I often get correspondence from scientists form all over the world. One such arrived a couple days ago asking about the intrinsic hyperpolarizability and why it is a useful quantity for comparing molecules. Below is the original message and my response:
Email to me:
Dear Sir,
I have a doubt regarding beta-intrinsic value. Which molecule is of greater practical importance, having a greater beta-intrisic value or a greater beta-value? If molecule has greater beta-intrinsic and lesser beta-value as compared to its related counterpart can it be regarded as a better molecule for practical applicability?
Thanks.
Kind regards,
Sincerely,
So-and-so
My response:
Dear Dr. So-and-so,
The intrinsic hyperpolarizability is used to understand the origin of the nonlinear response of a molecule. Making a molecule larger will yield a bigger value of beta; but, the intrinsic hyperpolarizability tells you how effective it is given its size. This kind of understanding can lead to the rational design of better molecules by first identifying ones that have a large intrinsic hyperpolarizability and then making them larger using the same "shape" or theme.
Having a molecule with a large hyperpolarizability in itself is not technological significant because that property alone will not necessarily make it useful in a device. It needs to be incorporated into a material with a large bulk response and then needs to be formed into a device component that is photochemically stable, etc. Thus, a molecule with large beta is not of technological interest without lots of other work to determine other properties; and, a small intrinsic beta makes it less interesting from the point of view of science.
A large beta molecule may be of interest to others if it has other unique properties, such as an ability to attach it to microdots to enhance local electric fields, or if it acts a charge sensitizer in a polymer, etc.
Best,
Mark G. Kuzyk
In the near future, I plan to write a description of our research aimed at the non-expert so (s)he can gain an appreciation of our work, which is based on trying to understand complex properties of a system by looking at large-scale patterns. Stay tuned.
Showing posts with label intrinsic nonlinearity. Show all posts
Showing posts with label intrinsic nonlinearity. Show all posts
Wednesday, December 21, 2011
Saturday, November 20, 2010
Simple Scaling and too much to do in too little time
This was a good week. Nathan successfully defended his dissertation with flying colors and our manuscript for Advanced Materials, a high impact journal, was accepted. Our paper is a comment on another paper that previously appeared in Advanced Materials.
One central theme of our work that uses fundamental limits and sum rules to understand the nonlinear-optical response is the idea of scale invariance. The Schrodinger Equation has the property that the shape of the wavefunction does not change when the width of the potential energy function is decreased by a scaling factor b and the depth of the well is simultaneously increased by b squared. Under such a transformation, the wavefunction is compressed by the factor b, but otherwise, the shape remains the same. We call this simple scaling.
The nonlinear-optical quantity of interest to many applications is called the hyperpolarizability. Making the hyperpolarizability as large as possible is an ongoing area of intense research activity. To nobody's surprise, a larger molecule will generally have a larger hyperpolarizability. To better understand what makes a material tick, we have defined a quantity called the intrinsic hyperpolarizability, which is simply the ratio of the hyperpolarizability of a quantum system, divided by the fundamental limit. Interestingly, the intrinsic hyperpolarizability is invariant under simple scaling, so large and small molecules that are related to each other by simple scaling will have the same intrinsic hyperpolarizability.
In examining all the molecules that had been studied for nonlinear-optical applications over a 3 decade period, we found that the large range of hyperpolarizability values could mostly be accounted for by simple scaling. Thus, researchers were making molecules larger and larger but the best intrinsic hyperpolarizabilities remained static at about 0.03 - suggesting that it would be possible to make a factor of 30 improvement; but to get there would undoubtedly requrie a major paradigm shift.
Several years ago, I published a paper that showed how to calculate a related quantity called the intrinsic two-photon absorption (TPA) cross-section. More recently, Javier Perez-Moreno and I published a paper that introduced a rough rule of thumb for determining the intrinsic TPA cross-section - simply divide it by the square of the number of electrons. My earlier paper showed how to determine the number of electrons.
To my delight, my paper on TPA gets lots of citations, not because of what I believe is the beautiful physics of the work, but because scientists refer to my method of counting the number of effective electrons - a quite trivial (and approximate) procedure. To my horror, when comparing molecules, most researchers then go on to divide by the number of electrons rather than by the square of the number of electrons as suggested by Javier's work. This leads to a flawed comparison between molecules.
A recent paper in Advanced Materials reported on TPA cross section measurements of a new class of dendrimers, molecules with ever-branching pieces much like veins and arteries. They referred to my paper when calculating the number of electrons; but, as is usually the case, they divided by the number of electrons and found that the new dendrimer class was an order of magnitude better than the best existing dendrimers - an impressive improvement.
