compute A(R′m← Rm) = min(
1, T(Rm←R′m)T(R′m←Rm)
|Ψ(R′m)|2|Ψ(Rm)|2
)Draw random number 0 < ζ < 1 from a uniform distribution,and
If ζ < A(R′m← Rm), make Rm+1 = R′m (accept move)Otherwise, set Rm+1 = Rm (reject move)
To achieve reasonable acceptance ratios, proposedconfigurations are the original plus a normally-distributedrandom displacement of variance τ
This causes serial correlation (ncorr > 1)
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Electron-by-electron sampling
It is possible to use a variation of the Metropolis algorithmwhere one proposes single-electron moves and accepts orrejects them individually
Advantage: larger steps can be taken with high acceptanceratios, thus reducing ncorr
Disadvantage: the evaluation of N single-electronwave-function ratios is more expensive than that of oneall-electron wave function ratio, and especially for complicatedfunctional forms (e.g., Slater determinants with backflowtransformations), which increases Titer
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Electron-by-electron sampling
It is possible to use a variation of the Metropolis algorithmwhere one proposes single-electron moves and accepts orrejects them individually
Advantage: larger steps can be taken with high acceptanceratios, thus reducing ncorr
Disadvantage: the evaluation of N single-electronwave-function ratios is more expensive than that of oneall-electron wave function ratio, and especially for complicatedfunctional forms (e.g., Slater determinants with backflowtransformations), which increases Titer
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Electron-by-electron sampling
It is possible to use a variation of the Metropolis algorithmwhere one proposes single-electron moves and accepts orrejects them individually
Advantage: larger steps can be taken with high acceptanceratios, thus reducing ncorr
Disadvantage: the evaluation of N single-electronwave-function ratios is more expensive than that of oneall-electron wave function ratio, and especially for complicatedfunctional forms (e.g., Slater determinants with backflowtransformations), which increases Titer
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Decorrelation loops
One can perform p > 1 Metropolis steps between evaluationsof the local energy
Advantage: ncorr decreases
Disadvantage: the extra moves increase Titer
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Decorrelation loops
One can perform p > 1 Metropolis steps between evaluationsof the local energy
Advantage: ncorr decreases
Disadvantage: the extra moves increase Titer
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Decorrelation loops
One can perform p > 1 Metropolis steps between evaluationsof the local energy
Advantage: ncorr decreases
Disadvantage: the extra moves increase Titer
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Averaging successive local energies
The mth local energy can be replaced by the average[1−A(R′m← Rm)]EL(Rm) + A(R′m← Rm)EL(R′m)
Advantage: more statistics, especially important at lowacceptance ratios, potentially reducing ncorr
Disadvantage: needs more energy evaluations, increasing Titer
This has proved inefficient in electron-by-electron sampling, sowill only test in configuration-by-configuration sampling
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Averaging successive local energies
The mth local energy can be replaced by the average[1−A(R′m← Rm)]EL(Rm) + A(R′m← Rm)EL(R′m)
Advantage: more statistics, especially important at lowacceptance ratios, potentially reducing ncorr
Disadvantage: needs more energy evaluations, increasing Titer
This has proved inefficient in electron-by-electron sampling, sowill only test in configuration-by-configuration sampling
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Averaging successive local energies
The mth local energy can be replaced by the average[1−A(R′m← Rm)]EL(Rm) + A(R′m← Rm)EL(R′m)
Advantage: more statistics, especially important at lowacceptance ratios, potentially reducing ncorr
Disadvantage: needs more energy evaluations, increasing Titer
This has proved inefficient in electron-by-electron sampling, sowill only test in configuration-by-configuration sampling
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
VMC samplingCommon modifications
Averaging successive local energies
The mth local energy can be replaced by the average[1−A(R′m← Rm)]EL(Rm) + A(R′m← Rm)EL(R′m)
Advantage: more statistics, especially important at lowacceptance ratios, potentially reducing ncorr
Disadvantage: needs more energy evaluations, increasing Titer
This has proved inefficient in electron-by-electron sampling, sowill only test in configuration-by-configuration sampling
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Things to look into
Optimal value of τ?
Electron-by-electron versus configuration-by-configuration -which to use when?
Decorrelation loops - optimal length?
Is averaging energies over proposed configurations useful?
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Things to look into
Optimal value of τ?
Electron-by-electron versus configuration-by-configuration -which to use when?
