From owner-chemistry@ccl.net Thu Jan 31 10:11:00 2019 From: "Juan-Carlos Sancho-Garcia jc.sancho]*[ua.es" To: CCL Subject: CCL: "18th DFT Conference" (Alicante, Spain) Message-Id: <-53603-190131034946-12345-yHow5zi2455udyRra50jQg()server.ccl.net> X-Original-From: "Juan-Carlos Sancho-Garcia" Date: Thu, 31 Jan 2019 03:49:41 -0500 Sent to CCL by: "Juan-Carlos Sancho-Garcia" [jc.sancho%ua.es] Dear CCLers: The International Scientific Committee is thrilled to announce the "18th International Conference on Density-Functional Theory and its Applications" to be held in Alicante, Spain, from July 22 to 26, 2019. It will be the next in the great series of biennial meetings, which have taken place in Paris (1995), Vienna (1997), Rome (1999), Madrid (2001), Brussels (2003), Geneva (2005), Amsterdam (2007), Lyon (2009), Athens (2011), Durham (2013), Debrecen (2015), and Tllberg (2017). The conference will cover from cutting-edge developments to applications and discoveries, bringing together scientists from all around the world and from many related fields. The scientific schedule will include plenary talks, invited talks, contributed talks, and poster sessions, including contributions to the following broad topics: - New developments for exchange-correlation functionals - Time-dependent and real-time density-functional theory - Application of density-functional theory in condensed matter physics - Application of density-functional theory in chemistry - Application of density-functional theory in materials science - Strongly correlated systems & solids - Biomolecular modeling and bioapplications Please note that the total number of participants (300) is strictly limited. The registration will close automatically as soon as that maximum number is reached. There is a reduced fee for PhD students. The registration fee will include: - Admission to all scientific sessions - Conference package and book of abstracts - Light welcome cocktail on the evening of 22nd July - Live music and banquet on the evening on 24th July - Door to door bus transfer to the venue of the gala dinner - Morning/afternoon refreshments and lunches on 22nd-26th July - Refreshments at two poster sessions ** Important information: Early registration: 10/05/2019 Abstract submission: 15/06/2019 Registration deadline: 28/06/2019 Updates of the information and the detailed program will be posted on-line at the conference WEBSITE: http://www.dft2019.es Any question can be addressed to the Organizing Committee at the following email: congreso.dft2019..ua.es We are very much looking forward to seeing you at this event! With our Best Wishes, on behalf of Scientific and Organizing Committees From owner-chemistry@ccl.net Thu Jan 31 16:46:01 2019 From: "Grigoriy Zhurko reg_zhurko*chemcraftprog.com" To: CCL Subject: CCL: =?utf-8?Q?The_=E2=80=9Cphilosophical_cornerstone=E2=80=9D_of_the_Moller-Plesset_pe?= =?utf-8?Q?rturbation_theory?= Message-Id: <-53604-190131140426-11424-bqy2sFboJ+w4Fl7bN8aj1Q!^!server.ccl.net> X-Original-From: Grigoriy Zhurko Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8 Date: Thu, 31 Jan 2019 22:09:01 +0400 MIME-Version: 1.0 Sent to CCL by: Grigoriy Zhurko [reg_zhurko^^^chemcraftprog.com] I am sorry if my post is too unusual for this list; if so, please suggest me some web forums where I can get answers to my question. It is known that the MP rows (MP2, MP3, MP4, etc) can converge both quickly and slowly, and for some cases (e.g. CeI4) they even diverge instead of converging. The first question is, whether this tendency becomes apparent for some molecules like CeI4 not only for the MP series, but also for other applications of perturbation theory. In other case, if we know that the MP series diverge for some molecule, can we predict that the CCSD(T) method gives worse results for this molecule in comparison to CCSD (at least the advantages of the CCSD(T) approach for this molecule are not as evident as for other ones). The second question is quite philosophic: what is the “mathematical cornerstone”, or “philosophical cornerstone” of the perturbation theory, and whether it can be shown with some simple samples. If yes, maybe this information will help us predict whether the MP rows will diverge for some molecule not yet investigated. I have asked this question on some web forums, and got some answers. Let’s consider the salvation of two equations: 1) x+sin(x)=3000 If we write the following: x=3000-sin(x) We can set x0=0 and get the following iterations: 0 3000 2999,78081002572 2999,5739029766 2999,39713977695 2999,26623684759 2999,18383222963 2999,13904100976 This series converge after 40 iterations. 2) 6000=(x−1)(x−3000)+sin(x) We transform this equation into the following: x=(6000-sin(x))/(x-3000)+1 Choosing x0=0 we get the following convergence: 0 -1 -0,999613952344155 -0,999614140048658 -0,999614139957402 -0,999614139957447 -0,999614139957447 -0,999614139957447 So, this series converges within 6 iterations. Some people said that the second example illustrates the суть of the perturbation theory, while the first one does not. Some other people said that both these examples are not really attributed to the perturbation theory. Can you suggest your opinion? From owner-chemistry@ccl.net Thu Jan 31 21:41:00 2019 From: "Robert Molt r.molt.chemical.physics[a]gmail.com" To: CCL Subject: CCL: =?UTF-8?Q?Re=3a_CCL=3a_The_=e2=80=9cphilosophical_cornerstone?= =?UTF-8?Q?=e2=80=9d_of_the_Moller-Plesset_perturbation_theory?