In our comment on this paper, we reanalyzed the data using the N squared rule and found that the new materials were in fact two orders of magnitude better. In addition, the dendrimers within each class, though of vastly differing sizes, all had approximately the same intrinsic TPA cross section. Thus, we were able to show that the authors had made an even more important discovery than they had realized. Usually, comments on a paper point out a negative flaw, leading to strong rebuttals and counter-rebuttals. In this case, all parties were winners.
Unfortunately, these small successes were overshadowed by a pile of work. After the Thanksgiving break, I am going to an NSF meeting in Hawaii (I hate to travel and I hate hot and humid places), where I will be reporting on the results of our projects. I need to prepare a glitzy poster as well as an oral presentation. This, on top of being hopelessly behind in preparing problem sets/solutions, grading, and catching up on lectures for my graduate mechanics class. In addition, I need to write a pile of recommendations and read a 350 page dissertation; the defense will take place early Monday morning.
Smack in the middle of this stressful week, after months of waiting for an estimate, a flooring contractor handed us an estimate and told us that he could get new floors in before Thanksgiving. Things moved fast, requiring us to immediately move large and heavy furniture back and forth between two rooms, which included taking down built-in cabinets and then replacing them, as well painting all the walls. After spending three solid days on manual labor (actually a satisfying break from work), my time pressures have become critical. I cringe at the accumulating piles of manuscripts waiting to be written and the papers that I need to review for journals.
So, how did I handle the stress? I squandered a couple hours writing about my frustrations on this blog. And now, back to work...
One central theme of our work that uses fundamental limits and sum rules to understand the nonlinear-optical response is the idea of scale invariance. The Schrodinger Equation has the property that the shape of the wavefunction does not change when the width of the potential energy function is decreased by a scaling factor b and the depth of the well is simultaneously increased by b squared. Under such a transformation, the wavefunction is compressed by the factor b, but otherwise, the shape remains the same. We call this simple scaling.
The nonlinear-optical quantity of interest to many applications is called the hyperpolarizability. Making the hyperpolarizability as large as possible is an ongoing area of intense research activity. To nobody's surprise, a larger molecule will generally have a larger hyperpolarizability. To better understand what makes a material tick, we have defined a quantity called the intrinsic hyperpolarizability, which is simply the ratio of the hyperpolarizability of a quantum system, divided by the fundamental limit. Interestingly, the intrinsic hyperpolarizability is invariant under simple scaling, so large and small molecules that are related to each other by simple scaling will have the same intrinsic hyperpolarizability.
In examining all the molecules that had been studied for nonlinear-optical applications over a 3 decade period, we found that the large range of hyperpolarizability values could mostly be accounted for by simple scaling. Thus, researchers were making molecules larger and larger but the best intrinsic hyperpolarizabilities remained static at about 0.03 - suggesting that it would be possible to make a factor of 30 improvement; but to get there would undoubtedly requrie a major paradigm shift.
Several years ago, I published a paper that showed how to calculate a related quantity called the intrinsic two-photon absorption (TPA) cross-section. More recently, Javier Perez-Moreno and I published a paper that introduced a rough rule of thumb for determining the intrinsic TPA cross-section - simply divide it by the square of the number of electrons. My earlier paper showed how to determine the number of electrons.
To my delight, my paper on TPA gets lots of citations, not because of what I believe is the beautiful physics of the work, but because scientists refer to my method of counting the number of effective electrons - a quite trivial (and approximate) procedure. To my horror, when comparing molecules, most researchers then go on to divide by the number of electrons rather than by the square of the number of electrons as suggested by Javier's work. This leads to a flawed comparison between molecules.
A recent paper in Advanced Materials reported on TPA cross section measurements of a new class of dendrimers, molecules with ever-branching pieces much like veins and arteries. They referred to my paper when calculating the number of electrons; but, as is usually the case, they divided by the number of electrons and found that the new dendrimer class was an order of magnitude better than the best existing dendrimers - an impressive improvement.
In our comment on this paper, we reanalyzed the data using the N squared rule and found that the new materials were in fact two orders of magnitude better. In addition, the dendrimers within each class, though of vastly differing sizes, all had approximately the same intrinsic TPA cross section. Thus, we were able to show that the authors had made an even more important discovery than they had realized. Usually, comments on a paper point out a negative flaw, leading to strong rebuttals and counter-rebuttals. In this case, all parties were winners.