Decorrelation loops - optimal length?
Is averaging energies over proposed configurations useful?
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Things to look into
Optimal value of τ?
Electron-by-electron versus configuration-by-configuration -which to use when?
Decorrelation loops - optimal length?
Is averaging energies over proposed configurations useful?
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Things to look into
Optimal value of τ?
Electron-by-electron versus configuration-by-configuration -which to use when?
Decorrelation loops - optimal length?
Is averaging energies over proposed configurations useful?
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Methodology
Choose 6 relevant systems of different sizes
Run short (but significant) VMC calculations spanning 16values of τ and 10 values of p
Run electron-by-electron and configuration-by-configurationversions of the above, the latter with and without averagingover successive energies
Use Slater-Jastrow and Slater-Jastrow-backflow wave functionforms
Total: 5760 runs
Use the data to locate maximum efficiency for each case,compare, analyze, etc
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Methodology
Choose 6 relevant systems of different sizes
Run short (but significant) VMC calculations spanning 16values of τ and 10 values of p
Run electron-by-electron and configuration-by-configurationversions of the above, the latter with and without averagingover successive energies
Use Slater-Jastrow and Slater-Jastrow-backflow wave functionforms
Total: 5760 runs
Use the data to locate maximum efficiency for each case,compare, analyze, etc
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Methodology
Choose 6 relevant systems of different sizes
Run short (but significant) VMC calculations spanning 16values of τ and 10 values of p
Run electron-by-electron and configuration-by-configurationversions of the above, the latter with and without averagingover successive energies
Use Slater-Jastrow and Slater-Jastrow-backflow wave functionforms
Total: 5760 runs
Use the data to locate maximum efficiency for each case,compare, analyze, etc
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Methodology
Choose 6 relevant systems of different sizes
Run short (but significant) VMC calculations spanning 16values of τ and 10 values of p
Run electron-by-electron and configuration-by-configurationversions of the above, the latter with and without averagingover successive energies
Use Slater-Jastrow and Slater-Jastrow-backflow wave functionforms
Total: 5760 runs
Use the data to locate maximum efficiency for each case,compare, analyze, etc
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Methodology
Choose 6 relevant systems of different sizes
Run short (but significant) VMC calculations spanning 16values of τ and 10 values of p
Run electron-by-electron and configuration-by-configurationversions of the above, the latter with and without averagingover successive energies
Use Slater-Jastrow and Slater-Jastrow-backflow wave functionforms
Total: 5760 runs
Use the data to locate maximum efficiency for each case,compare, analyze, etc
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Methodology
Choose 6 relevant systems of different sizes
Run short (but significant) VMC calculations spanning 16values of τ and 10 values of p
Run electron-by-electron and configuration-by-configurationversions of the above, the latter with and without averagingover successive energies
Use Slater-Jastrow and Slater-Jastrow-backflow wave functionforms
Total: 5760 runs
Use the data to locate maximum efficiency for each case,compare, analyze, etc
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Pseudo Nitrogen atom, Slater-Jastrow, EBES vs CBCS
0.001 0.01 0.1 1 10 100Timestep
0
50
100
Acc
. rat
io
0.001 0.01 0.1 1 10 1000
0.010.020.030.040.050.06
Diff
. con
st
0.001 0.01 0.1 1 10 1000
0.5
1
Inv.
cor
r. tim
e
0.001 0.01 0.1 1 10 1000
50000
1e+05
1.5e+05
2e+05
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: nitrogen_pp. Sampling method: ebe.
0.0001 0.001 0.01 0.1 1Timestep
0
50
100
Acc
. rat
io
0.0001 0.01 10
0.005
0.01
0.015
0.02
Diff
. con
st
0.0001 0.001 0.01 0.1 10
0.5
1
Inv.
cor
r. tim
e
0.0001 0.01 10
20000
40000
60000
80000
1e+05
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: nitrogen_pp. Sampling method: cbc.
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
HEG, Slater-Jastrow, EBES vs CBCS
0.001 0.01 0.1 1 10 100Timestep
0
50
100
Acc
. rat
io
0.001 0.01 0.1 1 10 1000
0.050.1
0.150.2
0.25
Diff
. con
st
0.001 0.01 0.1 1 10 1000
0.5
1
Inv.
cor
r. tim
e
0.001 0.01 0.1 1 10 1000
50010001500200025003000
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: heg. Sampling method: ebe.