= Message-Id: <-53605-190131204451-7535-NTUNpc5PjXoJlHlL7cdmaA]-[server.ccl.net> X-Original-From: Robert Molt Content-Language: en-US Content-Type: multipart/alternative; boundary="------------2FDB16973942896D56FB9D2F" Date: Thu, 31 Jan 2019 20:44:41 -0500 MIME-Version: 1.0 Sent to CCL by: Robert Molt [r.molt.chemical.physics\a/gmail.com] This is a multi-part message in MIME format. --------------2FDB16973942896D56FB9D2F Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit There are at least 3 "kinds" of divergences, IMO. That is to say, I apply a trichotomy in my thinking on the "origin" of a divergence. 1.)    A perturbation series can have zero denominators in the energy expression. If you look at the energy expressions of anything perturbative, there will always be a denominator with this property, be it MP4 or CCSDT(Q). There will always be a difference in the eigenvalues of the single particle functions (i.e., the so-called "orbital energies" of the reference wavefunction, not that such a physical meaning is warranted). This sort of divergence is a common sort of numerical instability. This can be because you have a poor starting guess, but it does not have to be. It's just having zeroes in denominators, whether or not the reference wavefunction was "good." 2.)    A very different kind of divergence is when there are no zero denominators, like in any infinite order method, but degeneracies in the reference determinant lead to oscillations because you privileged one determinant as your starting reference /and the real interactions were equally split between two determinants/. (Well, or between three, or four, whatever, point is degeneracies make multiple determinants equally important starting points). For example, if you take a system whose true reference wavefunction is 50% state A, 50% state B, and do CCSD, you likely will get a bad answer. As you increase excitations from state A, your answers will jump all over the place *until* such a time that you have enough excitations that can map your reference state (state A) onto the other state (state B), i.e., allow representation of both states equally. Here, the problem is that you started from a poor starting condition; you made an arbitrary decision to select state A. Having a poor starting guess /may /have the same problems as type 1 (divergent denominators), but this is a distinct mathematical problem. In type 1, the cause is a zero denominator. Here, there is no zero denominator, merely that you're summing interactions (diagrams) that are only "half" the total set of significant interactions (diagrams) (because you've neglected the interactions of state B). 3.)    In Piela's excellent book on quantum chemistry, he gives examples of the divergence of a Moller-Plesset-perturbation style for water. There is clearly no problem with divergent denominators, as there are no degenerate orbitals. There is clearly no other reference state wavefunction to describe water. The MP expansion oscillates. I have never understood this and would love to hear someone explain why this occurs. Casually, I wonder if it is just a problem of diffuse basis functions not being thrown out when linear dependencies occur (i.e., it's not a real problem), but that's total speculation. IMO, none of these situations are represented in your examples of finding roots. Those examples have oscillations depending on the specific numerical algorithm used to find the roots; some algorithms will have problems, others will not. That's a numerical analysis question. On 1/31/19 1:09 PM, Grigoriy Zhurko reg_zhurko*chemcraftprog.com wrote: > Sent to CCL by: Grigoriy Zhurko [reg_zhurko^^^chemcraftprog.com] > I am sorry if my post is too unusual for this list; if so, please suggest me some web forums where I can get answers to my question. > It is known that the MP rows (MP2, MP3, MP4, etc) can converge both quickly and slowly, and for some cases (e.g. CeI4) they even diverge instead of converging. > The first question is, whether this tendency becomes apparent for some molecules like CeI4 not only for the MP series, but also for other applications of perturbation theory. In other case, if we know that the MP series diverge for some molecule, can we predict that the CCSD(T) method gives worse results for this molecule in comparison to CCSD (at least the advantages of the CCSD(T) approach for this molecule are not as evident as for other ones). > The second question is quite philosophic: what is the “mathematical cornerstone”, or “philosophical cornerstone” of the perturbation theory, and whether it can be shown with some simple samples. If yes, maybe this information will help us predict whether the MP rows will diverge for some molecule not yet investigated. > I have asked this question on some web forums, and got some answers. Let’s consider the salvation of two equations: > 1) > x+sin(x)=3000 > If we write the following: > > x=3000-sin(x) > > We can set x0=0 and get the following iterations: > > 0 > 3000 > 2999,78081002572 > 2999,5739029766 > 2999,39713977695 > 2999,26623684759 > 2999,18383222963 > 2999,13904100976 > > This series converge after 40 iterations. > > 2) > 6000=(x−1)(x−3000)+sin(x) > > We transform this equation into the following: > > x=(6000-sin(x))/(x-3000)+1 > > Choosing x0=0 we get the following convergence: > > 0 > -1 > -0,999613952344155 > -0,999614140048658 > -0,999614139957402 > -0,999614139957447 > -0,999614139957447 > -0,999614139957447 > > So, this series converges within 6 iterations. > Some people said that the second example illustrates the суть of the perturbation theory, while the first one does not. Some other people said that both these examples are not really attributed to the perturbation theory. Can you suggest your opinion?> > -- Dr. Robert Molt Jr. r.molt.chemical.physics- -gmail.com --------------2FDB16973942896D56FB9D2F Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: 8bit