Unfortunately, these small successes were overshadowed by a pile of work. After the Thanksgiving break, I am going to an NSF meeting in Hawaii (I hate to travel and I hate hot and humid places), where I will be reporting on the results of our projects. I need to prepare a glitzy poster as well as an oral presentation. This, on top of being hopelessly behind in preparing problem sets/solutions, grading, and catching up on lectures for my graduate mechanics class. In addition, I need to write a pile of recommendations and read a 350 page dissertation; the defense will take place early Monday morning.
Smack in the middle of this stressful week, after months of waiting for an estimate, a flooring contractor handed us an estimate and told us that he could get new floors in before Thanksgiving. Things moved fast, requiring us to immediately move large and heavy furniture back and forth between two rooms, which included taking down built-in cabinets and then replacing them, as well painting all the walls. After spending three solid days on manual labor (actually a satisfying break from work), my time pressures have become critical. I cringe at the accumulating piles of manuscripts waiting to be written and the papers that I need to review for journals.
So, how did I handle the stress? I squandered a couple hours writing about my frustrations on this blog. And now, back to work...
Monday, August 2, 2010
Sophistication versus Understanding
I attended the SPIE meeting in San Diego over the weekend, where I gave an invited talk about work done in collaboration with David Watkins of the Math Department. The meeting was in a small room with perhaps a couple dozen attendees, all experts in organic nonlinear optics. We had a good time exchanging ideas and throwing about some new thoughts.
As I have mentioned in previous posts, I find travel physically draining. So, spending eight hours en route to San Diego on Saturday and eight hours on Sunday to return home took its toll. While I usually work on weekends, I find it much more relaxing than sitting on an airplane. So, I started the week in an uncharacteristically bad mood.
To add insult to injury, I learned on Sunday and Monday that two of my papers were outright rejected -- not something that I commonly experience. In addition, a paper submitted by my collaborators, to which my contribution was relatively minor, was also rejected. Thus, in a span of three days I had more rejection than in a typical decade. I think that my darker than usual mood was warranted given the extraordinary circumstances. In fact, I entertained the notion of quitting the professional life of physics altogether.
After a good-night's sleep, my mood dramatically improved so on Tuesday morning, I wrote a levelheaded email to the two editors who had rejected my papers. In the process of composing these letters, I realized that science has turned into a big efficient machine, with creativity a reluctant causality.
For more than three decades, lots of people have been expending a great deal of effort to make better molecules. In parallel, computational methods are getting more sophisticated so that theoretical chemists can calculate the properties of ever-larger molecules, taking into account more subtle effects and getting more accurate results. Similarly, chemists have made a huge number of very complex structures, many of which are pieces of art, such as the ever-branching dendrimers.
My own work, which uses sum rules to understand the nonlinear optical response of quantum systems (which I started ten years ago), illustrates how simple but powerful ideas can arise even in a mature field. The basic question that I asked was if there was a fundamental limit to the nonlinear optical response. The answer was a resounding "yes." This limit is not based on practical considerations, but on very fundamental quantum mechanical principles that span the basis of chemical reactions of life and govern the flow of electrons in electronic circuits. If the fundamental theory of quantum mechanics were to be wrong, then the world would be alien to us. In fact, we probably wouldn't exist. In short, I feel that my fundamental limits calculations stand on solid ground.
I expected great admiration for my theory when I first presented a talk on the topic a decade ago. Instead, I got some very nasty comments to the effect that my work was an insult to all the hard-working chemists who were trying to make better molecules. Who was I to say that it was not possible to do any better? Though that sentiment did not reflect my intentions, mother nature DOES place limits on what is possible.
To put this into perspective, my calculation does not imply a single numerical limit, but rather a limit in the presence of a contraint. For example, to investigate the largest possible area is nonsensical. It makes more sense to determine the largest possible area given a fixed perimeter. Similarly, when studying molecules, it is more appropriate to determine the largest nonlinear response for a given molecular size. Since size is not well defined in a quantum system, we used the more abstract concept of scaling.
The bottom line is that after three decades of research, the best molecules fall short of the fundamental limit by a factor of thirty. While people have been making bigger molecules with a larger nonlinear-optical response, the intrinsic nonlinearity has not changed since the birth of the field. That's why one of the reviewer's comments was particularly annoying. (S)he was critical of our simple fundamental approach as passe in light of all the sophisticated and precise methods available. Ironically, our simple approach has been the only one that has led to an improvement in the intrinsic hyperpolarizability.