0.0001 0.001 0.01 0.1 1Timestep
0
50
100
Acc
. rat
io
0.0001 0.001 0.01 0.1 10
0.0005
0.001
0.0015
0.002
Diff
. con
st
0.0001 0.001 0.01 0.1 10
0.5
1
Inv.
cor
r. tim
e
0.0001 0.001 0.01 0.1 10
100200300400500600
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: heg. Sampling method: cbc.
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Pseudo NiO molecule, backflow, EBES vs CBCS
0.001 0.01 0.1 1 10 100Timestep
0
50
100
Acc
. rat
io
0.001 0.01 0.1 1 10 1000
0.010.020.030.040.050.06
Diff
. con
st
0.001 0.01 0.1 1 10 1000
0.5
1
Inv.
cor
r. tim
e
0.001 0.01 0.1 1 10 1000
50100150200250300
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: nio_pp. Sampling method: ebe. Wfn: bf.
0.0001 0.001 0.01 0.1 1Timestep
0
50
100
Acc
. rat
io
0.0001 0.001 0.01 0.1 10
0.0005
0.001
0.0015
0.002
Diff
. con
st
0.0001 0.001 0.01 0.1 10
0.5
1
Inv.
cor
r. tim
e
0.0001 0.001 0.01 0.1 10
50
100
150
200
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: nio_pp. Sampling method: cbc. Wfn: bf.
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
All-electron N2H4, backflow, CBCS vs CBCS2
0.0001 0.001 0.01Timestep
0
50
100
Acc
. rat
io
0.0001 0.001 0.010
0.00010.00020.00030.00040.00050.00060.0007
Diff
. con
st
0.0001 0.001 0.010
0.5
1
Inv.
cor
r. tim
e
0.0001 0.001 0.010
50100150200250300
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: n2h4. Sampling method: cbc. Wfn: bf.
0.0001 0.001 0.01 0.1Timestep
0
50
100
Acc
. rat
io
0.0001 0.001 0.01 0.10
0.00010.00020.00030.00040.00050.00060.0007
Diff
. con
st
0.0001 0.001 0.01 0.10
0.5
1
Inv.
cor
r. tim
e
0.0001 0.001 0.01 0.10
50
100
150
200
Effic
ienc
y
Assorted quantities vs VMC timestepSystem: n2h4. Sampling method: cbc. Wfn: bf.
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Functional form of E (p)
Cost of one energy evaluation: Titer(p) = pTmove + Tenergy
Assuming M→ ∞, and that the autocorrelation of the localenergies is dominated by a single exponential,
ncorr(p) = 1 + 2 (ncorr−1)p
(ncorr+1)p−(ncorr−1)p
One can minimize Titer(p)ncorr(p) numerically if ncorr andTenergy/Tmove are know.
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Functional form of E (p)
Cost of one energy evaluation: Titer(p) = pTmove + Tenergy
Assuming M→ ∞, and that the autocorrelation of the localenergies is dominated by a single exponential,
ncorr(p) = 1 + 2 (ncorr−1)p
(ncorr+1)p−(ncorr−1)p
One can minimize Titer(p)ncorr(p) numerically if ncorr andTenergy/Tmove are know.
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
MethodologyTest resultsFunctional form of E (p)
Functional form of E (p)
Cost of one energy evaluation: Titer(p) = pTmove + Tenergy
Assuming M→ ∞, and that the autocorrelation of the localenergies is dominated by a single exponential,
ncorr(p) = 1 + 2 (ncorr−1)p
(ncorr+1)p−(ncorr−1)p
One can minimize Titer(p)ncorr(p) numerically if ncorr andTenergy/Tmove are know.
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
Summary and recommendations
Use electron-by-electron sampling
Optimize τ so as to achieve a 50% acceptance ratio
Set p to 3-5, or compute ncorr from a short run and maximizeE numerically
Do not average over successive energies
We’ve been doing it right all along!
Pablo Lopez Rıos VMC sampling efficiency
BackgroundPractical tests
Summary and recommendations
Summary and recommendations
Use electron-by-electron sampling
Optimize τ so as to achieve a 50% acceptance ratio
Set p to 3-5, or compute ncorr from a short run and maximizeE numerically
Do not average over successive energies
We’ve been doing it right all along!
Pablo Lopez Rıos VMC sampling efficiency
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