There are at least 3 "kinds" of divergences, IMO. That is to say, I apply a trichotomy in my thinking on the "origin" of a divergence.

1.)    A perturbation series can have zero denominators in the energy expression. If you look at the energy expressions of anything perturbative, there will always be a denominator with this property, be it MP4 or CCSDT(Q). There will always be a difference in the eigenvalues of the single particle functions (i.e., the so-called "orbital energies" of the reference wavefunction, not that such a physical meaning is warranted). This sort of divergence is a common sort of numerical instability. This can be because you have a poor starting guess, but it does not have to be. It's just having zeroes in denominators, whether or not the reference wavefunction was "good."

2.)    A very different kind of divergence is when there are no zero denominators, like in any infinite order method, but degeneracies in the reference determinant lead to oscillations because you privileged one determinant as your starting reference and the real interactions were equally split between two determinants. (Well, or between three, or four, whatever, point is degeneracies make multiple determinants equally important starting points). For example, if you take a system whose true reference wavefunction is 50% state A, 50% state B, and do CCSD, you likely will get a bad answer. As you increase excitations from state A, your answers will jump all over the place until such a time that you have enough excitations that can map your reference state (state A) onto the other state (state B), i.e., allow representation of both states equally.

Here, the problem is that you started from a poor starting condition; you made an arbitrary decision to select state A. Having a poor starting guess may have the same problems as type 1 (divergent denominators), but this is a distinct mathematical problem. In type 1, the cause is a zero denominator. Here, there is no zero denominator, merely that you're summing interactions (diagrams) that are only "half" the total set of significant interactions (diagrams) (because you've neglected the interactions of state B).

3.)    In Piela's excellent book on quantum chemistry, he gives examples of the divergence of a Moller-Plesset-perturbation style for water. There is clearly no problem with divergent denominators, as there are no degenerate orbitals. There is clearly no other reference state wavefunction to describe water. The MP expansion oscillates. I have never understood this and would love to hear someone explain why this occurs. Casually, I wonder if it is just a problem of diffuse basis functions not being thrown out when linear dependencies occur (i.e., it's not a real problem), but that's total speculation.

IMO, none of these situations are represented in your examples of finding roots. Those examples have oscillations depending on the specific numerical algorithm used to find the roots; some algorithms will have problems, others will not. That's a numerical analysis question.

On 1/31/19 1:09 PM, Grigoriy Zhurko reg_zhurko*chemcraftprog.com wrote:
Sent to CCL by: Grigoriy Zhurko [reg_zhurko^^^chemcraftprog.com]
I am sorry if my post is too unusual for this list; if so, please suggest me some web forums where I can get answers to my question.
It is known that the MP rows (MP2, MP3, MP4, etc) can converge both quickly and slowly, and for some cases (e.g. CeI4) they even diverge instead of converging.
The first question is, whether this tendency becomes apparent for some molecules like CeI4 not only for the MP series, but also for other applications of perturbation theory. In other case, if we know that the MP series diverge for some molecule, can we predict that the CCSD(T) method gives worse results for this molecule in comparison to CCSD (at least the advantages of the CCSD(T) approach for this molecule are not as evident as for other ones).
The second question is quite philosophic: what is the “mathematical cornerstone”, or “philosophical cornerstone” of the perturbation theory, and whether it can be shown with some simple samples. If yes, maybe this information will help us predict whether the MP rows will diverge for some molecule not yet investigated.
I have asked this question on some web forums, and got some answers. Let’s consider the salvation of two equations:
1)
x+sin(x)=3000
If we write the following:

x=3000-sin(x)

We can set x0=0 and get the following iterations:

0
3000
2999,78081002572
2999,5739029766
2999,39713977695
2999,26623684759
2999,18383222963
2999,13904100976

This series converge after 40 iterations.

2)
6000=(x−1)(x−3000)+sin(x)

We transform this equation into the following:

x=(6000-sin(x))/(x-3000)+1

Choosing x0=0 we get the following convergence:

0
-1
-0,999613952344155
-0,999614140048658
-0,999614139957402
-0,999614139957447
-0,999614139957447
-0,999614139957447

So, this series converges within 6 iterations.
Some people said that the second example illustrates the суть of the perturbation theory, while the first one does not. Some other people said that both these examples are not really attributed to the perturbation theory. Can you suggest your opinion?E-mail to subscribers: CHEMISTRY- -ccl.net or use:
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-- 
Dr. Robert Molt Jr.
r.molt.chemical.physics- -gmail.com
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