Being a scientist, my priority is to understand, not to participate in the frenzy of doing the most sophisticated calculations. I prefer to study broad principles that apply to all systems rather than seeking higher precision in more complex calculations that apply to specific molecules. My long-term goal is to build an understanding of the fundamental issues that identify universal properties of systems that approach the fundamental limit. And in this quest, my small effort continues.
I end this post with good news. In response to my emails, both editors reversed their decisions and are giving us the opportunity to submit a revised manuscript. While I am concerned that the trend of sophistication worship is wasteful, I take comfort in the fact that our group is supported to continue our work. Perhaps a time will come when I will become one of the dinosaurs that was left behind, but for now; I take great satisfaction in my research and the potential it has for making a lasting contribution to the body of science.
As I have mentioned in previous posts, I find travel physically draining. So, spending eight hours en route to San Diego on Saturday and eight hours on Sunday to return home took its toll. While I usually work on weekends, I find it much more relaxing than sitting on an airplane. So, I started the week in an uncharacteristically bad mood.
To add insult to injury, I learned on Sunday and Monday that two of my papers were outright rejected -- not something that I commonly experience. In addition, a paper submitted by my collaborators, to which my contribution was relatively minor, was also rejected. Thus, in a span of three days I had more rejection than in a typical decade. I think that my darker than usual mood was warranted given the extraordinary circumstances. In fact, I entertained the notion of quitting the professional life of physics altogether.
After a good-night's sleep, my mood dramatically improved so on Tuesday morning, I wrote a levelheaded email to the two editors who had rejected my papers. In the process of composing these letters, I realized that science has turned into a big efficient machine, with creativity a reluctant causality.
For more than three decades, lots of people have been expending a great deal of effort to make better molecules. In parallel, computational methods are getting more sophisticated so that theoretical chemists can calculate the properties of ever-larger molecules, taking into account more subtle effects and getting more accurate results. Similarly, chemists have made a huge number of very complex structures, many of which are pieces of art, such as the ever-branching dendrimers.
My own work, which uses sum rules to understand the nonlinear optical response of quantum systems (which I started ten years ago), illustrates how simple but powerful ideas can arise even in a mature field. The basic question that I asked was if there was a fundamental limit to the nonlinear optical response. The answer was a resounding "yes." This limit is not based on practical considerations, but on very fundamental quantum mechanical principles that span the basis of chemical reactions of life and govern the flow of electrons in electronic circuits. If the fundamental theory of quantum mechanics were to be wrong, then the world would be alien to us. In fact, we probably wouldn't exist. In short, I feel that my fundamental limits calculations stand on solid ground.
I expected great admiration for my theory when I first presented a talk on the topic a decade ago. Instead, I got some very nasty comments to the effect that my work was an insult to all the hard-working chemists who were trying to make better molecules. Who was I to say that it was not possible to do any better? Though that sentiment did not reflect my intentions, mother nature DOES place limits on what is possible.
To put this into perspective, my calculation does not imply a single numerical limit, but rather a limit in the presence of a contraint. For example, to investigate the largest possible area is nonsensical. It makes more sense to determine the largest possible area given a fixed perimeter. Similarly, when studying molecules, it is more appropriate to determine the largest nonlinear response for a given molecular size. Since size is not well defined in a quantum system, we used the more abstract concept of scaling.
The bottom line is that after three decades of research, the best molecules fall short of the fundamental limit by a factor of thirty. While people have been making bigger molecules with a larger nonlinear-optical response, the intrinsic nonlinearity has not changed since the birth of the field. That's why one of the reviewer's comments was particularly annoying. (S)he was critical of our simple fundamental approach as passe in light of all the sophisticated and precise methods available. Ironically, our simple approach has been the only one that has led to an improvement in the intrinsic hyperpolarizability.
Being a scientist, my priority is to understand, not to participate in the frenzy of doing the most sophisticated calculations. I prefer to study broad principles that apply to all systems rather than seeking higher precision in more complex calculations that apply to specific molecules. My long-term goal is to build an understanding of the fundamental issues that identify universal properties of systems that approach the fundamental limit. And in this quest, my small effort continues.
I end this post with good news. In response to my emails, both editors reversed their decisions and are giving us the opportunity to submit a revised manuscript. While I am concerned that the trend of sophistication worship is wasteful, I take comfort in the fact that our group is supported to continue our work. Perhaps a time will come when I will become one of the dinosaurs that was left behind, but for now; I take great satisfaction in my research and the potential it has for making a lasting contribution to the body of science.
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